High School Science Texts A Textbook for High School Students Studying Chemistry

The Free High School Science Texts A Textbook for High School Students Studying Chemistry FHSST Authors1 June 12, 2005 1See http savannah nongnu orgprojectsfhsst Copyright c© 2003 “Free High Schoo. High School Science Texts A Textbook for High School Students Studying Chemistry

Models of the atom

The Plum Pudding Model

The discovery of the electron by J.J Thomson in 1897 led to the understanding that atoms consist of even smaller particles, prompting the proposal of the plum pudding model This model envisions atoms as negative electrons suspended in a positively charged "soup," resembling plums in a pudding or raisins in a fruitcake.

The Bohr Model

In 1911, Rutherford discovered that atoms consist of a positively charged nucleus surrounded by negatively charged electrons, debunking the plum pudding model and leading to the visualization of atoms as mini solar systems However, this model struggled to explain why atoms emit light at specific wavelengths Niels Bohr addressed this issue by proposing that electrons can only orbit the nucleus in defined energy levels unique to each type of atom, such as Helium and Carbon When an electron transitions from a higher energy level to a lower one, it emits light, with the emitted light's energy corresponding to the difference between the two energy levels.

Light exhibits both particle and wave characteristics, as revealed by Einstein's discovery of photons, which are energy packets of light When an electron transitions between energy levels in an atom, it emits a photon that carries energy equivalent to the difference between those two levels.

An electron in its lowest energy level cannot move to a lower orbit Bohr determined the size of the hydrogen atom, which includes the nucleus and a single electron, by calculating the distance between them at this lowest energy state, a measurement referred to as the Bohr radius.

Definition: TheBohr radius,a0, is the radius of the lowest energy electron orbit in the Hydrogen atom. a0= 5.29177210810 − 11 m

The Wave Model / Quantum Mechanical Model

Bohr's discovery that electron energy levels in atoms can only exist at specific values indicated the need for new physics, leading to the development of quantum mechanics This modern framework describes the behavior of tiny particles at minuscule distances, treating them as waves rather than solid objects Just as light can be conceptualized as both a wave and a particle (the photon), quantum mechanics represents particle properties, such as position and velocity, through probabilities.

Probabilities quantify the likelihood of an event occurring, ranging from 0 (no chance) to 1 (certainty) They are essential in situations where outcomes are uncertain, such as weather predictions, where one might say there is a 50% chance of rain.

In the quantum mechanical model of the atom, electrons are envisioned as waves that do not follow a defined path in their orbits Instead, they traverse numerous possible paths with varying probabilities When attempting to locate an electron, one would find it can exist anywhere around the nucleus, from very close to very far distances However, the likelihood of detecting the electron differs based on its distance from the nucleus.

In quantum mechanics, the electron is visualized as a cloud surrounding the nucleus, with varying density that indicates the probability of locating the electron in specific areas The density of this cloud is crucial, as it allows for calculations of the likelihood of finding the electron at any point in space around the nucleus For the hydrogen atom, these calculations reveal that the highest probability of finding the electron corresponds to the Bohr radius, as illustrated in the provided graph, where the y-axis represents the probability of locating the electron and the x-axis indicates the distance from the nucleus.

Figure 3.1: Probability density P(r) for finding the electron at a distance rfrom the proton in the ground state of the hydrogen atom.

The mass of electrons in an atom is negligible, constituting only 0.027% of the total mass, with the majority stemming from the nucleus For instance, in silicon atoms, which are prevalent in the rocks around us, the combined weight of all 14 electrons is minimal Therefore, when you hold a heavy rock, you are primarily feeling the weight of the numerous nuclei contained within it.

Atomic Structure

The Electron

Electrons are extremely lightweight particles, with a mass of just 9.11 x 10^(-31) kg Scientists currently classify electrons as point particles or elementary particles, indicating that they cannot be subdivided into smaller components.

The Nucleus

Unlike the electron, the nucleuscan be broken up into smaller building blocks: protonsand neutrons Collectively the protons and neutrons are called nu- cleons.

In the early 1920s, physicists like Rutherford conducted experiments that transformed one element into another by bombarding them with energetic helium nuclei, consistently emitting hydrogen nuclei in the process This led to the realization that the hydrogen nucleus was essential to nuclear structure and a key component of all other nuclei By the late 1920s, the hydrogen nucleus became commonly known as the proton among physicists.

Atomic nuclei are composed of protons, each with a positive charge of +1, meaning the total positive charge of a nucleus equals the number of protons To maintain electrical neutrality, the number of protons in an atom must equal the number of electrons, balancing the positive and negative charges to achieve a net charge of zero.

Having only protons in the nucleus presents significant challenges, primarily due to the repulsive electrostatic forces that would cause the nucleus to disintegrate Additionally, the mass of various atoms cannot be solely attributed to the presence of protons For instance, a helium nucleus, which contains two protons, would theoretically have only double the mass of hydrogen However, it is actually four times heavier, indicating that there must be additional particles within the nucleus alongside protons.

In 1920, Rutherford predicted the existence of another particle in the nucleus alongside the proton, necessary for maintaining nuclear stability and contributing to atomic mass This particle needed to be electrically neutral to keep the atom balanced In 1932, James Chadwick confirmed the presence of the neutron and found its mass to be nearly equal to, but slightly greater than, that of the proton.

Isotopes

The chemical properties of an element are defined by the charge of its atomic nucleus, which is determined by the number of protons, known as the atomic number (Z) Additionally, the mass of an atom is influenced by the total count of nucleons in its nucleus, comprising both protons and neutrons, referred to as the atomic mass number (A).

Standard notation shows the chemical symbol, the mass number and the atomic number as follows:

Z X number of nucleons number of protons chemical symbol

For example, the iron nucleus which has 26 protons and 30 neutrons, is denoted as

Iron, represented as 26Fe, has a total nuclear charge of Z = 26 and a mass number of A = 56 The number of neutrons in iron can be calculated using the formula N = A − Z The identity of an element is determined by the number of protons in its nucleus, denoted by Z, which is why the lower index may be omitted, leading to the notation 56Fe.

Adding or removing neutrons from an atomic nucleus does not change the atom's chemical properties, as its charge remains constant Consequently, the atom retains its position in the Periodic Table For instance, an atom with 6 protons, regardless of the number of neutrons, will always be identified as carbon Atoms that have the same number of protons but differ in neutron count are known as isotopes.

Fact: In Greek, “same place” reads as`ισoς τ`oπoς (isos topos) This is why atoms which have the same number of protons, but different numbers of neutrons, are calledisotopes!

Isotopes of an element share the same atomic number (Z) but differ in mass numbers (A) due to variations in neutron count (N) While their chemical properties remain identical, isotopes can exhibit significant differences in nuclear stability For lighter elements, stable isotopes typically have a neutron count nearly equal to that of protons, whereas heavier elements require a greater number of neutrons than protons, with this neutron excess increasing as Z rises Neutrons act as a binding force that counteracts the repulsion between protons; hence, more neutrons are needed as the repelling charge increases Notably, protons and neutrons are not elementary particles; they consist of smaller components known as quarks, with each proton and neutron made up of three quarks.

Energy quantization and electron configuration

Periodicity of ionization energy to support atom arrangement in

atom arrangement in Periodic Table

Successive ionisation energies to provide evidence for arrange-

idence for arrangement of electrons into core and valence

• A chemical bond as the net electrostatic force between two atoms sharing electrons.

• Oxidation number of atoms in molecules to explain their relative ‘richness’ in electrons.

• Molecular shape as predicted using the Valence Shell Electron Pair Re- pulsion (VSEPR) theory

What is a molecule?

Van Der Waals forces

There are three types of intermolecular forces which are classified as Van Der Waals forces These are iondipole, dipole-dipole and London forces.

Ion-dipole forces arise when an ionic compound, such as potassium chloride (KCl), dissolves in a polar solvent like water (H2O) In this process, the positive and negative poles of the polar liquid attract the corresponding negative and positive ions of the ionic substance, facilitating its dissolution.

Dipole-dipole forces: These forces occur when polar molecules arrange them- selves such that their oppositely charged ends can attract each other, e.g.

London forces are weak intermolecular attractions that occur between nonpolar molecules Although these molecules are neutral, the proximity of two molecules causes a slight attraction between their protons and electrons This interaction distorts their electron clouds, creating a temporary dipole As the weakest type of Van der Waals forces, London forces contribute to the low melting points of substances like CH4 and CCl4.

Bonding and energy

The potential energy of two distant atoms is zero due to the absence of attractive or repulsive forces As the atoms draw near, their negatively charged electron clouds and positively charged nuclei repel one another; however, the electron cloud of one atom can attract the nucleus of another This interaction continues until the atoms reach their lowest energy state Bonding energy is considered negative because energy must be supplied to break a bond, known as dissociation energy.

Types of bonding

Covalent bonding

Covalent bonding takes place between nonmetal atoms when their half-filled orbitals overlap, allowing them to share a pair of electrons with opposite spins, in accordance with Pauli’s Exclusion Principle Electronegativity, which measures an atom's ability to attract shared electrons, increases from left to right across a period and from top to bottom down a group in the periodic table.

Polar and non-polar covalent bonds

Electronegativity plays a crucial role in distinguishing between two types of covalent bonds Non-polar covalent bonds form between identical non-metal atoms, such as H2, Cl2, and O2, where the electron pair is shared equally due to identical electronegativity In contrast, when different non-metal atoms bond, the shared electron pair is attracted more strongly by the atom with the higher electronegativity, resulting in a polar covalent bond.

This will result in the formation of apolar covalent bondin which one atom will have a slightly negative charge) and the other a slightly positive charge, e.g.

Molecules with covalent bonds can exist in several shapes which depends on the number of atoms and whether there are lone pairs on these atoms.

Shape Composition Bond angle Example

Pyramidal 4 atoms : 1 lone pair 107.3 ◦ NH3 :

Polar molecules, such as water (H2O), contain polar covalent bonds and are characterized by their asymmetrical shape In contrast, carbon dioxide (CO2) has polar covalent bonds but is not considered a polar molecule due to its linear and symmetrical structure, which results in no charge difference between its ends The polarity of a molecule increases with the difference in electronegativity between the bonded atoms.

Ionic bonding

Ionic bonding takes place between metal and non-metal atoms when the electronegativity difference exceeds 1.7 In this process, an electron pair is transferred from the metal, which acts as an electron donor, to the non-metal, serving as an electron acceptor This transfer results in the metal acquiring a positive charge and the non-metal a negative charge, leading to a strong electrostatic attraction between the two atoms.

Sodium (Na) and chlorine (Cl) form a compound due to sodium's low ionization energy, allowing it to easily lose an electron pair In contrast, chlorine has a high electron affinity, enabling it to readily accept the electron pair from sodium.

Ionic substances consist of numerous ions bonded together, forming a giant molecule characterized by a crystal lattice structure This geometric arrangement of ions is influenced by their relative sizes and charges For example, sodium chloride (NaCl) does not merely comprise one sodium ion and one chloride ion, but rather reflects a more complex arrangement within its crystal lattice.

Sodium chloride (NaCl) forms a crystal lattice structure characterized by a 1:1 ratio of sodium ions (Na⁺) to chloride ions (Cl⁻) This arrangement creates a stable and organized framework, as illustrated in the accompanying figure.

Energy involved in ionic bonding

Let us consider the example of a KBr molecule There are several steps involved in the formation of the ionic bo-nd between K and Br.

• Sublimation energy: this is the energy required for K metal to change to the gaseous state.

• Dissociation energy: this is the energy required for a Br2 molecule to divide into separate Br atoms.

• Ionisation energy: this is the energy required for a K atom to donate an electron, resulting in the formation on a K + ion.

• Electron affinity: this is the energy released when a Br atom accepts an electron to form a Br − ion.

• Lattice energy: this is the energy released when K + and Br − ions arrange in a crystal lattice.

The difference between the energy required and the energy released during the bonding process is called thebonding energy.

Ionic compounds are characterized by high bonding energies resulting from the strong electrostatic forces between their ions, which leads to elevated melting and boiling points While these compounds do not conduct electricity in solid form, they are capable of electrical conductivity when melted Additionally, ionic compounds are known for their hardness and brittleness.

Charge associated with ions and polyatomic ions

The charge on an ion is related to its group number in the periodic table There are two general rules:

Cations possess a charge that corresponds to their group number, as this number reflects the valence electrons available for donation Consequently, the maximum charge of a cation is determined by the number of valence electrons it can contribute.

Anions can hold a maximum charge equal to their group number, reflecting the number of valence electrons an atom possesses Since an atom can be surrounded by a maximum of eight electrons, the difference between this number and the group number indicates the maximum number of electrons an atom can gain For example, an element in Group 7 can accept one additional electron to achieve a stable electron configuration.

Ionic compounds always have a net charge of zero, meaning the positive and negative charges are equal in magnitude This allows for the determination of a compound's chemical formula based on the charges of its individual ions.

PbO Pb 2+ (Group II) 2+ charge and O 2 − (Group VI) 2- charge one Pb 2+ ion and one O 2 − ion are needed to make up a neutral PbO molecule

CaCl2 Ca 2+ (Group II) 2+ charge and Cl − (Group VII) 1- charge one

Ca 2+ ion and two Cl − ions are needed to make up a neutral CaCl2molecule

K2O K + (Group I) 1+ charge and O 2 − (Group VI) 2- charge two K+ ions and one O 2 − ions are needed to make up a neutral K2O molecule

Na3N Na + (Group I) 1+ charge and N 3 − (Group V) 3- charge three Na + ions and one N 3 − ions are needed to make up a neutral Na3N molecule

Al2S3 Al 3+ (Group III) 3+ charge and S 2 − (Group VI) 2- charge two Al 3+ ions and three S 3 − ions are needed to make up a neutral Al2S3molecule

Some groups of atoms behave as a unit and therefore we need to learn the charge associated with these ion groups.

More examples of ionic formulae:

BaCO3, K2Cr2O7, (NH4)2SO4, Ca3(PO4)2

ClO 3 − Chlorate CO3 2 − Carbonate NH 4+ Ammonium

CN − Cyanide CrO4 2 − Chromate H3O + Oxonium

CH3COO − Ethanoate (acetate) Cr2O7 2 − Dichromate

HCO 3 − Hydrogen carbonate MnO4 2 − Manganate

HSO 4 − Hydrogen sulphate SO4 2 − Sulphate

Metallic bonds

Metals possess crystal structures organized in a lattice formation, akin to ionic compounds In this arrangement, valence electrons become delocalized, resulting in positively charged metal ions, known as atomic kernels These kernels are enveloped by a sea of delocalized electrons, creating a strong metallic bond due to their electrostatic attraction The specific arrangement of metals within the crystal lattice is primarily influenced by the size of the atoms.

Metals have several unique properties as a result of this arrangement:

• Good electrical and thermal conductors: electrons are loosely bound and are able to move from areas of high potential/temperature to low poten- tial/temperature

• Malleable and ductile: bonds are not spatially directed so atoms can easily slide over one another, making metals easy to shape and mould or draw into threads

Metals are characterized by high density due to closely packed atoms, resulting in their substantial mass Additionally, they exhibit a distinctive metallic luster, as loosely bound electrons can absorb and reflect light across all frequencies, creating a highly polished appearance.

The figure below shows the arrangement of the atomic kernel and the sea of delocalised electrons in a crystal lattice.

Representation of molecular structure

There are two forms of notation used to represent covalent bonding Lewis notationuses dots and crosses to represent electrons on different atoms. e.g.H • + x xx

In Couper notation, only the electrons participating in the bond between hydrogen (H) and bromine (Br) are depicted, represented by lines indicating covalent bonds rather than dots and crosses For example, H is shown as H • combined with Br as x xx.

• fission and fusion and their consequences

• nucleosynthesis - the sun and stars

• age determination in geology and archaeology

The human mind, housed within just a few liters of brain matter, has the remarkable capacity to comprehend both the vastness of the universe and its tiniest components The universe is composed of galaxies, which contain stars and their orbiting planets These planets, in turn, are formed from molecules, which are structured groups of atoms that serve as the fundamental building blocks of matter.

The universe is home to over 10^20 stars, while scientists have identified more than 12 million chemical compounds, all composed of just around 100 different atoms For those who appreciate the beauty and harmony of nature, this vast number of molecules seems excessive, as they might expect a simpler foundation of elements from which all substances are derived In this chapter, we will explore the fundamental building blocks of matter.

What is the atom made of?

The term "atom" originates from the Greek word ατ oàoν, meaning indivisible The realization that atoms are complex systems capable of being divided marked a pivotal moment in the evolution of modern physics.

In 1911, Rutherford discovered that an atom is composed of a positively charged nucleus surrounded by negatively charged electrons Initially, this led to the simplistic analogy of the atom as a miniature solar system, with electrons orbiting the nucleus like planets around the sun However, this planetary model inaccurately applies classical Newtonian mechanics to the behavior of subatomic particles, which do not adhere to these laws.

Figure 5.1: Probability density P(r) for finding the electron at a distance rfrom the proton in the ground state of hydrogen atom.

The microscopic realm operates under the principles of quantum mechanics, which lacks the concept of a defined trajectory Instead, it explains particle dynamics through quantum states, characterized by probability distributions of observable quantities.

An electron within an atom does not follow a specific path; instead, it exists along numerous possible trajectories, each with varying probabilities If we attempted to locate this electron, we would find it at various distances from the nucleus, both near and far However, the likelihood of finding the electron at different distances is not uniform, with the highest probability aligning with the classical trajectory.

You can visualize the electron inside an atom as moving around the nucleus chaotically and extremely fast so that for our “mental eyes” it forms a cloud.

The density of an electron cloud varies across different regions, reflecting the probability of locating an electron in a specific area Quantum mechanics allows us to calculate this spatial distribution of electron density, with the results for the hydrogen atom illustrated in Fig 5.1 Notably, the most probable distance for finding the electron, represented by the peak of the curve, aligns with the Bohr radius.

In quantum mechanics, bound systems, such as atoms, exhibit discrete energy levels represented by solutions E1, E2, E3, and so on Notably, there are no possible solutions for energies that fall between these defined values, highlighting the quantized nature of energy in these systems.

In a bound system of microscopic particles, energy levels are quantized, meaning the system cannot possess arbitrary energy values but must exist in specific quantum states Each quantum state is characterized by a distinct energy level and spatial configuration, representing the probability distribution of the particles within the system.

A bound quantum system can transition between quantum states either spontaneously or through interactions with other systems The law of energy conservation, a fundamental principle, applies equally in both quantum and classical realms Consequently, any transition between states with energies Ei and Ej involves the emission or absorption of energy, represented as ∆E = |Ei - Ej| This process explains how atoms emit light.

Electrons are extremely light particles with a negligible mass compared to the total mass of an atom For instance, in hydrogen, the lightest atom, electrons account for just 0.054% of its atomic mass, while in silicon, which makes up most rocks, all 14 electrons contribute only 0.027% to the mass Therefore, when you hold a heavy rock, you are primarily feeling the weight of the atomic nuclei within it.

Nucleus

Proton

To study tiny entities like atoms and nuclei, researchers must collide them and observe the outcomes While this method may seem crude—akin to crashing a "Mercedes" and a "Toyota" to inspect their engines—it's the only viable approach for investigating microscopic particles.

In the early 1920s, physicists like Rutherford conducted experiments that transformed one element into another by bombarding them with energetic helium nuclei During these experiments, they consistently observed the emission of hydrogen nuclei, highlighting the fundamental role of the hydrogen nucleus in nuclear structure By the late 1920s, the hydrogen nucleus became widely recognized and referred to as the proton, establishing its significance as a constituent of all other atomic nuclei.

“proton” seems to have been coined by Rutherford, and first appears in print in 1920.

Neutron

Atomic nuclei are composed of protons, and the number of protons determines the nucleus's positive charge This number corresponds to the atomic number of the element in Mendeleev's periodic table.

While the idea of protons coexisting in a nucleus seems logical, it raises significant questions Specifically, how do positively charged protons remain bound together despite their natural tendency to repel each other due to electric forces? This leads to the crucial inquiry: what force holds them together in the nucleus?

The mass of protons alone cannot explain the total mass of atomic nuclei, as demonstrated by the helium nucleus, which contains two protons but is four times heavier than hydrogen This discrepancy indicates the presence of additional particles within nuclei beyond just protons.

In 1920, Rutherford predicted the existence of electrically neutral particles that bind protons and contribute to nuclear mass, which he named neutrons This prediction was confirmed in 1932 by his assistant James Chadwick, who discovered and measured the neutron's mass, finding it to be nearly equal to but slightly greater than that of the proton.

Isotopes

In the early 1930s, it was established that the atomic nucleus is made up of two types of particles: protons and neutrons Protons carry a positive charge, while neutrons are electrically neutral The charge of a proton is equal in magnitude but opposite in sign to that of an electron Additionally, the masses of protons and neutrons are nearly identical, with protons weighing about 1836 times that of an electron and neutrons approximately 1839 times.

Protons and neutrons, collectively known as nucleons, share nearly identical properties aside from their electric charge In scientific literature, protons are represented by the letter 'p' and neutrons by 'n.' When the distinction between them is negligible, the term 'N' is often used to refer to nucleons, similar to how 'person' encompasses both men and women.

The chemical properties of an element are primarily influenced by the charge of its atomic nucleus, which is determined by the number of protons, known as the atomic number (Z) Additionally, the mass of an atom is contingent upon the total number of nucleons in its nucleus, comprising both protons and neutrons, referred to as the atomic mass number (A).

Standard nuclear notation shows the chemical symbol, the mass number and the atomic number of the isotope.

Z X number of nucleons number of protons chemical symbol

For example, the iron nucleus (26-th place in the Mendeleev’s periodic table of the elements) with 26 protons and 30 neutrons is denoted as

Iron, represented by the chemical symbol Fe, has a total nuclear charge (Z) of 26 and a mass number (A) of 56 The number of neutrons in iron is calculated by subtracting the atomic number from the mass number, resulting in N = A - Z It is common to see the notation simplified as 56Fe, where the lower index indicating the atomic number may be omitted.

Adding or removing neutrons from an atomic nucleus does not alter the atom's chemical properties, as its charge remains unchanged Consequently, the atom retains its position in the Periodic Table The term "isotopes" refers to nuclei that have the same number of protons but differ in their neutron count, derived from the Greek phrase for "same place," which is `ισoς τoπoς` (isos topos).

Isotopes of an element share the same atomic number (Z) but differ in mass numbers (A) due to varying neutron counts (N) While their chemical properties remain identical, isotopes can exhibit significant differences in nuclear stability For stable isotopes of lighter elements, the neutron count is typically close to the proton count, whereas heavier elements tend to have more neutrons than protons, with this excess increasing as atomic number (Z) rises This phenomenon occurs because neutrons act as a binding force that helps counteract the repulsion between protons; thus, a greater repelling charge necessitates more neutrons for stability.

Nuclear force

Atomic nuclei are highly stable due to a strong force that keeps protons and neutrons tightly bound within them This fundamental force has been the focus of modern particle physics, driving extensive research to uncover its nature and implications.

At the beginning of the 20th century, physicists realized that their understanding of fundamental forces was insufficient, as they only recognized gravitational and electromagnetic forces They discovered that the forces binding nucleons together could not be electromagnetic, since positively charged protons repel one another, which would lead to the rapid decay of atomic nuclei without another force to hold them together Additionally, gravitational forces were deemed too weak to account for the stability of atomic structures.

Nucleons exhibit a strong attraction towards one another due to mysterious nuclear forces that surpass electromagnetic interactions Subsequent research confirmed the validity of this hypothesis.

Nuclear force exhibits unique characteristics, being charge independent, which means it remains consistent across different nucleon pairs such as nn, pp, and np At distances around 10^-13 cm, this force is not only attractive but also exceptionally strong, approximately 100 times more powerful than electromagnetic repulsion However, its effectiveness is limited to a very short range; once nucleons separate by more than a few femtometers (1 fm = 10^-13 cm), the nuclear attraction diminishes significantly Thus, the nuclear force can be likened to a "strong man with very short hands."

Binding energy and nuclear masses

Binding energy

To disintegrate a bound system of particles, a specific amount of energy, known as binding energy (denoted as B), must be applied This can be achieved by striking the system with a moving particle that possesses kinetic energy, similar to how a bullet or stone can shatter a glass bottle If the striking particle's speed is insufficient, it will not break the system apart Conversely, if the particle moves too quickly, the system will disintegrate, and the resulting particles will gain kinetic energy and move away Therefore, there exists an optimal energy level that effectively disrupts the system without imparting additional speed to the separated particles.

Nuclear energy units

In nuclear physics, the standard unit of energy, the Joule, is often too large to measure the energies of individual nuclei, making the Mega-electron-Volt (MeV) a more practical choice One MeV represents the energy gained by an electron when it moves between two charged plates with a potential difference of one million volts, highlighting the substantial energy levels involved in nuclear interactions.

In the nuclear realm, energy is often measured in mega-electronvolts (MeV), where 1 MeV equals 1.602×10 − 13 joules This unit allows for the expression of most nuclear energies with just a few digits before the decimal, eliminating the need for exponential notation For instance, the binding energy of the simplest nuclear system, known as the deuteron, which consists of a proton and a neutron, can be conveniently represented in MeV.

The unit MeV offers significant advantages beyond its numerical simplicity, particularly in nuclear physics experiments Most of these experiments involve particle collisions, where particles are accelerated by electric fields before colliding with others, making MeV a practical choice for measuring energy in such contexts.

To break up deuterons, a flux of electrons must be accelerated through a voltage of at least 2.225 million volts This process eliminates the need for complex calculations Additionally, when a charged particle with a unit charge passes through a voltage of 5 million volts, it acquires an energy of 5 MeV, making it a straightforward and convenient concept to understand.

Mass defect

When comparing the masses of atomic nuclei to the combined masses of their constituent nucleons, it is surprising to find that the total mass of the nucleons exceeds that of the nucleus itself For instance, in the case of the deuteron, the relationship can be expressed as md < mp + mn, where md represents the mass of the deuteron, while mp and mn denote the masses of the proton and neutron, respectively Notably, this discrepancy in mass is relatively small.

The equation (mp + mn) - md = 3.968 × 10^(-30) kg highlights the concept of "mass defect," a phenomenon observed on the nuclear scale Despite the minuscule mass of nucleons, such as the proton, which has a mass of mp = 1.672623 × 10^(-30) kg, the mass defect signifies that some mass appears to vanish when nucleons are bound together This raises the question of where this missing mass goes.

The energy of a bound state is lower than that of free particles, indicating that energy must be supplied to liberate them from a bound complex Conversely, when particles form a bound state, they release an amount of energy equal to the binding energy This phenomenon is experimentally demonstrated when a proton captures a neutron to create a deuteron, resulting in the emission of 2.225 MeV of excess energy through electromagnetic radiation.

When protons and neutrons bind together, a portion of their mass is converted into energy, which is emitted as radiation Conversely, when a deuteron is split, energy is supplied to the system, partially accounting for the mass that was previously lost.

Albert Einstein proposed the concept of mass-energy equivalence in his theory of relativity, well before experimental evidence supported it He demonstrated that the total energy (E) of a moving body is directly related to its mass (m).

, (5.1) wherev is its velocity andcthe speed of light Applying this equation to a not moving body (v= 0), we conclude that it possesses therest energy

E0=mc 2 (5.2) simply because has mass As you will see, this very formula is the basis for making nuclear bombs and nuclear power stations!

Prior to the theory of relativity, the foundations of physics and chemistry relied on the principle that mass and energy within a closed system are conserved independently during all processes However, it was later revealed that the true conserved quantity is mass-energy, highlighting a fundamental shift in our understanding of these concepts.

Ekin+Epot+Erad+mc 2 = const, i.e the sum of kinetic energy, potential energy, the energy of radiation, and the mass of the system.

In chemical reactions, the mass converted into energy is negligible and often undetectable, even with precise measurements In contrast, nuclear processes release energy on a much larger scale, frequently millions of times greater, making it easily observable.

Mutual transformations of mass and energy are not exclusive to nuclear and atomic processes; they can also occur in everyday situations, such as breaking a piece of rubber or chewing gum When divided, the combined mass of the two parts is slightly greater than the original piece, a phenomenon known as "mass defect." Although this mass defect is undetectable by standard scales, it can be calculated using Einstein's formula To determine the mass defect, one must measure the mechanical work required to break the piece, which involves assessing the force and displacement during the process.

To estimate the potential impact, we can consider a scenario where a rubber piece requires a stretch of 10 cm before breaking, with an average force of 10 N (roughly equivalent to 1 kg) needed for this stretch.

This is very small value for measuring with a scale, but huge as compared to typical masses of atoms and nuclei.

Nuclear masses

Apparently, an individual nucleus cannot be put on a scale to measure its mass. Then how can nuclear masses be measured?

Mass spectrometers utilize a beam of identical nuclei, accelerated to specific energies, to create visible marks on a screen As this beam passes through a magnetic field perpendicular to its velocity, it is deflected at an angle determined by the mass of the particles; heavier particles deflect less due to greater inertia By measuring the displacement of the mark from the center of the screen, one can calculate the deflection angle and subsequently determine the mass of the particles For instance, the mass of an electron is 0.511 MeV, a proton is 938.272 MeV, and a neutron is 939.566 MeV.

Table 5.1: Masses of electron, nucleons, and some nuclei.

In nuclear physics, it is standard practice to express the masses of all particles in energy units, specifically in MeV, due to the equivalence of mass and energy Table 5.1 provides examples of the masses of subatomic particles, with the values representing the energies equivalent to their nuclear masses according to Einstein's formula.

Using MeV as a unit to measure particle masses offers several advantages It simplifies calculations by avoiding extremely small numbers, such as the electron mass of 9.1093897×10^−31 kg When masses are expressed in energy units, calculating mass defects becomes straightforward; for instance, by adding the masses of protons and neutrons and subtracting the mass of deuterium, we can easily derive the deuteron binding energy of 2.225 MeV Additionally, in particle physics, the conversion of kinetic energy into mass allows for a clear understanding of the energy required to create new particles, such as electrons, during high-speed collisions, eliminating the need for complex calculations.

Radioactivity

Discovery of radioactivity

Nuclear radioactivity was discovered by Antoine Henri Becquerel in 1896 Fol- lowing Wilhelm Roentgen who discovered the X-rays, Becquerel pursued his own investigations of these mysterious rays.

Henri Becquerel discovered that uranium-containing crystals could produce images on photographic plates, even when wrapped in black paper and exposed to sunlight He initially believed that the sun's energy was absorbed by the uranium, causing it to emit X-rays However, this misconception was corrected when poor weather conditions prevented sunlight from reaching the crystals, leading to new insights about radioactivity.

On February 26 and 27, 1896, the skies in Paris were cloudy, preventing Henri Becquerel from exposing uranium crystals to sunlight Instead, he placed the crystals over photographic plates, and when he developed them on March 1, he was astonished to discover clear and strong images This groundbreaking finding demonstrated that uranium emits radiation independently, marking the first observation of nuclear radioactivity.

Becquerel discovered that uranium radiation resembled X-rays but could be deflected by a magnetic field, indicating it consisted of charged particles For this groundbreaking discovery of radioactivity, he was awarded the Nobel Prize in Physics in 1903.

Nuclear α, β, and γ rays

A classical experiment demonstrated the complex nature of nuclear radiation by placing radium crystals at the bottom of a narrow channel carved in a thick lead block, which absorbed all radiation except for particles traveling through the channel This setup generated a stream of particles moving in a single direction, akin to bullets from a machine gun, with a photoplate positioned in front to capture and record the emitted particles.

In the absence of a magnetic field, the photographic plate displayed only a single dot However, when the device was exposed to a perpendicular magnetic field, the particle flux divided into three distinct streams, resulting in three separate dots on the plate.

In a recent experiment, one of the three observed fluxes remained straight, while the other two were deflected in opposite directions This observation indicated that the initial flux comprised positive, negative, and neutral particles, which were subsequently identified as α, β, and γ particles, respectively.

Alpha rays consist of helium nuclei, comprising two protons and two neutrons, and have limited penetrating ability, easily blocked by a few centimeters of air or paper In contrast, beta rays are electrons with greater penetration, capable of passing through 3 mm of aluminum Gamma rays, high-energy photons, are not deflected and share characteristics with radio waves, visible light, and X-rays, but possess much shorter wavelengths and higher energy Among these types of radiation, gamma rays exhibit the highest penetrating power, able to traverse several centimeters of lead while remaining detectable on the other side.

Danger of the ionizing radiation

Alpha, beta, and gamma particles interact with matter by colliding with atoms, resulting in the ejection of electrons and the formation of positive ions This process is the reason these rays are classified as ionizing radiation.

Nuclear radiation poses a significant threat to humans and all living organisms by not only ionizing atoms but also destroying vital molecules This destructive process can be likened to thousands of tiny bullets traversing the body, causing cellular damage that can lead to illness or even death The effects of exposure to nuclear radiation may not be immediately apparent, as diseases can manifest years later due to the random modification of DNA This alteration can result in cells with faulty DNA, increasing the risk of cancer development.

Our bodies possess the remarkable ability to repair certain radiation-induced damages We are continually exposed to radiation from outer space and the Earth's interior, yet we manage to thrive However, when the extent of damage exceeds our body's repair capacity, it can lead to serious health consequences.

Established safety norms dictate acceptable radiation limits for the human body If you work with or near radioactive materials, it is crucial to monitor exposure doses and adhere to these safety limits.

It's important to note that no costume can shield you from gamma rays; only thick concrete or metal barriers can provide protection The specialized suits and masks worn by individuals dealing with radioactive materials are designed to prevent contamination rather than block radiation Consider the risks of radioactive particles coming into contact with your clothing or being inhaled, which underscores the necessity of proper protective gear.

They will remain with you all the time and will shoot the “bullets” at you even when you are sleeping.

To effectively protect yourself from radiation, maintaining a safe distance is crucial, as radiation from nuclear sources disperses uniformly in all directions The intensity of radiation decreases quadratically with distance, meaning that doubling your distance reduces your exposure to radiation by a factor of four This relationship can be expressed mathematically, where the number of dangerous particles passing through a unit area is calculated by dividing the total particles emitted per second by the surface area of a sphere Therefore, increasing the distance from the radiation source significantly lowers your risk of exposure.

Decay law

Unstable nuclei undergo spontaneous decay, which can occur at any moment—be it the next second, day, or even century—making it impossible to predict the exact timing of this process Despite the randomness of nuclear decay, there exists a strict order governing these events.

Atomic nuclei operate under quantum probabilistic laws, making them microscopic entities whose decay cannot be precisely predicted However, it is possible to calculate the likelihood of a nucleus decaying within specific time frames This decay occurs due to the nucleus's internal dynamics rather than external factors.

Imagine discovering that a particular nucleus has a 50% probability of decaying within 24 hours If, after this time, the nucleus is still intact, it does not imply that the decay probability has increased; it remains at 50% The nucleus's condition has not changed, and this scenario could persist indefinitely.

In quantum physics, we typically analyze large ensembles of identical nuclei rather than individual ones As the number of nuclei increases, probabilistic laws transition into statistical laws For instance, if we start with one million identical nuclei, after 24 hours, we would expect approximately half, or 500,000, to remain due to a decay probability of 50% Following this pattern, by the next day, around 250,000 of the remaining nuclei would decay, leaving about 125,000 after another 24 hours, illustrating the predictable nature of decay in large collections of quantum objects.

The quantity of unstable nuclei diminishes over time, following the decay curve illustrated in Fig 5.2 Starting with an initial count of N0 at time t=0, only half, or 1/2 N0, will persist after the first half-life interval, T1/2 Subsequently, another half of the remaining nuclei will decay during the next half-life, resulting in only one-quarter of the original nuclei remaining after 2T1/2.

The half-life time, denoted as T1/2, is the duration required for half of the initial quantity of unstable particles or nuclei to decay This specific time interval varies for each unstable nucleus, ranging from mere fractions of a second to thousands or even millions of years Examples of these diverse lifetimes can be found in Table 5.2.

Radioactive dating

Radioactive dating, particularly Carbon dating, allows scientists to determine the age of once-living materials by analyzing their decay products This method is specifically applicable to organic matter that has been in equilibrium with the atmosphere, as it incorporates carbon dioxide during photosynthesis.

Cosmic ray protons collide with atmospheric nuclei, generating neutrons that subsequently interact with nitrogen, the primary component of the atmosphere This interaction creates the radioactive isotope carbon-14, which then combines with oxygen to form carbon dioxide, becoming an integral part of the biological carbon cycle.

The isotope carbon-14 (¹⁴C) maintains a stable concentration in living organisms due to continuous replenishment from air and food sources However, once an organism dies, this replenishment ceases, and the existing carbon-14 isotopes begin to decay at a known rate, characterized by its half-life.

The half-life of several unstable isotopes, including carbon-14, is crucial for understanding radioactive decay Over a span of approximately 4.41 × 10^14 years, carbon-14 (14C) continues to decay, leading to a gradual decrease in its concentration in organic materials The graph in Fig 5.2 illustrates this decay curve, where time t=0 represents the moment of death, and N0 indicates the equilibrium concentration of 14C in living organisms.

By analyzing the radioactive emissions from once-living materials and comparing them to current emissions, scientists can estimate the time since the organism's death For instance, if the radioactive decay of carbon-14 in a wood sample is measured to be half that of living trees, it indicates that approximately one half-life, or 5,730 years, has passed since the tree was cut down This method enables physicists to assist archaeologists in dating organic materials accurately.

Nuclear reactions

Those of you who studied chemistry, are familiar with the notion of chemical re- action, which, in essence, is just regrouping of atoms that constitute molecules.

As a result, reagent chemical compounds are transformed into product com- pounds.

In the realm of nuclear particles, nucleons can transfer between nearby nuclei due to the attractive and repulsive forces acting between them This complex interaction of forces can lead to the regrouping of nucleons, demonstrating the dynamic nature of nuclear interactions.

As a result, the reagent particles are transformed into product particles Such processes are callednuclear reactions.

When two isotopes of helium, specifically 3 2He, collide, their six nucleons can rearrange to form the isotope 4 2He, resulting in the liberation of two protons This nuclear reaction process is analogous to chemical reactions.

Nuclear reactions, similar to chemical reactions, can be classified as either exothermic, which release energy, or endothermic, which require energy input In the specific reaction discussed, a significant energy release of 12.86 MeV occurs This energy release is attributed to the difference in total mass, with the mass on the left side of the equation being 12.86 MeV greater than that of the resulting products on the right side.

When analyzing a specific nuclear reaction, it is essential to determine whether it releases or absorbs energy by comparing the total masses on both sides of the equation This comparison highlights the convenience of expressing mass in energy units, facilitating a clearer understanding of the reaction's energy dynamics.

When composing equations such as (5.3), it is essential to verify that the superscripts and subscripts of the nuclei match, ensuring that the total number of nucleons and the overall charge are equal on both sides of the equation For instance, in the provided example, both the initial and final states of the reaction exhibit six nucleons and a charge of +4.

To simplify the verification of nucleon number and charge conservation, protons and neutrons are often represented with superscripts and subscripts, such as ¹₁p for protons and ¹₀n for neutrons This notation allows for an easy check, ensuring that the sums of the superscripts and subscripts are equal on both sides of the equation.

Detectors

Geiger counter

The most familiar device for registering charged particles is the Geiger counter.

A particle passing through a gas-filled metal cylinder counter generates an electric discharge due to ionization of the gas atoms The counter features a wire electrode at a high voltage (approximately 2000 V) that detects these discharges Each event produces an electric pulse, which can be recorded by a computer or emitted as a sound in a loudspeaker The rate of counts per second indicates the intensity of the radiation detected.

Fluorescent screen

The fluorescent screen was the first type of detector, producing a visible flash of light when a charged particle strikes its surface This technology is commonly encountered in everyday life, such as when watching television or using a computer with a traditional electron-ray tube, where images are created by accelerated electrons.

Photo-emulsion

Nuclear photographic emulsion, a particle detector originating from Becquerel's work, captures the passage of charged particles similarly to how traditional black and white photographic film records images The key distinction lies in its thicker composition, designed to capture a substantial portion of the particle's path Once developed, this emulsion provides a lasting record of the trajectory of charged particles.

Wilson’s chamber

Wilson's cloud chamber is a crucial instrument in sub-atomic and nuclear physics for tracking particle trajectories Developed by C T R Wilson in 1897, this innovative device was first utilized practically in 1911.

The cloud chamber, featuring glass coverings on the top and sides, contains a piston at its base and is filled with air saturated with water vapor Rapidly pulling down the piston expands the chamber's volume, lowering the temperature and causing the air to become supersaturated with vapor When a charged particle enters this state, it forms ions, prompting the water vapor to condense along the ion's path, creating a visible trace that can be photographed To enhance visibility, side illumination is sometimes used By placing the cloud chamber in a magnetic field, researchers can gather valuable information about the charged particles by analyzing the curvature of the traces Although the bubble chamber and spark chamber have largely replaced the cloud chamber in practical applications, Wilson's cloud chamber remains significant in the history of physics.

Bubble chamber

The bubble chamber, a crucial particle detector in the early years of high-energy physics, significantly contributed to the field from 1955 to the 1970s Operating on the principle of bubble formation in a superheated liquid, it captures the trails of charged particles that ionize the liquid's atoms This innovative technique earned D Glaser the Nobel Prize in 1960 and continues to offer stunning visualizations of subnuclear collisions through its photographs.

Spark chamber

The spark chamber is a significant historical device that utilizes electric discharges across a gap between two electrodes with a high potential difference to visualize passing particles Ionization of the gas results in visible sparks, and while multiple short gaps are commonly used, some chambers feature gaps as wide as 40 cm Despite advancements in technology, spark chambers maintain their scientific relevance due to their simplicity and cost-effectiveness, allowing observers to track the trajectories of charged particles effectively.

Nuclear energy

Nuclear reactors

Since the discovery of radioactivity, it has been established that heavy nuclei release energy during spontaneous decay, a process that occurs slowly and cannot be manipulated by humans for large-scale energy production However, this decay is suitable for powering devices that operate autonomously in remote locations with minimal energy needs Heat generated from spontaneous decay can be converted into electricity using radioisotope thermoelectric generators, which have successfully powered space probes and Russian lighthouses A more efficient method of harnessing nuclear energy involves a different type of nuclear decay, which will be discussed next.

In 1939, German physicists O Hahn, L Meitner, F Strassmann, and O Frisch made a groundbreaking discovery that marked the beginning of the nuclear energy era They demonstrated that a uranium nucleus can undergo induced fission after absorbing a neutron, splitting into two fragments and releasing approximately 185 MeV of energy along with two additional neutrons This crucial finding enables the possibility of chain reactions, where the emitted neutrons can trigger further fission events in surrounding nuclei.

Figure 5.4: Chain reaction on uranium nuclei.

In this process, a single neutron splits a heavy nucleus, releasing two additional neutrons that can each break two more heavy nuclei, resulting in the production of four new neutrons This chain reaction continues rapidly, leading to an exponential increase in neutron production and nuclear fission.

In a split of a second a huge amount of energy can be released, which means explosion In fact, this is how the so-called atomic bomb works.

Can we control the development of the chain reaction? Yes we can! This is done in nuclear reactors that produce energy for our use How can it be done?

The critical mass is the minimum amount of fissile material required to sustain an explosive chain reaction; if the sample is smaller than this threshold, neutrons may escape without causing further fissions For instance, the critical mass of Uranium-235 (U-235) is approximately 50 kg While a mass below the critical value cannot trigger a nuclear explosion, it can still release energy and heat up the material As the mass approaches the critical limit, energy release increases, along with the intensity of neutron radiation emitted from the sample.

The criticality of a nuclear sample can be managed by altering its geometry to increase surface area or by incorporating materials like boron or cadmium that absorb neutrons Conversely, surrounding the sample with neutron reflectors enhances criticality by reflecting escaped neutrons back into the sample By strategically adjusting the presence of absorbing materials and reflectors, it is possible to maintain the sample near its critical state.

In a typical nuclear reactor, fuel is organized into several hundred vertical rods resembling a brush, while control rods containing neutron-absorbing material can move up and down between them When fully inserted, these control rods absorb enough neutrons to shut down the reactor To initiate the reactor, operators gradually raise the control rods, and in emergency situations, they are automatically dropped to ensure safety.

Water flows through the reactor core, absorbing heat and becoming extremely hot before transferring its energy to a steam generator In this generator, the heat is transferred to water in a secondary circuit, converting it into steam This steam is then utilized to rotate turbines, which ultimately generate electricity outside the reactor enclosure.

Nuclear power in South Africa

By 2004 South Africa had only one commercial nuclear reactor supplying power into the national grid It works in Koeberg located 30 km north of Cape Town.

A small research reactor was also operated at Pelindaba as part of the nuclear weapons program, but was dismantled.

Koeberg Nuclear Power Station operates as a uranium Pressurized Water Reactor (PWR), where the primary coolant loop is pressurized to prevent boiling It utilizes steam generators to transfer heat to a secondary coolant, which then boils to generate steam To maximize heat removal, the primary loop's water temperature can reach approximately 300 °C, necessitating a pressure of 150 atmospheres to maintain the water in a liquid state.

Koeberg Power Station, located in South Africa, boasts the largest turbine generators in the Southern Hemisphere, generating approximately 10,000 MWh of electricity Construction of the facility commenced in 1976, with two units officially commissioned between 1984 and 1985 Since its inception, Koeberg has operated continuously without any significant incidents, highlighting its reliability in energy production.

Eskom, a leader in power generation technology, is advancing the development of a modular pebble-bed reactor (PBMR), which represents a significant innovation in nuclear energy Unlike traditional reactors that use fuel rods, the PBMR utilizes uranium, thorium, or plutonium in ceramic oxide form, encapsulated within spherical pebbles made of pyrolitic graphite, each about the size of a tennis ball These pebbles are housed in a bin, with an inert gas such as helium, nitrogen, or carbon dioxide circulating between them to effectively carry heat away from the reactor.

In an ideal scenario, heated gas is directed through a turbine; however, due to the potential radioactivity of the primary coolant gas caused by reactor neutrons, it typically passes through a heat exchanger first, where it transfers heat to another gas or steam.

Pebble-bed reactors offer a significant safety advantage due to their inherent design As the temperature rises in a pebble-bed reactor, the increased atomic motion within the fuel enhances the likelihood of neutron capture, contributing to a safer operational environment.

Doppler broadening affects the 92U isotopes, preventing them from splitting after neutron capture This process decreases the number of neutrons available for 235U fission, ultimately lowering the reactor's power output Consequently, this natural negative feedback mechanism imposes an intrinsic upper limit on the fuel temperature, eliminating the need for operator intervention.

The reactor is cooled by an inert, fireproof gas, so it cannot have a steam explosion as a water reactor can.

A pebble-bed reactor is designed to remain safe even if all supporting machinery fails, avoiding risks of cracking, melting, or explosions Instead, it reaches a predetermined "idle" temperature and maintains that state, ensuring the reactor vessel and fuel spheres remain intact and undamaged In this condition, the reactor safely radiates heat, allowing for machinery repairs or fuel removal when necessary.

The pebble bed reactor offers a significant advantage over conventional water reactors by operating at elevated temperatures, which enables direct heating of fluids for low-pressure gas turbines This capability allows systems to extract greater mechanical energy from the same quantity of thermal energy.

Fusion energy

For a given mass of fuel, a fusion reactions like

Nuclear fusion, represented by the reaction 1H + 3 1H → 4 2He + n + 17.59 MeV, produces several times more energy than fission reactions, as illustrated in Fig 5.3 The change in binding energy per nucleon is significantly greater in fusion processes, making fusion a far more powerful energy source.

Extracting 10 grams of Deuterium from 500 liters of water, along with producing 15 grams of Tritium from 30 grams of Lithium, can provide sufficient fuel to meet the lifetime electricity requirements of an average individual in an industrialized nation.

Fusion has garnered significant attention from physicists not only for its potential energy applications but also because fusion reactions played a crucial role in synthesizing light elements during the universe's primordial formation Additionally, these fusion processes continue within stars, generating the energy that we receive as light.

Despite the advantages of fusion over fission reactors, its practical application is hindered by the electric repulsion between positively charged nuclei To achieve fusion, these nuclei must be brought within approximately 10^-13 cm of each other, a challenging task due to their natural tendency to repel one another.

To achieve nuclear fusion, we can create a mixture of atoms with specific nuclei and heat it to high temperatures At these elevated temperatures, the atoms move rapidly and collide violently, resulting in the loss of their electrons This process transforms the mixture into plasma, consisting of bare nuclei and freely moving electrons If the temperature reaches a sufficiently high level, the colliding nuclei can overcome their electric repulsion and come close enough to initiate fusion.

When atomic nuclei fuse, they generate significantly more energy than the energy required to heat the plasma, making the initial energy investment worthwhile To initiate this type of reaction, temperatures must reach extraordinarily high levels.

In fact, it is the same temperature that our sun has in its center, namely, ∼15 million degrees This is why the reactions (5.3), (5.5), and the like are called thermonuclear reactions.

Thermonuclear reactions, like fission reactions, were initially utilized in weaponry, particularly in the hydrogen bomb In this process, fusion is initiated by the explosion of a conventional plutonium fission bomb, which generates the extreme temperatures necessary to ignite the fusion fuel, reaching levels comparable to those found in the sun.

Achieving controllable fusion presents a significant challenge, particularly in containing the plasma While generating high temperatures is relatively straightforward—often accomplished through methods like laser pulses—maintaining that temperature proves difficult as plasma rapidly cools upon contact with the container walls To prevent this, researchers have experimented with various innovative techniques, including strong magnetic fields and omnidirectional laser beams directed at the plasma Despite these efforts, all attempts to effectively contain the plasma have thus far been unsuccessful, suggesting that the conventional approach to controllable fusion may be inherently flawed, as it involves managing a "piece of burning sun."

To understand the interaction of nuclei as they come closer together, envision pushing a metallic ball up a slope The greater the kinetic energy imparted to the ball, the higher it ascends The ultimate goal is to guide the ball into a narrow well situated behind a barrier.

Figure 5.5: Effective nucleus–nucleus potential as a function of the separation between the nuclei.

The curve in Fig 5.5 illustrates the relationship between the relative potential energy (Veff) of two nuclei and the distance (R) between them A deep, narrow well signifies a strong short-range attraction, while the ∼ 1/R barrier indicates Coulomb repulsion For the nuclei to fuse, they must overcome this repulsive barrier and enter the potential well This can be achieved by increasing their kinetic energy, which involves raising the temperature, but there is also a quantum mechanical approach to facilitate this process.

In discussing electron motion within an atom, we noted that electrons create a probability "cloud" around the nucleus This cloud's density decreases at both short and long distances, yet it never entirely vanishes Consequently, there remains a small probability of locating the electron even within the nucleus.

Nuclei, as microscopic objects, adhere to quantum laws, resulting in a probability density that describes the likelihood of finding one nucleus at a distance R from another This density remains non-zero even beneath and beyond potential barriers, indicating that quantum particles, such as nuclei, can tunnel through barriers despite lacking sufficient energy to surpass them This phenomenon is known as the tunneling effect.

The tunneling probability is significantly influenced by the barrier's thickness Instead of increasing the temperature to lift the nuclei over the barrier, we can focus on reducing the barrier's thickness or maintaining the nuclei near the barrier for an extended period, allowing even a low penetration probability to be achieved.

To achieve fusion at room temperature, the strategy involves encapsulating the nuclei within a molecule, allowing them to remain in close proximity for extended periods This method benefits from reduced Coulomb barrier effects due to electron screening, facilitating the fusion process even at lower temperatures.

The concept of cold fusion was first introduced in 1947 by F C Frank and later proposed by A D Sakharov in 1948, who is renowned as the "father" of the Russian hydrogen bomb and a notable human rights advocate and Nobel Peace Prize laureate During his work on the bomb project, Sakharov pioneered research into the peaceful uses of nuclear energy, suggesting the fusion of two hydrogen isotopes through a reaction that involves forming a molecule where one electron is replaced by a muon.

Elementary particles

β decay

Radioactivity consists of three types, with α particles and γ rays being the most easily understood The emission of α particles occurs during a fission reaction, where an unstable nucleus spontaneously decays into two fragments, one of which is the helium nucleus (4 2 He) In contrast, γ rays are electromagnetic quanta released by a nuclear system when it transitions between quantum states, similar to how an atom emits light.

Beta rays, consisting of electrons, present an intriguing paradox; while they may seem straightforward, they originate from within the nucleus rather than the atomic shell This discovery reveals that following beta decay, the nucleus experiences an increase in charge by one unit.

Z(parent nucleus) −→ Z+1 A (daughter nucleus) +e , which is in accordance with the charge conservation law.

The puzzling nature of β decay revealed that emitted electrons exhibit a range of kinetic energies, from very fast to very slow, raising questions about energy conservation in quantum mechanics This variation suggested that identical parent nuclei could lose different amounts of energy yet still produce identical daughter nuclei The phenomenon was so surprising that even renowned physicist Niels Bohr proposed a statistical interpretation of the energy conservation law, challenging traditional notions of energy conservation in the quantum realm.

Initially, the neutron was thought to be a bound state of a proton and an electron Physicists at the time believed that any emitted particle must have existed within the object prior to its emission, making it difficult for them to conceive that a particle could emerge from a vacuum.

The naive (pe) model of the neutron is inconsistent with established facts, as it inaccurately suggests a tight binding similar to that of a hydrogen atom, despite the neutron's significantly smaller size This raises questions about additional factors that may contribute to its compactness, potentially preserving the energy conservation law In 1930, Wolfgang Pauli proposed that β decay involves not only the electron but also another particle, ν, which is emitted alongside the electron and carries away part of the energy.

The neutrino, meaning "small neutron" in Italian, is an electrically neutral particle with an extremely small mass, potentially even zero, a topic still under investigation as of 2004 Due to its weak interaction with matter, the neutrino remained undetected until 1956 In the reaction represented in Eq (5.6), the "bar" over ν indicates that an anti-neutrino is emitted, which is further discussed in Section 5.9.2 regarding anti-particles.

Particle physics

Particle physics emerged to explain β decay and investigate the internal structure of neutrons By colliding sub-atomic particles with other particles, scientists can uncover their constituent parts Essentially, stronger impacts allow for the extraction of smaller components.

Initially, cosmic rays were the sole source of energetic particles impacting other particles Earth is continuously bombarded by various particles from outer space, and while our atmosphere shields us from the majority, many still manage to reach the surface.

In 1932, Carl Anderson utilized a bubble chamber to study cosmic rays, capturing a photograph that revealed two symmetrical tracks of charged particles Analysis indicated that one track corresponded to an electron, while the other was produced by a particle with the same mass but a positive charge These particles were generated from the collision of a high-energy cosmic gamma quantum with a nucleus.

The positron, denoted as e+, was the first antiparticle discovered, distinct from the electron, represented as e− Each particle has a corresponding antiparticle, symbolized by placing a bar over the particle's symbol For instance, the anti-proton is denoted as ¯p, possessing the same mass as a regular proton but with a negative charge.

When a particle encounters its mirror reflection, they annihilate completely, converting their entire mass into electromagnetic energy as gamma quanta For instance, in the collision between an electron and a positron, the reaction e− + e+ → γ + γ occurs, producing two photons to ensure the conservation of total momentum in the system.

Stable antimatter can theoretically exist, as demonstrated by the formation of anti-hydrogen atoms from positrons and antiprotons, which mirror the energy states of regular hydrogen Although experiments have successfully created anti-helium atoms, their lifespan is drastically reduced when interacting with ordinary matter, leading to rapid annihilation upon collision with regular atoms.

Speculations suggest that the universe should exhibit symmetry between particles and antiparticles, raising the question of why matter is favored over antimatter This leads to the hypothesis that there may exist an equal amount of antimatter in a distant anti-universe The potential consequences of a collision between matter and antimatter are intriguing and could have significant implications for our understanding of the cosmos.

Muon, mesons, and the others

In 1935, a particle with properties similar to the electron but approximately 207 times heavier was discovered and named the muon, represented by the symbol μ Initially deemed an "unnecessary" particle, modern theories have since integrated the muon as an essential component of matter.

In 1947, cosmic rays led to the discovery of π (pions) and K mesons, with pions being predicted by Yukawa as mediators of strong forces between nucleons twelve years earlier In contrast, K mesons were an unexpected find, exhibiting unusual behavior by only being created in pairs, while their decay occurred at a rate 10^13 times lower than their creation probability.

Recent studies suggest that certain particles exhibit a unique charge known as strangeness, which is conserved during strong interactions When a pair of these particles is produced, one carries a strangeness of +1 while the other has -1, resulting in a total strangeness of zero However, during their decay, these particles behave independently, leading to a violation of strangeness conservation This phenomenon occurs exclusively through weak interactions, which are significantly weaker than strong interactions, resulting in a much lower decay probability.

The golden age of particle physics commenced in the 1950s with the introduction of particle accelerators, which generated high-energy beams of electrons and protons This advancement allowed experimentalists to design and replicate experiments, moving away from the unpredictable nature of cosmic rays As particle accelerators became the primary instruments for exploration, the field evolved into what is now known as high energy physics.

Over the past fifty years, experimentalists have identified numerous new particles, indicating that not all can be classified as elementary These particles exhibit a key characteristic: they can transform into one another during collisions Notable examples include stable particles like photons and electrons, as well as short-lived particles such as muons and pions The mass and lifetime of various particles, including leptons, kaons, and hadrons, further highlight the complexity of particle interactions in the universe.

Table 5.3: Few representatives of different particle families.

Physicists encounter challenges in classifying particles akin to the classification of animals, plants, and chemical elements Initially, they adopted a straightforward method, categorizing particles into four groups based on mass: leptons, which are light particles such as electrons; mesons, which have intermediate mass like pions; baryons, which are heavier particles like protons and neutrons; and hyperons, which are very heavy particles.

Particles are categorized into three families based on their interactions: weak, electromagnetic, and strong forces, while all particles experience gravitational attraction Photons exclusively engage in electromagnetic interactions, leptons participate in both weak and electromagnetic interactions, and hadrons can interact through all fundamental forces of nature.

In addition to the conservation of strangeness, several other conservation laws have been identified, including the conservation of lepton number For instance, in reaction (5.6), the presence of an electron contributes a lepton number of +1, while the anti-neutrino contributes -1, resulting in a conserved total lepton number Likewise, baryon number conservation is upheld in all reactions.

Quarks and leptons

Experimentalists faced challenges in their research, while theoreticians sought solutions through complex mathematical methods They successfully categorized hadrons into families, suggesting that all known and unknown hadrons are composed of just six types of particles with fractional charges This groundbreaking work earned M Gell-Mann and G Zweig the Nobel Prize.

Initially, researchers focused on a subset of hadrons and formulated a theory involving three fundamental particles Murray Gell-Mann drew inspiration from James Joyce's "Finnegan’s Wake," where he encountered the phrase "Three quarks for Mister Mark." This led him to adopt the term "quark," which not only served as a name for the three particles but also has a playful connection to the German word for cottage cheese.

The theory was expanded to encompass all known particles, necessitating the existence of six types of quarks Additionally, modern theories stipulate that the number of distinct leptons must match the number of quark types Consequently, the universe is composed of just twelve fundamental building blocks, as outlined in Table 5.4 Notably, the electron, discovered over a century ago, is one of these essential particles.

Forces of nature

The Universe operates through four fundamental forces: strong, weak, electromagnetic, and gravitational Within this framework, elementary particles are categorized into families, including leptons and quarks Leptons consist of the electron (e−), muon (μ−), and tau (τ−), each carrying a negative charge, with masses of approximately 0.511 MeV, 105.7 MeV, and 1777 MeV, respectively Additionally, neutrinos associated with these leptons—electron neutrino (νe), muon neutrino (νμ), and tau neutrino (ντ)—are electrically neutral and have negligible mass Quarks, on the other hand, include up (u), down (d), strange (s), charmed (c), top (t), and bottom (b) varieties, with charges of +2/3 or -1/3 and varying masses, ranging from 360 MeV for up and down quarks to a staggering 174,000 MeV for the top quark.

Table 5.4: Elementary building blocks of the universe.

Physicists are on a quest to discover a unified theory that encompasses all natural forces under a single law Currently, they have developed a theory known as the electroweak force, which successfully combines the weak and electromagnetic forces However, the strong and gravitational forces remain outside the scope of this theory, highlighting the ongoing pursuit of grand unification in physics.

Origin of the universe

The Big Bang model is currently the leading theory explaining the history of the universe, illustrating the sequence of events that resulted in the formation of matter as we know it today.

The origins of the universe prior to the Big Bang remain a mystery, with the aftermath of this cosmic event characterized by extreme density and heat During this initial phase, the four fundamental forces of nature—strong, electromagnetic, weak, and gravitational—were indistinguishable, suggesting that gravity operated under quantum laws alongside the other forces Despite ongoing research, a comprehensive theory of quantum gravity has yet to be developed, leaving this primordial epoch as enigmatic as the Big Bang itself.

10 32 K quantum gravity quarks, X hadrons, leptons, Z, W n+ν→p+e − , p+ ¯ν→n+e + p+n→d+γ, d+d→ 4 He+γ pp–chain

Figure 5.7: Schematic “history” of the universe.

The concept of an ideal "democracy" among the fundamental forces in the universe was fleeting, lasting only a fraction of a second At approximately 10^-43 seconds after the Big Bang, the universe cooled to around 10^32 K, leading to the separation of gravity from the other forces Meanwhile, the remaining three forces continued to operate as a single universal interaction, facilitated by the extremely heavy X boson, which had the ability to convert leptons into quarks and vice versa.

Approximately 10 to 35 seconds after the Big Bang, most X bosons decayed, leading quarks to combine into nucleons, mesons, and other hadrons The only enduring symmetry until around 10 to the power of -10 seconds was between the electromagnetic and weak forces, facilitated by Z and W particles Once this symmetry was broken at approximately 10 to the power of -10 seconds, neutrinos became crucial in mediating neutron-proton transmutations and establishing the balance between neutrons and protons in the universe, which lasted until it was about one second old.

In the moments following the Big Bang, nuclear reactions began almost instantaneously, as protons and neutrons quickly combined to form deuterium and helium Initially, the high energy of surrounding photons annihilated these nuclei upon their formation However, as the universe expanded, conditions shifted, leading to a decrease in density that allowed these newly formed nuclei to persist without being destroyed by photons.

Between approximately 10 and 500 seconds after the Big Bang, the universe functioned as a massive nuclear fusion reactor, primarily converting hydrogen through a series of nuclear reactions known as the proton-proton (pp) chain This process begins with proton collisions that create deuterons To validate the Big Bang theory and understand events that occurred 15 billion years ago, scientists focus on the pp-chain fusion, which serves as crucial evidence for this cosmic history The reactions in the pp-chain can be summarized as follows: p + p → 2 H + e+ + νe and p + 2 H → 3 He + γ.

With the onset of nucleosynthesis, there was a significant increase in the abundance of deuterons, helium isotopes, and other light nuclei, as illustrated in Fig 5.8 for 2 H and 4 He Despite this, the temperature and density continued to decrease.

After the Big Bang, the temperature of the universe decreased significantly within a few minutes, halting nuclear fusion due to insufficient kinetic energy to overcome electric repulsion among nuclei This process fixed the primordial abundances of light elements, such as deuterium and helium, which have remained largely unchanged over time Astronomers can now measure these primordial abundances, allowing for comparisons with theoretical predictions to validate our understanding of the universe's early moments.

Thermal Properties & Ideal Gases (Grade 11)

Our interest in this chapter is to describe the behaviour of gases and to develop a simple mathematical model that allows us to predict and calculate how they behave.

This article explores the fundamental principles of gas behavior, specifically Boyle's Law, Charles's Law, and Avogadro's Hypothesis However, it is important to note that these laws provide reliable predictions only within a limited range of physical conditions.

This article explores the connection between macroscopic laws, which govern everyday phenomena, and the microscopic behavior of atoms and molecules By utilizing this framework, we develop the Ideal Gas Model to describe gases Additionally, we examine the limitations of these laws and discuss scenarios where they fail to apply.

Boyle’s Law : Pressure and volume of an enclosed sample of gas 50

When using a syringe or bicycle pump, you may notice that as you apply more force to push the plunger, it becomes increasingly difficult to do so, illustrating an inverse relationship between applied force and volume Essentially, reducing the volume of the enclosed air requires greater force, resulting in increased pressure within that space.

Scientific advancement and technological innovation are interdependent, continually enhancing one another Significant strides in gas research only became possible in the 17th century with the invention of efficient vacuum pumps.

Robert Boyle, an English scientist, created advanced vacuum pumps that enabled precise measurements across various pressures and volumes His groundbreaking discovery revealed that pressure and volume are not merely inversely related, but are in fact exactly inversely proportional to each other.

Definition: Boyle’s Law: The pressure of a fixed quantity of gas is inversely proportional to the volume it occupies so long as the temperature remains constant.

The modern laboratory apparatus features a vertical glass tube sealed at the top, with the bottom end filled with oil and connected to an oil reservoir that has a layer of air above it This design ensures that the trapped air remains separate from the oil By using a bicycle pump to introduce air through a non-return valve, various pressures can be applied to the trapped air, which are measured by a Bourdon gauge As the air pressure increases above the oil in the reservoir, the oil exerts greater pressure on the trapped air, causing a change in its volume that can be observed on a scale adjacent to the tube.

We may write this symbolically as p∝1/V which becomes the equation p=a/V where a is a proportionality constant These two relations can be interpreted in two ways:

Here we relatepandV and view the relationship between them as inverse proportion : pis inversely proportional toV; this yields a hyperbolic graph if we plotpagainst V

The relationship between pressure (p) and the inverse of volume (1/V) is directly proportional, resulting in a straight line that passes through the origin when plotted This relationship demonstrates a consistent gradient, represented as 'a', when comparing values of pressure against values of 1/V.

The law stipulates two essential conditions: the gas volume must remain constant, and the temperature must be unchanged Allowing any air to escape from the syringe reduces the force needed to push the plunger, disrupting the inverse relationship Additionally, variations in temperature lead to the contraction or expansion of matter, further affecting the system's behavior.

Heating the gas in a syringe causes it to expand, requiring increased force to maintain the plunger's position, thus disrupting proportionality Although Boyle did not fully comprehend the concept of temperature during his time and did not account for this variable, his findings remained remarkably accurate due to the relatively stable room temperature of his apparatus.

The parameter 'a' is a variable constant that depends on temperature and the amount of gas, specifically the number of moles This relationship is further explored through the other two laws that govern these factors.

Worked Example 1 : Ideal Gas Laws I

Question: A sample of helium occupies 160 cm 3 at 100 kPa and 25

C What volume will it occupy if the pressure is adjusted to 80 kPa and if the temperature remains unchanged ?

According to Boyle's Law, with temperature (T) and the number of moles (n) held constant, pressure (p) is inversely proportional to volume (V), expressed as p ∝ 1/V Given that the pressure has decreased by a factor of 0.8, the volume must increase by a factor of 1.25 Therefore, the new volume is calculated to be 200 cm³, based on an initial volume of 160 cm³.

2 SincepV =awhereais constant (it depends on T and n, and is thus constant), we have p2V2=p1V1

(where 1 and 2 represent the initial and final states of the gas). Thus,

In this article, we explore two methods for understanding the behavior of gases during changes in state Although SI units are not utilized, this is permissible since the conversion factor cancels out The first method directly applies the concept of inverse proportion, while the second method establishes an equation connecting the gas's conditions before and after the change.

Here are some of Boyles original data Plot graphs of p versus V and of p versus 1/V Does the law follow from these data ?

The volume is represented in arbitrary marks, while pressure is measured with a mercury manometer, where enclosed air supports a mercury column At standard temperature and pressure (STP), a gas can uphold a 76 cm column of mercury, equivalent to 101.325 kPa or 760 mmHg (also referred to as torr, named after 17th-century physicist Torricelli) This relationship demonstrates that pressure is directly proportional to the height of the mercury column, as indicated by the equation p = F/A.

Charles’s Law: Volume and temperature of an enclosed sample

an enclosed sample of gas

About a hundred and fifty years after Boyles discovery, the Frenchman JacquesAlexandre Charles found the Law that carries his name :

Definition: Charless Law : The volume of an enclosed sample of gas is directly proportional to its absolute temperature provided the pressure is kept constant.

V =bT which yields a straight line graph through the origin with a gradient of b Now, b is a function of the two parameters of pressure (p) and molarity (n).

The apparatus consists of a gas syringe filled with air, connected to a Bourdon gauge through a rubber tube To measure pressure and temperature accurately, the plunger must move freely as the syringe is heated or cooled in a water bath equipped with a thermometer This setup allows for precise readings of both pressure and temperature.

Charles's Law, often referred to as Gay-Lussac's Law, is named after Joseph Louis Gay-Lussac, who independently rediscovered the principle years after Charles originally formulated it but did not publish his findings.

Worked Example 2 : Ideal Gas Laws II

When ammonium chloride reacts with calcium hydroxide, ammonia gas is produced and collected in a gas syringe After the reaction, the gas is sealed and allowed to reach room temperature.

At a temperature of 32°C, the volume of ammonia is measured at 122 ml When the ammonia is transferred to a water bath maintained at 7°C, the volume will change After allowing sufficient time for the syringe to equilibrate in the cooler bath, the final volume reading can be determined, assuming the plunger operates without resistance.

1 SinceV =bT andbis fixed (since it depends on p and n, both of which are constant here) we have that

According to Charles's Law, when pressure and the number of moles remain constant, the volume of a gas is directly proportional to its temperature Given that the temperature changes by a factor of 280/305, the volume must also change by the same ratio Consequently, the new volume can be calculated based on this temperature change.

When converting temperature from degrees Celsius to Kelvin, it's essential to remember that the conversion involves addition rather than multiplication by a fixed ratio, as is the case with pressure and volume.

Avogadro’s Hypothesis: The link between number of gas particles

number of gas particles and volume

In the early 19th century, Amedeo Avogadro, an Italian contemporary of Charles, proposed that different gases with the same volume, temperature, and pressure contain an equal number of freely moving particles, such as atoms or molecules This hypothesis emerged shortly after John Dalton's pioneering work on the atomic nature of matter, which significantly advanced the understanding of atoms during that period.

Definition: Avogadros Hypothesis: Equal volumes of gases kept at the same pressure and temperature contain the same number of independent units.

This essentially states that the volume occupied by any kind of gas is directly proportional to the number of gas atoms or molecules Symbolically we can write this as

V ∝n for p and T constant As an equation we have

V =cn wherec is a parameter depending on p and T.

Calculations very similar to the previous worked examples can be done. Heres a more advanced application :

Worked Example 3 : Ideal Gas Laws III

When 5 dm³ of oxygen reacts completely with excess sulfur dioxide at a specific pressure and temperature, it produces sulfur trioxide If the resulting sulfur trioxide is then allowed to return to the initial pressure and temperature conditions, it will occupy a volume that can be determined based on the ideal gas law.

Answer: The balanced reaction equation is :

Thus 1 mol of oxygen produces 2 mol of sulphur trioxide SinceAvogadros Hypothesis holds, the volume must change by the same factor as the number of moles yielding 25dm 3 = 10dm 3

Two General Equations

The three laws we have done can be summarized as follows : p∝1/V i.e pV or n and T constant

We can combine these three relations into one as pV ∝nT or as an equation : pV =nRT

The universal gas constant, denoted as R, is valued at 8.3143 J·K⁻¹·mol⁻¹ and applies to all gases under specific physical conditions It is commonly represented in the equation pV = mRT/M, where n is defined as n = m/M.

Note that any of the three laws can be obtained from this equation by keeping two ofp,V,norT constant For example, ifnandT are kept constant then pV =nRT =a.

A forth relation emerges if we keepV andnconstant: p = (nR/V)T

To test the relationship between pressure and temperature, we can design an experimental setup that allows for the measurement of gas properties under controlled conditions By keeping the number of gas molecules constant, we can observe how pressure (p), volume (V), and temperature (T) interact, leading to the equation pV = kT, which indicates that pressure and volume are directly proportional to temperature This relationship can be expressed as pV ∝ T, providing a clear framework for understanding gas behavior in practical applications.

Now you can relate two states by saying that p2V2/T2=p2V2/T2.

Worked Example 4 : Ideal Gas Laws IV

Question: Calculate the number of air particles in a 10 m by 7 m by 2 m classroom on a day when the temperature is 23 0 C and the air pressure is 98 kPa.

Answer: The volume of the classroom is 1072 = 140 m 3 The absolute temperature is 296 K The pressure in SI is 981000 = 9.8

104 Pa Thus we can calculate the number of moles of air particles : (9.8104).(140) = n.(8.31).(296) which yields n = 5.6 103 mol Then the number is given by N = nNA = (5.6103).(6.0221023) = 3.31027.

Worked Example 5 : Ideal Gas Laws V

Question: Calculate the molar volume of a gas at STP.

Answer: You should know at this stage that one mole of a gas at STP occupies 22,4 dm3 It is easy to show

Overview of the Kinetic Theory of Matter

There are two very basic postulates (assumptions) that underlie the Kinetic Theory :

Matter consists of particles that are always in motion, possessing kinetic energy This motion manifests as heat; when matter absorbs heat energy, the average speed of its particles increases, and conversely, when it loses heat, the particle speed decreases.

2 There are forces of attraction and repulsion between the particles

This model effectively illustrates phase changes, starting with the solid phase where particles primarily vibrate around fixed points, lacking sufficient kinetic energy to break free from the lattice structure As temperature rises, particle vibrations increase, enabling some to gain enough kinetic energy to overcome attractive forces, leading to the melting of the solid In the liquid phase, particles move around each other but still do not possess enough energy to fully separate It is only at the boiling point, when the temperature reaches a critical level, that most particles gain enough energy to transition into a gas Notably, absolute temperature is directly proportional to the average kinetic energy of particles within an object.

The relationship between temperature and kinetic energy is expressed as T ∝ Ek average ∝ v² average, where Ek is the kinetic energy given by the formula Ek = 1/2 mv² This concept helps to define fluid pressure, which is the ratio of force to area (p = F/A) Each collision of gas or liquid particles with the walls of a container exerts a small force Consequently, an increase in the frequency of collisions—due to reduced volume—or more forceful collisions—resulting from higher temperatures—leads to an increase in pressure This understanding is fundamental to the ideal gas model.

• Organic molecular structures functional groups saturated and unsatu- rated structures, isomers

• systematic naming and formulae, structure physical property relation- ships

• substitution, addition and elimination reactions

(NOTE TO SELF: NOTE: I have changed the headings given in your chapter outline.)

Introduction

What is organic chemistry?

Organic chemistry focuses on carbon compounds, which are characterized by the presence of carbon and hydrogen atoms These compounds, known as hydrocarbons, may also include elements such as oxygen, nitrogen, sulfur, phosphorus, and halogens The primary sources of organic compounds are fossil fuels, including coal, petroleum, and natural gas.

Unique properties of carbon

Carbon has some unique properties that are important to the understanding of organic chemistry.

Carbon, located in Group IV of the periodic table, has four valence electrons that enable it to primarily form covalent bonds This characteristic results in most organic compounds being non-polar The minimal electronegativity difference between carbon (2.5) and hydrogen (2.1) indicates that carbon-hydrogen (C-H) bonds are nearly purely covalent.

Carbon atoms have the unique ability to form up to four covalent bonds with other carbon atoms, enabling the creation of diverse structures These structures can take the form of long chains, which may be either straight or branched, as well as ring formations.

Special properties of organic compounds

There are several interesting properties of organic compounds which will help explain their reactions.

• Organic compounds can have the same molecular formula but different structural formula These substances are called structural isomers and they have different names and chemical properties.

In this example, we will illustrate two structural isomers of the molecular formula C4H10 Although the naming of these compounds will be addressed later, it is important to recognize the distinct structures that can arise from the same molecular formula.

Most organic compounds are non-polar, leading to fewer collisions between them According to collision theory, this results in slower reaction rates, which typically yields low outputs in organic reactions.

• Since most organic compounds are non-polar, they are usually insoluble or only slightly soluble in water.

• The majority of organic compounds are gases or liquids which implies that their intermolecular forces are not very strong.

Most organic reactions are characterized by non-stoichiometric behavior, indicating that the mass of the reactants does not equal the mass of the products This discrepancy can be attributed to the generally low yields observed in organic reactions.

• Two or more of the same molecule can bond together to form a long chain or polymer The type of reaction is called polymerisation.

Worked example 2: List the dimer (two molecules) and polymer of the monomer ethene (C2H4).

Dimer: CH3CH2CH=CH2

Polymer: CH3CH2(CH2CH2)nCH = CH2 (polythene, where n is the number of ethene molecules)

Classification of organic compounds

Organic compounds are classified into categories based on their bonding properties due to the vast number of carbon compounds Saturated organic compounds, such as alkanes, contain only single bonds, while unsaturated compounds, like alkenes and alkynes, have at least one double or triple bond and may also include single bonds Hydrocarbons are primarily divided into these two categories.

Aliphatic hydrocarbons primarily consist of long-chain structures, although they can also form ring structures, which share similar properties with the long chains Acyclic aliphatic compounds are categorized into three main types: alkanes, alkenes, and alkynes.

• Aromatic hydrocarbons all have unsaturated ring structures An example of such a compound in benzene, but we will not consider aromatics in this syllabus.

Aliphatic Aromatic (not part of syllabus)

Functional groups

Organic compounds are characterized by specific bonds or groups of atoms known as functional groups, which play a crucial role in defining the compound's reactivity and naming conventions Compounds sharing the same functional group are categorized into a homologous series.

Certain letters in the names of the examples are highlighted in bold to indicate the specific functional group endings This concept will become clearer in the following section that discusses the naming of compounds.

INSERT FIGURES IN TABLE Homologous series Functional group Sim- plest example

(R=alkyl group; eg CH3) methyl methanoate

Naming and Representation of Organic Compounds

Naming of organic compounds

Understanding the naming of organic compounds involves adhering to a set of established rules Before delving into these regulations, it's essential to grasp two fundamental concepts that underpin the naming process.

1 You must learn how to recognise a compound’s functional group We have already discussed this in the previous section.

2 You must learn the prefixes that we use to indicate the number of carbon atoms in a main or branched chain If the carbon atoms are in a main chain, the prefix will get an ending which shows the compound’s functional group (eg. methane) If the carbon atoms form part of a branched group, then the prefix will be given the ending ”yl” (eg methyl).

No of carbons Alkanes Alkenes Alkynes Substituents 1 methane methene methyne methyl 2 ethane ethene ethyne ethyl 3 propane propene propyne propyl

4 butane butene butyne butyl 5 pentane pentene pentyne pentyl 6 hexane hex- ene hexyne hexyl 7 heptane heptene heptyne heptyl 8 octane octene octyne octyl

9 nonane nonene nonyne nonyl 10 decane decene decyne decyl

We are now prepared to explore the naming conventions for organic compounds, which are established by the International Union of Pure and Applied Chemistry (IUPAC) This system is commonly referred to as IUPAC nomenclature for organic compounds.

We will concentrate on the naming of hydrocarbons The rules below will be illustrated with the following example:

1 Identify the functional group of the compound This will determine the ending of the name.

Example: The compound is an alkene so the ending will be ”ene”.

2 Find the longest continuous carbon chain (it won’t necessarily be a straight chain) and think of the prefix for this number of carbon atoms If there is a double or triple bond, this must be part of the longest chain.

Example: The longest chain has 9 carbons (in this example they are in a straight line) We use the prefix ”non” for nine carbon atoms.

3 Number the longest carbon chain If there are double or triple bonds,start numbering so that these have the lowest possible number If there are only single bonds, start at the end nearest the first branched group The branched groups should have the lowest numbers possible but this does not take priority over the number of the double or triple bond.

Example: The numbering must begin closest to the double bond This means that the double bond is at carbon 2 and the compound name will end with

4 Name the branched groups according to the number of carbons atoms that they contain, and give them a number according to their position along the longest carbon chain.

Example: There is a branched group at carbon number 2 which has one carbon atom (methyl) There are 2 branched groups attached to carbon number 5 and they both have 3 carbon atoms (propyl).

5 Use the prefixes di-, tri-, tetra- and penta- to show the presence of 2, 3,

4 or 5 identical branched groups, or identical double and triple bonds.

Example: There are 2 propyl branched groups so they will be listed as ”dipropyl”.

6 Arrange the names of the branched groups alphabetically Separate num- bers and letters by hyphens and separate numbers by commas When listing the branched groups in alphabetical order, ignore the prefixes di-, tri-, tetra- and penta-.

Example: The branched groups will be listed as: 2-methyl-5-dipropyl.

7 Combine the elements of the name into a single word in the following order: branched groups, prefix, name ending according to the functional group and its position along the longest carbon chain.

Example: The name of the compound is: 2-methyl-5,5-dipropylnon-2-ene.

The naming conventions outlined for hydrocarbons also apply to other organic compounds, with the primary distinction being the suffix used, which varies according to the functional group present.

Representation of organic compounds

Understanding the various methods of representing organic compounds is essential, as you may encounter different formats and will need to accurately name the compound presented to you Familiarity with these representations is crucial for effective communication in organic chemistry.

The example 2methylpropane will be used to illustrate the three represen- tations.

• Molecular formula: list the number of each atom as a subscript following the atomic symbol, e.g C4H10

• Structural formula: all of the bonds between atoms must be shown, e.g. INSERT

The condensed structural formula presents a molecular formula that lists each carbon atom along with the directly bonded hydrogen atoms This format continues sequentially for neighboring carbon atoms, and any branched groups are indicated in brackets following the corresponding carbon atom to which they are attached.

The structural formula CH3CH(CH3)CH3 illustrates a compound where a combination of structural and condensed formulas is utilized for convenience, often omitting the representation of all C−H bonds.

Examples

Question: Name the following compounds according to the IUPAC nomenclature: a) f) b) g) c) h) d) i) e)

Answer: a) 2-chloro-3-methylbutane; b) 6-ethyl-4-methylnon-2-ene; c) butan-2-ol; d) 3-methylpentanoic acid; e) 4,4-bromochlorohexan-2-ol; f) 3-methylbutan-2-one; g) ethanal; h) 2,2-dichloro-3-methylpentanol; i) 1,2,3-propantriol

Question: Give three representations for each of the following com- pounds a) 1,2-dibromoethane, b) hex-2-yne, c) 1,3-pentadiene, d) 2-butanol

Answer: Compound Molecular formula Structural formula Con- densed structural formula a b c d

Hydrocarbons

Alkanes

Alkanes are hydrocarbons characterized by single covalent bonds, which render them unsaturated and relatively unreactive The general formula for alkanes is CnH2n+2, where n represents the number of carbon atoms.

Here are the first three alkanes in the series:

Substitution reactions occur when a hydrogen atom in an alkane is replaced by a halogen atom, such as fluorine, chlorine, bromine, or iodine, resulting in the formation of a haloalkane Due to the low reactivity of alkanes, the reaction requires an external energy source, such as heat (∆) or light (hf), to initiate the process.

?/ hf e.g CH4 + Br2 ? CH3Br + HBr ? CH2Br2 ? CHBr3 ? CBr4

Alkanes undergo combustion reactions when burned in air, reacting with oxygen to produce heat, carbon dioxide, and water This process is an exothermic oxidation reaction, characterized by a negative heat of enthalpy (∆H) For example, the combustion of methane (CH4) with oxygen yields carbon dioxide and water along with the release of heat.

Alkenes

Alkenes have the general formulaCnH2n They contain at least one double bond and since these are less stable than single bonds, alkenes are more reactive than alkanes.

Here are the first three alkenes in the series:

In IUPAC nomenclature, if the position of the double bond is not indicated, it is assumed to be at carbon number 1 The previously shown structures illustrate this concept Additionally, there exists another structural isomer for the molecular formula C4H8.

Alkenes, being unsaturated hydrocarbons, readily participate in addition reactions with substances such as hydrogen, water, and halogens During these reactions, the double bond in alkenes is converted into a single, saturated bond, allowing for the attachment of new groups to one or both carbon atoms that were part of the original double bond.

H2 /Pt e.g H2C=CH2 ? H3C-CH3 (hydrogenation reaction; a catalyst such as Pt is needed) HBr ? H3C-CH2Br (halogenation reaction) H2O ? H3C-CH2OH

Alkynes

Alkyne compounds are characterized by a triple covalent bond, making them unsaturated and highly reactive due to the weaker nature of triple bonds compared to double bonds The general formula for alkynes is CnH2n − 2, and for our discussion, we will focus on the reactions of ethyne Ethyne can be synthesized by adding water to calcium carbide, which provides the two carbon atoms necessary for its formation.

CaC2 + 2H2O ? HC?CH + Ca(OH)2

When ethyne is combusted, it reacts with atmospheric oxygen to generate carbon dioxide and water, releasing heat in an exothermic reaction The chemical equation for this process is 2HC?CH + 5O2 → 4CO2 + 2H2O + heat, indicating that the oxidation of ethyne is energetically favorable.

Alcohols, carboxylic acids and esters

Alcohols

Alcohols, also known as alkanols, are compounds derived from hydrocarbons that contain a hydroxyl (OH) group in place of a hydrogen or alkyl group The introduction of the hydroxyl group imparts polarity to alcohols, enhancing their solubility in water.

The simplest example of an alcohol is methanol:

H-C-OH or CH3OH INSERT

Oxidation reactions

Alcohols undergo oxidation when treated with oxidizing agents like KMnO4 or K2Cr2O7, resulting in the formation of aldehydes If an excess of the oxidizing agent is used, carboxylic acids are produced instead For example, the reaction of ethanol (C2H5OH) with potassium permanganate (KMnO4) in an acidic medium yields ethanal (CH3CHO) and manganese ions, demonstrating the transformation from a purple solution of ethanol to a colorless solution of ethanal.

5CH3-CH2-OH + 4MnO4- + 12H+ ? 5CH3-CHO + 4Mn2+ + 11H2O ethanol ethanoic acid

IfK2Cr2O7is used as the oxidizing agent, then the orange colour ofCr2O 7 2 − changes to green with the formation ofCr 3+ ions.

Carboxylic acids

Carboxylic acids are characterized by the presence of a carboxyl group (–COOH) and are classified as weak acids due to their low ionization constants (Ka values) This results in partial ionization in water, with the equilibrium favoring the reactants, as illustrated in the reaction: H3C-COOH + H2O ⇌ H3C-COO- + H3O+.

The simplest carboxylic acids are methanoic acid and ethanoic acid:H-C-OH H-C-C-OH INSERT

Esters

Esters are the products of a reaction between an alcohol and a carboxylic acid. They all contain the functional groupCOORwhere Rcan be any alkyl group (e.g CH3 orCH2CH3).

A fundamental example of an ester is methyl methanoate; however, we will focus on the reaction to synthesize ethyl methanoate, as previously detailed in the table of functional groups in section 18.1.5.

H3C-CH2-OH + H-C-OH ? H3C-C-O-C-H + H2O INSERT ethanol methanoic acid ethyl methanoate

Notice that when naming an ester, the prefix of the name is derived from the alcohol and the suffix is derived from the name of the carboxylic acid.

Here are some more examples to help you test your knowledge of organic chem- istry.

Question: 1 Write down the full and condensed structural formula for: a) 2,4-dimethylhex-2-ene b) 3-ethylpentanoic acid.

2 Answer the following questions with regard to the compound be- low.

The compound H2C=CH2 belongs to the alkene homologous series, characterized by the presence of a carbon-carbon double bond The general formula for this series is CnH2n, where n represents the number of carbon atoms When H2C=CH2 reacts with water, it produces ethanol (C2H5OH) This reaction is known as hydration In comparing H2C=CH2 and ethanol, the former is an unsaturated compound due to its double bond, while ethanol is a saturated compound, as it contains only single bonds.

3 Write a balanced equation for the oxidation of propane.

4 a) Name the two organic compounds which, when reacted with each other, will produce the ester ethyl propanoate. b) Give structural formulae for the two reactants and the ester prod- uct.

5 Give structural formula and names for the structural isomers of

CH3C(CH3)CHCH(CH3)CH2CH3 CH3CH2CH(CH2CH3)CH2COOH 2a) alkenes d) addition reaction b) CnH2n e) alkene is unsaturated; c) compound (c) is saturated H-C-C-OH

5) From the molecular formula, we can tell that this compound is an alkene since the number of carbons and hydrogens agree with the formula CnH2n This is helpful in determining the possible structures, the most obvious of which should be butene. but-1-ene but-2-ene 2-methylprop-1-ene

Natural polymers, like synthetic plastics, consist of long molecular chains made up of monomers, which can be single or multiple types of chemicals The sequence of these links allows the entire chain to encode information Both natural and synthetic macromolecules are collectively referred to as polymers.

Biological macromolecules, primarily composed of sugars, are essential to life The two most significant sugars are glucose and fructose, categorized as carbohydrates with the general chemical formula (CH2O) These sugars typically form five or six-membered rings, with individual sugar units referred to as monosaccharides When two monosaccharides link together, they create a disaccharide, the most common being sucrose, which is made from glucose and fructose Additionally, linking three or more sugars results in polysaccharides, with the most important types being derived from glucose.

Animals utilize polysaccharides for energy, primarily storing glucose as glycogen, while plants convert glycogen into starch Cellulose, the most significant polysaccharide, serves as a structural component for plants but is indigestible to most animals due to its unique polymerization, where every other glucose molecule is inverted However, certain fungi and protozoa can metabolize cellulose, enabling larger animals like termites and cows to rely on these microorganisms to break down cellulose into glucose This process of glucose metabolism is referred to as respiration.

Aerobic respiration involves the use of oxygen to convert sugars into carbon dioxide and water, while anaerobic respiration breaks down sugars into alcohols in the absence of oxygen Additionally, plants harness sunlight energy to transform carbon dioxide and water into carbohydrates through photosynthesis.

Plants thus recycle carbon dioxide and manufacture food for animals.

Biological macromolecules, particularly proteins, are intricate structures that function like tiny machines They are formed from polypeptide chains made up of about 20 different amino acids, each containing a central carbon atom bonded to an amine group, a carboxylate group, a hydrogen atom, and a unique chemical group This central carbon, known as a "chiral center," leads to the existence of stereoisomers, which are similar to mirror-image pairs, like hands Notably, all life on Earth can only metabolize amino acids with an "L" configuration and glucose with a "D" configuration, highlighting the significance of these molecular structures in biological processes.

Amino acids are linked together by combining the amine group on one end with the carboxylate group on the other amino acid.

(amino acid)−NH2+HCO2−(amino acid)→(amino acid)−NHCO2−(amino acid)+H2O

The protein's primary structure consists of a chain featuring an amine group at one end and a carboxylate group at the other, allowing for further polymerization As the chain lengthens, it twists into a spiral configuration, stabilized by weak hydrogen bonds between hydrogen and atoms like oxygen or nitrogen This spiral formation is referred to as an "alpha helix."

”secondary structure” of the protein Finally, the helix itself can bend and twist into a particular three-dimensional shape known as the protein’s tertiary structure.

Proteins serve various essential functions, with structural proteins providing strength and protection to animal cells, similar to the role of cellulose in plant cells A prominent example of structural proteins is keratin, which constitutes horns, hooves, hair, and scales in animals, while natural silk also falls under this category Additionally, proteins act as chemical catalysts known as enzymes, which accelerate chemical reactions without altering themselves Enzymes are crucial for cellular life, facilitating vital processes such as respiration, photosynthesis, and reproduction.

Enzymes are primarily made up of amino acids, but they often require a non-protein component called a coenzyme Typically, coenzymes are organic compounds that include metal atoms such as iron, magnesium, or zinc For instance, in the enzyme hemoglobin, the coenzyme heme contains iron.

Deoxyribonucleic acid (DNA) is a polymer made up of four distinct chemicals that create links in its structure, known as nucleotides Similar to proteins, DNA forms a twisted alpha helix, consisting of two intertwined chains held together by hydrogen bonds The outer structure of the DNA chain is comprised of simple sugars and phosphate groups.

DNA consists of a chain with four nitrogen-containing ring structures: adenine (A), thiamine (T), cytosine (C), and guanine (G) Each type of ring pairs specifically—adenine with thiamine and cytosine with guanine—forming hydrogen bonds that encode information about amino acid sequences in proteins, with every three links corresponding to one amino acid Unlike proteins, DNA can replicate itself by separating into two chains, creating identical DNA molecules through base pairing While DNA can contain billions of base pairs, replication errors, known as mutations, can occur; although most are harmful, some beneficial mutations contribute to the evolution of new species Simple organisms like bacteria have circular DNA, while multicellular organisms have their DNA organized into chromosomes When new enzymes are needed, a section of a chromosome activates, revealing its DNA for use.

In multicellular organisms, DNA is housed in the nucleus, which safeguards it from damage Protein synthesis is carried out by RNA (ribonucleic acid), a polynucleotide that features ribose sugar and uracil instead of thymine The enzyme RNA polymerase transcribes RNA from the DNA in the nucleus, allowing the RNA to exit and reach the ribosome There, the RNA and ribosome work together to construct protein chains from amino acids This process is advantageous because RNA can be easily replaced if damaged, whereas damaged DNA cannot be repaired.

Fats are the smallest biological macromolecules, primarily made up of long hydrocarbon chains They consist of fatty acids, with three fatty acids bonded to a carbohydrate molecule called glycerin The linkage occurs between the carboxylic group of the fatty acid and the hydroxyl group of glycerol.

Writing Chemical Equations

A chemical equation is a symbolic representation of a chemical reaction, showcasing the reactants and products through their chemical formulas For instance, H2O denotes water, illustrating how each molecule is depicted within the equation.

The first equations of the Oswald Process will be used to explain how to read a chemical equation This equation is written as:

In chemical reactions, each compound represents a distinct molecule, such as NH3 for ammonia, O2 for oxygen, NO for nitrogen oxide, and H2O for water The compounds on the left side of the reaction arrow are known as reactants, while those on the right are referred to as products Reactants, such as NH3 and O2, are essential for the reaction to take place, resulting in the formation of products, which in this case are NO and H2O The coefficients associated with each molecule indicate the relative quantities of reactants required and products generated; for instance, four molecules of ammonia react with five molecules of oxygen to produce four molecules of nitrogen oxide and six molecules of water.

A catalyst is a substance that accelerates a chemical reaction without being altered in the process In chemical equations, the catalyst is indicated by placing its formula above the reaction arrow For instance, when platinum is used as a catalyst, it enhances the reaction rate while remaining unchanged.

In chemical reactions where heat is essential, a Greek delta (∆) is indicated above the reaction arrow, similar to how catalysts are represented A prime example of this is the decomposition of calcium carbonate when heated, resulting in the formation of calcium oxide and carbon dioxide, as illustrated in the corresponding chemical equation.

The state of compounds in a chemical equation is indicated by specific labels placed on the right side of the formula There are four labels that can be utilized to represent these states accurately.

4 (aq) for aqueous (water) solution.

The decomposition of calcium carbonate can now be written as:

Balancing Chemical Equations

In a chemical reaction, elements are neither created nor destroyed; they are simply rearranged To achieve a balanced equation, the number of each type of atom on the left side of the reaction must equal that on the right side For example, the formation of water from hydrogen and oxygen illustrates this principle.

An oxygen molecule (O2) comprises two oxygen atoms, resulting in two O atoms on the left side of the equation Water (H2O) contains one oxygen atom, and with two water molecules on the right side, there are also two O atoms present This balances the oxygen atoms on both sides of the equation Additionally, hydrogen (H2) consists of two hydrogen atoms, and with two hydrogen molecules, there are four H atoms on the left side By applying the same method, there are four hydrogen atoms accounted for on the right side as well.

H atoms on the right hand side Since all elements are equal on both sides, the chemical equation is said to be balanced.

Worked Example 6 : Balancing Chemical Equations I

Question: Solid zinc metal reacts with aqueous hydrochloric acid to form an aqueous solution of zinc chloride and hydrogen gas Write a balanced equation.

Step 1 : Identify the reactants and products and their chemical for- mula:

The reactants are zinc (Zn) and hydrochloric acid (HCl) The prod- ucts are zinc chloride (ZnCl2) and hydrogen (H2).

Step 2 : Place the reactants on the left hand side and the products on the right hand side of the arrow:

In balancing the chemical equation, it's important to observe that while the zinc atoms are balanced, the chloride and hydrogen atoms are not To achieve balance, we can assign a coefficient of two to HCl, ensuring that there are two chloride atoms on both sides of the equation.

Step 4 : Recheck the balancing of the equation:

By re-examing the equation you will notice that all the atoms are now balanced.

Step 5 : Ensure all detail was added:

We were told initially that Zinc was a metal, hydrochloric acid and zinc chloride were in aqueous solutions and hydrogen was a gas.

Zn(s) + 2HCl(aq)→ZnCl2(aq) +H2(g)

Worked Example 7 : Balancing Chemical Equations II - The first reaction of the Oswald process

Question: You are told that ammonia reacts with oxygen over a platinum catalyst to produce nitrogen oxide and water Produce a balanced equation.

Step 1 : Identify the reactants and products and their chemical for- mula:

The reactants of this equation are ammonia (N H3) and oxygen (O2). The products are nitrogen oxide (N O) and water (H2O).

Step 2 : Place the reactants on the left hand side and the products on the right hand side of the arrow:

To effectively balance an equation, begin with atoms that appear only once on each side, such as nitrogen (N) and hydrogen (H) In this example, there is one nitrogen atom on the left side and one on the right side, indicating that the nitrogen atoms are balanced.

There are three H atoms on the left and only two on the right The

To achieve balance in the equation, we need to assign a coefficient of two to NH3 and a coefficient of three to H2O, resulting in six hydrogen atoms on each side of the equation.

Step 4 : Recheck the balancing of the equation:

Upon closer inspection of the equation, we observe that while the hydrogen (H) atoms are balanced, the nitrogen (N) atoms are not, with two N atoms present on the left side and only one on the right It is crucial to recheck all atoms for balance whenever any modifications are made to the equation To achieve balance for the nitrogen atoms, we must assign a coefficient of two to the NO molecule.

To achieve balance in the chemical equation, we first note that while the nitrogen (N) and hydrogen (H) atoms are equal, the oxygen (O) atoms are not, with two O atoms on the left and five on the right To rectify this imbalance, we assign a coefficient of 2 to O2 To avoid dealing with fractions, we then multiply all molecules in the equation by two.

Again we have to check each of the atoms individually in the same manner as earlier After doing this, you will notice that each of the atoms are balanced.

Step 5 : Ensure all detail was added:

We were told that platinum was used as a catalyst, we addP t(sym- bol for platinum) to the reaction above the arrow.

Worked Example 8 : Balancing Chemical Equations III

Question: Balance the following equation:

In this example steps one and two are not necessary as the reactants and products have already been given.

To balance a complex chemical equation, begin with atoms that appear only once on each side, such as sodium (Na), nitrogen (N), and sulfur (S) Since the sulfur atoms are already balanced, focus on the sodium and nitrogen atoms With two sodium atoms on the right and one on the left, adjust the coefficient of NaOH to two to achieve balance.

N atoms on the left and one on the right To balance the N atoms NH3 will be given a coefficient of two The equation will now look as follows:

Step 2 : Recheck the balancing of the equation:

N, Na and S atoms balance, but O and H atoms do not There are six O atoms and ten H atoms on the left and five O atoms and eight

To balance the equation, we need to add one oxygen atom and two hydrogen atoms on the right side This can be achieved by incorporating an additional H2O molecule on the right After making this adjustment, it is essential to recheck the balance of the equation.

On re-examination of the equation we see that all atoms balance!

Quantitative Aspects of Chemical Change (Grade 11)

• determining the composition of substances

• amount of substance (mole) molar volume of gases, concentration

Energy and Chemical Change (Grade 11)

• energy changes in reactions related to bond energy changes

• acid-base and redox reactions

• Acids and Bases (in progress)

Chemical Reactions

Chemical reactions, or chemical changes, involve alterations in molecular structures, leading to the formation of larger molecules, the breakdown into smaller ones, or the rearrangement of atoms within molecules These reactions primarily focus on the making and breaking of chemical bonds, while the atomic nucleus remains unaffected Instead, it is the electron clouds surrounding the atoms that engage in interactions during these processes.

A chemical reaction can result in:

• molecules attaching to each other to form larger molecules

• molecules breaking apart to form two or more smaller molecules

• rearrangements of atoms within molecules

A chemical reaction almost always involves a change in energy, conveniently measured in terms of heat The energy difference between the ”before” and

The energy changes in a chemical reaction can be theoretically calculated using data tables or computer simulations For instance, in the combustion of methane (CH4 + 2 O2 → CO2 + 2 H2O), we can determine the energy required to break the bonds of the reactants and products This energy difference is denoted as ∆H, with ∆ representing difference and H representing enthalpy, which measures energy equivalent to heat transfer at constant pressure ∆H is typically expressed in kJ (kilojoules) or kcal (kilocalories) A negative ∆H indicates that energy has been released, classifying the reaction as exothermic.

An exothermic reaction, defined as a process that releases heat, is more favorable and likely to occur A common example of this is the combustion of gas in air, which generates heat, illustrating the concept of exothermicity in everyday life.

An endothermic reaction is characterized by a positive ∆H, indicating that it requires an external input of energy to proceed This type of reaction absorbs heat from its surroundings, resulting in a decrease in temperature in the immediate environment.

Types of Chemical Reactions

There are various types of chemical reactions that can occur The main groups of reactions are:

Ionic reactions

What are ionic reactions?

Ionic reactions occur when oppositely charged ions, specifically a negatively charged anion and a positively charged cation, combine to create a neutral compound These reactions typically happen in a solution, where an element or compound with high electronegativity loses an electron, forming a cation, while another with high electron affinity gains that electron to become an anion.

Ions, which can be simple single atoms like sodium in table salt (sodium chloride) or more complex structures such as calcium carbonate, are defined by their electrical charge This charge arises from an imbalance between the number of protons and electrons, resulting in either a positive or negative ion.

Ionic reactions take place between metals and non-metals, where metals typically lose electrons and form cations, while non-metals gain electrons to form anions For instance, in the reaction between lithium (Li) and fluorine (F), lithium loses an electron to become Li⁺, and fluorine gains an electron to become F⁻.

Precipitation reactions

When some soluble element or compound react in water, an insoluble salt is formed These insoluble salts are known as precipitates.

Formation of gases

In some reactions, the product is not a salt or a precipitate but a gas, which escapes from the solution.

• mechanism of reaction and of catalysis

Chemical reactions occur at varying rates influenced by factors such as temperature and the characteristics of the reactants involved The substances that participate in the reaction are known as reactants, while the resulting substances produced are referred to as products.

Definition: Thereaction rate of a reaction describes how quickly reactants are used up orproducts are formed.

The units are: mols/second For example:

The reaction rate is influenced by how quickly the reactants, solid magnesium and oxygen gas, are consumed, as well as the speed at which magnesium oxide, the product, is produced.

The average rate of a chemical reaction is calculated by dividing the number of moles of reactants or products by the total time taken for the reaction For example, in the case of the magnesium reaction, this formula can be applied to determine the reaction rate effectively.

Ave rate = mols Mg/reaction time(s) or Ave rate = mols O2/reaction time(s) orAve rate = mols MgO/reaction time(s).

Factors affecting reaction rates

The rate of a chemical reaction is influenced by various factors, which are essential to understand for controlling reaction rates By managing these factors, it is possible to enhance product yields and improve efficiency in industrial processes.

1 nature of reactants: substances have different chemical properties and therefore react differently and at different rates

2 concentration(or pressurein the case of gases): as the concentration of reactants increases, so does the reaction rate

3 temperature: depending on the type of reaction (i.e endothermic or exothermic) increasing the temperature can speed up (endothermic) or slow down (exothermic) the reaction rate

4 catalyst: adding a catalyst will increase the reaction rate

5 surface area of solid reactants: increasing the surface area of the reactants (e.g if a solid reactant is finely broken up) will increase the reaction rate because there is more area for the reactants to touch and react with each other

Energy changes in chemical reactions

Exothermic and endothermic reactions

During a chemical reaction, energy undergoes changes, resulting in either endothermic or exothermic reactions In endothermic reactions, heat energy is absorbed, causing the solution to cool down, while in exothermic reactions, heat energy is released, making the solution hot If a reaction is non-spontaneous, additional energy, such as heat or light, may be required for it to occur The energy difference between the reactants and products is referred to as the heat of the reaction, denoted by the symbol ∆H.

It is possible to draw an energy diagram to show energy changes that take place during a particular reaction Let’s consider an example:

The reaction between hydrogen (H2) and fluorine (F2) requires activation energy to initiate During the process, an intermediate state known as the activated complex (H2F2) is formed, where the reactants combine Ultimately, the final product is hydrofluoric acid (HF), which possesses lower energy than the original reactants, resulting in a negative change in enthalpy (∆H) and indicating that the reaction is exothermic.

In an endothermic reaction, the products have a higher energy than the reactants An energy diagram is shown below for the endothermic reaction

Energy diagrams effectively demonstrate how catalysts influence reaction rates by lowering the activation energy needed for reactions to occur This reduction is represented by a smaller "hump" in the diagram, indicating that the presence of a catalyst accelerates the reaction rate Importantly, when the activated complex H2F2 breaks down into the final product, the catalyst remains unchanged and is released Thus, while catalysts significantly impact the reaction rate, they do not alter the fundamental occurrence of the reaction itself.

Question: 2N O2(g)⇔2N O(g) +O2(g) and ∆H >0 How will the rate of the reverse reaction be affected by:

3 the addition of more NO gas?

1 The rate of the reverse reaction will decrease since temperature is directly proportional to the reaction rate So will the forward reaction since temperature affects both directions.

2 The rate of the reverse (and the forward) reaction will increase.

3 The rate of the reverse (and the forward) reaction will increase since the pressure of a substance is directly proportional to the reaction rate.

Worked Example 10 : Reaction Rates II

1 Write a balanced equation of the exothermic reaction between Zn(s) and HCl.

2 Name 3 ways to increase the reaction rate between hydrochloric acid and zinc metal.

1 Zn(s) + 2HCl(aq)⇔ZnCl2(aq) +H2(g)

2 A catalyst could be added, the zinc solid could be ground into a fine powder to increase its surface area, the HCl concentra- tion could be increased or the reaction temperature could be increased.

Chemical equilibrium

Reversible reactions

Reversible reactions involve two processes: the forward reaction, where reactants combine to form products, and the reverse reaction, in which products react to regenerate the original reactants This dynamic is represented by a double-headed arrow, illustrating the equilibrium between the two states, as seen in the equation XY + Z ⇔ X + Y + Z.

Dynamic equilibrium

A system is in dynamic equilibrium when the rates of the forward reaction (XY + Z → X + Y Z) and the reverse reaction (X + Y Z → XY + Z) are equal At this point, macroscopic changes cease, yet both reactions persist at the microscopic level, resulting in continuous activity within the system.

The equilibrium constant

The equilibrium constant, denoted as Kc, is calculated for a reversible reaction occurring in a closed system at a constant temperature For the reaction A + B ⇌ C + D, the expression for Kc is given by the formula Kc = ([C][D])/([A][B]), where the concentrations are measured in mol·dm⁻³.

In the case of a gas, pressure is used instead of concentration in the above formula Solids and liquids do not affect Kc. e.g N H3(g) +HN O3(l)⇔N H3N O3(s)

If the equation requires balancing, you will need to take into account the molar ratios of reactants and products. e.g aA+bB⇔cC+dD

So it is important to first balance an equation before calculating Kc.

The Kc formula features the concentration of products in the numerator and reactants in the denominator A high Kc value indicates a high concentration of products and a successful reaction yield, suggesting that the equilibrium shifts significantly to the right Conversely, a low Kc value reflects a lower concentration of products and a less favorable reaction yield.

Kc value This implies a low yield and that the equilibrium lies far to the left.

Three factors can influence which direction the equilibrium of a reaction lies. These are:

A catalyst accelerates the attainment of equilibrium by affecting the reaction rate, but it does not alter the equilibrium state itself To enhance the yield of a crucial chemical process, we can favor the forward reaction by adjusting the reaction conditions.

Le Chatelier’s Principle is a fundamental concept in chemistry that predicts how changes in temperature, concentration, or pressure affect the equilibrium position of a chemical reaction It asserts that when a closed system's equilibrium is disturbed, the system will adjust to counteract the change and restore balance Essentially, the principle illustrates the system's natural tendency to return to equilibrium after any disruption.

Increasing the concentration of a substance in a reaction will cause the equilibrium to shift in a direction that reduces this concentration According to Le Chatelier's principle, if the concentration of a reactant increases, the system will adjust to decrease that concentration, while the equilibrium constant (Kc) remains fixed at a specific temperature For example, in the reaction involving CoCl2·4H2O and 6H2O, the equilibrium will shift to counteract the change in concentration.

(NOTE TO SELF: Get colours here - check original)

When water is added to the solution, it turns pink due to the forward reaction being favored, which consumes the water Conversely, adding hydrochloric acid introduces Cl- ions, shifting the equilibrium to favor the reverse reaction and resulting in a blue solution.

Increasing the temperature of a reaction mixture causes the equilibrium to shift in a way that reduces the temperature, favoring the endothermic reaction that absorbs heat energy Conversely, lowering the temperature favors the exothermic reaction that releases heat For example, in the reaction N2(g) + 3H2(g) ⇔ 2NH3(g) with a ΔH of -92 kJ, a decrease in temperature will promote the formation of ammonia.

Observation:If we increase the temperature then the yield of NH3 will de- crease.

The reaction described is exothermic, releasing heat in the forward direction while consuming heat in the reverse direction Consequently, an increase in temperature favors the endothermic reverse reaction, leading to a decrease in the yield of NH3.

Pressure: n the case of gases, we refer to pressure instead of concentration.

A similar principle applies as that described before for concentration. e.g 2SO2(g) +O2(g)⇔2SO3(g)

Observation:If we increase the pressure on the closed system, more SO3 will be produced.

The equilibrium will adjust to lower the pressure, as pressure is directly related to the number of gas moles (pV = nRT) Since the right-hand side (RHS) has 2 moles of gas while the left-hand side (LHS) has 3 moles, the equilibrium will favor the forward reaction, resulting in increased production of SO3.

The common ion effect

The solubility product

• relation of current and potential to rate and equlibrium

• understanding of the processes and redox reactions taking place in cells standard electrode potentials

Introduction

Oxidation and reduction

Definition: Theoxidation number of an atom is the indicator as to what the atom’s charge is The oxidation number of

M g 2+ is +2 whereas the oxidation number ofCl − is -1.

Definition: Oxidation is defined as the process whereby an atom experiences anincrease in its oxidation number.

Oxidation is the process in which an atom loses electrons, resulting in a more positive charge For example, when magnesium reacts with chlorine, the magnesium atom undergoes oxidation.

M g+ 2Cl → M g 2+ + 2Cl − (15.1) can be written as 2 half reactions:

In the process of exchange of electrons when the two species react, the mag- nesium becomes oxidized.

Definition: Reduction is defined as the process in which an atom experiences adecrease in its oxidation number.

In the redox reaction involving magnesium, chlorine atoms gain electrons, resulting in a negative charge This process of gaining electrons is referred to as reduction.

Redox reagents

In the reaction described, magnesium is oxidized while chlorine is reduced, highlighting the interplay between oxidation and reduction processes.

Chlorine acts as an oxidizing agent, meaning it facilitates the oxidation of other substances during chemical reactions By accepting electrons, the oxidizing agent itself undergoes reduction, highlighting its crucial role in redox reactions.

Magnesium acts as a reducing agent by donating electrons during chemical reactions, leading to the reduction of other species involved As it facilitates this process, magnesium itself becomes oxidized.

In summary, magnesium acts as a reducing agent in chemical reactions by donating electrons, which leads to its oxidation and an increase in its oxidation number Conversely, chlorine serves as an oxidizing agent, accepting electrons during the reaction, resulting in its reduction and a decrease in its oxidation number.

Balancing redox reactions

The ion-electron method

The ion-electron method is a systematic approach used to balance redox reactions by utilizing oxidation and reduction half-reactions In this article, we will demonstrate this method through a redox reaction involving potassium permanganate and iron chloride in hydrochloric acid (HCl).

KM nO4(aq)+F eCl2(aq)+HCl(aq)→M nCl2(aq)+F eCl3(aq)+H2O

(15.2) Step 1 : (NOTE TO SELF: step is deprecated, use westep instead.) Balancing the Oxidation half reaction:

The first step in balancing this equation is to consider what species are being oxidized or reduced This involves splitting the reaction into 2 half reactions.

The equation describes the oxidation process of the ferric ion (Fe²⁺) to the ferrous ion (Fe³⁺), where the loss of a negatively charged electron results in a higher oxidation number and a more positive charge To maintain charge balance, an electron is added to the right side of the equation.

Step 2 : (NOTE TO SELF: step is deprecated, use westep instead.) Balancing the Reduction half reaction:

This reaction is an incomplete half reaction involving the reduction of manganese.

1 Balancing Oxygen atoms with water:

To balance the oxygen on the left side of the equation, it is necessary to add four water molecules to the right side This reaction occurs in an aqueous environment, as illustrated in equation 15.2.

2 Balancing Hydrogen atoms with H + ions:

This means that the hydrogen atoms on the right have to be balanced as well:

It can be seen that the hydrogen, manganese and oxygen bal- ance but the left side has a net charge of +7 and the right has a charge of +2.

This unbalanced charge can be balanced by adding 5 negatively charged electrons to the left hand side of the equation:

Step 3 : (NOTE TO SELF: step is deprecated, use westep instead.) Combination and balancing of 2 half reactions:

The two balanced half reactions are, 15.3 and 15.6 When combined they are as follows:

To balance the electrons for both equations when combined, the equation 15.3 needs a factor of 5 by which it must be multiplied to balance the electrons:

5F e 2+ →5F e 3+ + 5e − Combining both of the equations the resultant is as follows:

The two sides both have 5 electrons and these can be taken out to simplify the equation Thespectator ionscan also be added into the final equation to complete the reaction.

Spectator ions are ions that do not participate in redox reactions and remain unchanged in their oxidation state For example, the chloride ion (Cl−) and potassium ion (K+) simply exchange cations and anions, respectively, without altering their own identities during the reaction process.

KM nO4+ 8HCl+ 5F eCl2→M nCl2+ 5F eCl3+ 4H2O+KCl

(15.8) Step 4 : (NOTE TO SELF: step is deprecated, use westep instead.) The final species check:

The final check is to see if all species balance on both sides of the equation.

Note: If the redox reaction occurs in a basic solution, theH + ions can be substituted withOH − ions to balance the equations.

Question: Try a few examples with the following reactions:

M nO − 4 (aq) +SO 2 3 − (aq)→M nO2+SO 4 2 −

M nO − 4(aq) +I − (aq)→M nO2+IO − 3

M nO 4 − (aq) +Cl − (aq)→M n 2+ +Cl2

HN O3(aq) +Cu2O(s)→Cu(N O3)2(aq) +N O(g) +H2O(l)

The Cu-Zn electrochemical cell

Direct electron transfer

Direct electron transfer is a key mechanism in Redox reactions, occurring between two species at the same site For instance, when zinc metal is introduced into a copper sulfate solution, a chemical reaction takes place.

Zn(s) +CuSO4(aq)→Cu+ZnSO4

This overall reaction comprises of 2 half reactions:

Copper oxidizes zinc, leading to the deposition of solid copper on the dissolving zinc metal, resulting in a solution of zinc sulfate This process occurs because zinc loses its electrons more easily than copper, making it the more readily oxidized metal.

The following table explains the definitions of anode and cathode:

Standard electrode potentials

The cell potential

An electrochemical cell consists of two electrodes immersed in electrolyte solutions, enabling the flow of current due to the varying oxidizing and reducing strengths of the electrodes.

The cell has an Electromotive Force with is defined as the following:

The Electromotive Force (EMF) of a cell refers to the maximum potential difference between its two electrodes or half-cells, serving as the electrical driving force behind cell reactions and redox processes A higher EMF indicates a stronger reaction, highlighting the significance of EMF in determining the efficiency and effectiveness of electrochemical cells.

Definition: TheStandard EMF (E cell 0 ) is the EMF of a voltaic cell operating under standard state conditions (solute concentrations 1M), gas pressures = 1 atm, and temperatures = 298K The symbol

E cell 0 = oxidation potential for half rxn + reduction potential for other half rxn

Thus for a Daniel cell: (ZnandCu)

From the redox reaction tables:

Thus the redox reaction of copper and zinc in a Daniel Cell will have a standard EMF

Definition: Potential difference is the difference in electric po- tential (electric pressure to move electrons) between two points It is measured in the S.I units of Volts (V).

An electrode potential refers to one of the half potentials that contribute to the electromotive force (EMF) of a cell In a Daniel cell, which consists of zinc and copper electrodes, the overall EMF is determined by the individual electrode potentials of both zinc and copper.

The anode of a voltaic cell has a higher negative potential than the cathode and electrons flow from the anode to the cathode.

To accurately measure half-cell electrode potentials, it is essential to compare them against a standard reference point, as only the complete cell (EMF) can be quantified Consequently, the development of a standard reference electrode was established to facilitate these measurements.

The standard hydrogen electrode

The hydrogen cell serves as the reference point for determining the electrode potentials of various substances, established under standard conditions of temperature (298K), pressure (1 atm), and a solute concentration of 1 Molar.

In this method, different substances are connected in a cell arrangement alongside the hydrogen cell, allowing the measured electromotive force (EMF) to determine the standard electrode potential of the substance being tested The EMF, recorded under standard conditions, is denoted as E⁰.

As an example, the electrode potential of copper in acidic conditions is mea- sured as follows:

At the anode: (At S.T.P conditions)

The reaction of Cu²⁺ ions with electrons to form solid copper can be represented as Cu²⁺ (1M) + 2e⁻ → Cu(s) In a hydrogen/copper voltaic cell, the measured electromotive force (EMF) is 0.337V This indicates that the standard electrode potential for copper is E° = 0.337V.

There are lists available for many of the standard electrode potentials of substances/metals They are measured either in acidic conditions (pH = 0 , [H + ]=1M) or under alkaline (pH, [OH + ]=1M) conditions.

The table of Standard Electrode Potentials is at the end of the chapter.

Examples of electrochemical cells

The dry cell (Leclanche cell)

The Lechlanche cell is a Zinc-Carbon dry cell battery commonly used to power devices such as radios, torches, and walkmen In this battery design, the anode is represented by the Zinc can, which also serves as the outer container.

The structure of the battery consists of a shell containing a graphite rod cathode, which is enveloped by a mixture of manganese dioxide (MnO2) and graphite carbon (carbon black) The remaining space within the zinc can is filled with a paste made of zinc chloride (ZnCl2) and ammonium chloride (NH4Cl).

The following reactions occur in this cell: At the anode:

The carbon acts as an electrode transfer point and allows the current to flow between the Znanode and theM nO2/Chloride cathode. zinc anode

H + MnO(OH) MnO 2 electolytic paste

MnO4/graphite paste graphite cathode e- e-

The alkaline dry cell

The alkaline dry cell, akin to the Lechlanche cell, utilizes potassium hydroxide (KOH) instead of ammonium chloride (NH4Cl) This design enhances its performance in low temperatures, extends its shelf life, and improves efficiency during high current drain applications.

The article discusses a non-dry battery design featuring aqueous paste solutions The anode consists of zinc powder combined with KOH paste, which encases a brass current collector In contrast, the cathode is composed of a mixture of manganese dioxide (MnO2) and graphite carbon, specifically carbon black.

The following reactions occur in this cell: At the anode’:

Zn(s) + 2OH − (aq)→Zn(OH)2(s) + 2e −

The lead-acid accumulator

The lead-acid battery, commonly referred to as the 12 Volt car battery, is composed of lead alloy grids immersed in a sulfuric acid (H2SO4) solution It features an anode made of spongy lead and a cathode composed of lead dioxide, facilitating essential electrochemical reactions within the cell.

P bO2(s) + 3H + (aq) +HSO − 4 (aq) + 2e − → P bSO4(s) +H2O(l)

In a lead-acid battery, both electrodes are coated with white PbSO4 during use, producing a 2V EMF per cell, and when six cells are combined, they create a 12V battery This battery can be recharged by applying electric currents that reverse the half reactions, generating hydrogen and oxygen in the process Consequently, it is essential to periodically add water to the battery to ensure a sufficient supply for its operation.

The recharged battery facilitates the replacement of lead dioxide (PbO2) and lead (Pb) while eliminating the lead sulfate (PbSO4) buildup This process, known as electrolytic reversal, utilizes electric current within the electrolytic cell to drive the reverse chemical reactions, restoring the battery's functionality.

Banks of lead and lead dioxide plates sulfuric acid electrode connected to spongy lead plates electrode connected to lead dioxide plates

The fuel cell

A fuel cell operates like a battery but relies on a constant supply of energetic reactants It generates electric current by facilitating the oxidation of fuel using air, effectively converting chemical energy into electrical energy.

For a hydrogen fuel cell (Hydrocarbon fuel cells are also in development) the following reactions occur:

2H2(g) + 4OH − (aq)→4H2O(l) + 4e − Oxygen Reduction:(cathode)

Fuel cells primarily rely on solid catalysts, such as Platinum, Palladium, and Silver, to enhance oxidation reactions However, the high cost of these materials and the challenges associated with safely managing potentially explosive hydrogen have hindered the rapid development and economic viability of this technology.

Electrolysis

The Chlor-alkali Process

In the Chlor-alkali process, the electrolysis of aqueous brine takes place to pro- duce chlorine gas and hydrogen This takes place by means of the following reactions:

At theanode two reactions can occur:

2Cl − → Cl2(g) + 2e − 2H2O(l) → O2(g) + 4H + + 4e − whereas at thecathode, the following happens:

High chloride concentrations promote chloride oxidation, while low concentration brines favor water oxidation The resulting products—chlorine, hydrogen, sodium, sodium hydroxide, and oxygen—are all valuable industrial raw materials for various processes.

The Downs process

The Downs process involves passing electric current through molten sodium chloride (NaCl) at approximately 900 °C, where resistive heating maintains the salt in a liquid state This process leads to the production of sodium metal and chlorine gas through specific redox reactions.

2N a + + 2e − →N a(l)The electric current acts as a driving force for the redox reactions to occur.

Electrolysis of water

Electrolysis of water for hydrogen gas production is commonly conducted in areas with low electricity costs due to its high energy demands This energy-intensive process involves applying an electric current to a water solution containing sodium hydroxide (NaOH) or sulfuric acid (H2SO4), where dissolved ions serve as current carriers, enabling the decomposition of water into hydrogen and oxygen The fundamental redox reactions that take place during this process are crucial for efficient hydrogen generation.

Extraction of Aluminium

Aluminum is a widely utilized metal in various industrial applications due to its lightweight and strong characteristics It plays a crucial role in the manufacturing of airplanes, automobiles, and more This versatile metal is extracted from bauxite deposits, which consist of a combination of silicas, iron oxides, and hydrated alumina (Al2O3 xH2O).

Aluminum extraction makes use of a the ‘Bayer’ process This involves the following steps:

1 Bauxite is digested in hot sodium hydroxide under pressure

2 This forms Tetrahydroxoaluminate, N a[Al(OH)4] and leads to the pre- cipitation of SiO2 in complex forms.

3 The iron oxides are insoluble and are filtered from the solution.

4 The pregnant alumina carrying solution is then diluted with water and cooled.

5 TheAl(OH)3 is then precipitated out and filtered.

6 Heat is then applied to drive off the water, leaving anhydrous Al2O3.

Another method uses electrolysis for the extraction of Aluminum The ‘Hall’ process makes of the following process for extraction and produces 99% pure aluminum:

1 Aluminum is melted along with cryolite (N a3AlF6) which acts as the electrolyte.

2 The anode carbon rods provide sites for the oxidation of O 2 − and F − ions Oxygen and flourine gas are given off at the anodes and also lead to anode consumption.

3 At thecathodecell lining, theAl 3+ ions are reduced and metal aluminum deposits on the lining.

4 TheAlF 6 3 − electrolyte is stable and remains in its molten state.

The basic electrolytic reactions involved are as follows: At thecathode:

Electro-refining of copper

Copper is essential in the electrical reticulation industry due to its excellent conductivity, making it the preferred choice for electric cables However, to function effectively as a current carrier, it is crucial that the copper used is of high purity.

One of the methods used to purify copper, is electro-winning The copper electro-winning process is as follows:

1 Bars of crude (impure) copper containing other metallic impurities is placed on theanodes.

2 Thecathodes are made up of pure copper with little impurities.

3 The electrolyte is a solution of aqueous CuSO4andH2SO4.

4 areful control of the voltage and current allows the favorable electro- winning and deposition of pure copper onto the cathodes as the copper in the anodes slowlydissolves.

Metal impurities such as zinc, gold, silver, iron, and lead do not dissolve during the process, resulting in a solid sludge that settles at the bottom of the tank or remains in the electrolyte solution The reactions take place at the anode.

Electroplating

Electroplating is widely utilized in industry, particularly for galvanizing iron and steel, which safeguards these metals from oxidation and offers cathodic protection Zinc is the primary agent used in this galvanizing process.

The process of zinc electroplating (Galvanising) is as follows:

1 A zinc salt is dissolved in an aqueous bath.

2 Prior to the electroplating, the steel structure is dipped in acid (usually HCl) to pickle the metal and remove oxides that may prevent a good electroplating finish.

3 The steel is then dried of the acid and then dipped in the zinc salt bath.

4 An electric current is provided to oxidize the zinc ions, which are reduced and deposit on the steel structure.

5 Thecathode half reaction is as follows:

At the cathode: Zn 2+ (aq) + 2e − →Zn(s) the solid zinc deposits onto the steel as a covering.

Faraday’s laws of electrolysis

British chemist Michael Faraday established the connection between the flow of electric current, driven by electron movement, and the quantity of substance consumed or deposited at the electrodes of an electrochemical cell.

1 In the electroplating of zinc, every atom of zinc deposited onto the steel structure, requires 2 electrons to be donated to form an atom of deposited zinc.

2 The same concept can be used when determining how many electrons will be given off by the chloride ions at the anode in the Chlor-alkali process to produce chlorine gas.

Definition: Faradays laws for Electrolysis:

1 The quantity of a substance liberated is directly proportional to the quantity of electric charge that has flowed in the circuit.

2 For a given quantity of charge, the amount of metal that is deposited is proportional to its equivalent weight (Equivalent weight

= Atomic Weight/Charge of metal ion)

Some more definitions to learn:

• Coulomb (C): A coulomb is the S.I unit for electric charge An electron has the charge of 1.6022 x 10-19 Coulombs.

• Mole: 1 mole is equivalent to the number of atoms in 12g of carbon 1 mole = Avogadros Number (6.022 x 1023 atoms).

• Faraday (F):A faraday is the charge contained in 1 mole of electrons.

1F araday = Avogadro 0 sN umberxChargeof1electron

• Ampere (A): The ampere is the S.I unit for current It is defined as follows:

Therefore, if 1 ampere of current travels in a conductor for 1 second, 1 coulomb of charge has passed.

Question: In Zinc electroplating the following example will help to show the concept of the Faraday laws.

Step 1 : (NOTE TO SELF: step is deprecated, use westep instead.) The cathode half reaction is:

Thus for every atom of Zinc deposited, 2 electrons are required For

1 mole of zinc to be deposited, the number of electrons required is:

= Number of atoms in 1 mole of zinc x 2

Step 2 : (NOTE TO SELF: step is deprecated, use westep instead.) The charge to be passed to deposit 1 mole of zinc is:

= 1.2044 x 10 24 e-/mole Zn x Charge of one electron

Step 3 : (NOTE TO SELF: step is deprecated, use westep instead.)

If 3 Amperes flow for 30s, the number of Zinc atoms deposited is: 1

For 1 mole of zinc to be deposited, 1.9297 x 10 5 Coulombs must be passed.

Therefore in that 30 seconds, (90 C/1.9297 x 10 5 C/mol Zn) moles of zinc are deposited.

Therefore:- The number of zinc atoms deposited is:

Worked Example 19 : Faradays Laws II

Question: Chlorine gas is given off at theanode in the Chlor-alkali process as follows:

The complete half reaction shows that 2 electrons are required to be removed from the anode for every molecule of chlorine gas generated.

If a current of 100 kA runs for 2 hours, what mass of gas is generated at the anode?

Step 1 : (NOTE TO SELF: step is deprecated, use westep instead.)

1 mole Chlorine gas (Cl2) requires 2 moles ofe − to be deposited at the anode The charge deposited per mole of chlorine generated is:

= No electrons per moleCl2 x Charge of 1 mole of electrons

Step 2 : (NOTE TO SELF: step is deprecated, use westep instead.) The charge discharged when the current was operating is as follows:

2 hours = 2 x 60 minutes/hour x 60 seconds/minute = 7200 seconds 1ampere = 1Coulomb / second

Therefore 100kA running for 7200 s is:

Step 3 : (NOTE TO SELF: step is deprecated, use westep instead.) Thus the number of moles of chlorine generated is:

Charge discharged by current flow / (Charge deposited per mole of

Properties Anode Cathode Reduction / Oxidation Oxidation Reduction

Anions (Cl − or SO4 2 − ) migrate to anode in solution of cell: e.g.Zndonates easily

Cations (K + orN a + ) migrate to cathode in solution of cell: e.g Cu 2+ receivese − from cathode

Electrons enter (deposits) Charge (Voltaic cell) Negative Positive Charge (Electrolytic cell) Positive Negative

Table 15.1: Properties of anodes and cathodes

• Physical changes and energy transfers: The movement of water from the ocean and land surfaces as controlled by energy in sunlight Resevoirs for water on earth.

• Macroscopic properties of the three phases of water related to their mi- croscopic structure

• Chemical changes and energy transfers: The movement of nitrogen be- tween interrelated biological and geological systems

• Nitrogen and Nitrogen Compounds (in progress)

Nitrogen Gas (N 2 )

Industrial Preparation of N 2

Nitrogen gas is prepared by the fractional distillation of liquid air Purified air is liquefied at a very low temperature (below−200 o C) and under very high pressure The temperature is then raised and as nitrogen has the lowest boiling point (bp=−196 o C) it is the first to boil off, it then cools and condenses and is collected for storage The liquid oxygen (bp= −183 o C) and liquid argon (bp- 186 o C) are left behind.

Uses of Nitrogen

• Liquid nitrogen is used for quick freezing food.

• Liquid nitrogen is used in medicine for the freezing of superficial skin tumours and growths.

• Nitrogen is used in the manufacture of ammonia (using the Haber process) which is used in cleaning agents and fertilizers

• All proteins are made of nitrogen and therefore it is necessary for life.

Ammonia (N H 3 )

Laboratory Preparation

Ammonia can be prepared by heating any ammonium salt with a stable base, in this case calcium hydroxide The gas is collected by the downward displacement of air.

2N H4Cl + Ca(OH)2 → CaCl2 + 2N H3 + 2H2O Net: N H4 + (aq) + (OH) − (aq) → N H3 + H2O

The gas jar in which the ammonia is collected is seen to be full when wet indicator paper held at the mouth indicates the presence of an alkali (basic solution), i.e damp litmus paper will be turned blue.

This is seen in the reaction:

N H3+H2O→N H 4 + +OH − Note: It is theOH − which causes the indicator to change colour.

Industrial Preparation of N H 3

The industrial preparation of ammonia is known as the ‘Haber Process’ or

At a high pressure and a temperature of about 500 o C and in the presence of a suitable catalyst, nitrogen and hydrogen produce ammonia in a reversible reaction.

(NOTE TO SELF: in equation below replace arrow with equilibrium arrow)

N2+ 3H2→2N H3+heat Four considerations according to Le Chateliers principle:

• Decrease temperature: forward reaction is favoured to generate heat and more ammonia is produced (decrease to 450 o C)

• Increase pressure: forward reaction is favoured to decrease pressure (4mol→ 2mol)

• Change concentration of the gases: If N H3 is removed as it is formed, the forward reaction is favoured to make up for the decrease in N H3 concentration and moreN H3is formed.

• Catalyst: iron or iron oxide can be used to change the rate of the reaction,not the amount of product formed.

Properties of N H 3

N H3 is extremely soluble in water and ionizes to form an alkaline solution due to the formation of OH − ions).

This can be demonstrated by the fountain experiment The bromothymol blue turns blue as a result of the basic property of ammonia.

An example of an ionization reaction:

Uses of N H 3

• Preparation of fertilizers like (N H4)2SO4 and urea

• In cleansing and washing agents

• Preparation of wood pulp for preparation of paper

• The preparation ofHN O3 (nitric acid) by the catalytic oxidation of am- monia This occurs in the presence of heated platinum or copper (See nitric acid section for details of the process)

Ammonium Salts

Preparation of Ammonium Salts

Ammonium salts are formed when ammonia reacts with a strong acid Below are some examples of these reactions:

Properties of Ammonium Salts

• They are soluble in water and give off ammonia when heated withCa(OH)2.

• They are thermally unstable (i.e they decompose upon heating) An example of this is as follows:

N H4Cl+heat→N H3(g) +HCl(g) (Insert diagram no 2)

Note: The N H4Cl sublimes on heating, i.e it changes directly from a solid to a gas.

Uses of Ammonium Salts

• N H4Cl is used to clean metal surfaces before soldering and as an elec- trolyte in dry cells

• (N H4)2SO4 is used as a fertilizer.

• N H4N O3 is used as a fertilizer, as an explosive and in the preparation of laughing gas.

Nitrogen Dioxide (N O 2 )

Laboratory Preparation

Nitrogen dioxide can be prepared in the laboratory by reacting concentrated nitric acid (HNO3) with copper This gas can be collected through the upward displacement of air or by cooling it to a low temperature to liquefy it.

Cu + 4HN O3 → Cu(N O3)2 + 2H2O + 2N O2 blue reddish brown

The liquefied gas (N O2) is a light yellow liquid.

Equilibrium between N O 2 and N 2 O 4

N O2 is nitrogen dioxide and dark, reddish brown in colour N2O4 is dinitrogen tetroxide and is light, yellowy brown in colour So:

(NOTE TO SELF: in the reaction below replace the arrow with an equilib- rium arrow)

2N O2 → N2O4 + heat dark brown light brown Effect of change of temperature:

The forward reaction is exothermic, releasing heat, while the reverse reaction is endothermic, consuming heat Although heating supports both reactions, the endothermic process is favored more due to the absorption of excess heat Consequently, an increase in temperature results in the production of more reddish-brown nitrogen dioxide.

Cooling slows down both reactions, but the endothermic reaction is slowed down more Therefore cooling favours the formation of more yellowy brown

Effect of change of pressure:

An increase in pressure results in a decrease in volume, promoting the forward reaction and leading to the production of more N2O4 Conversely, a decrease in pressure causes an increase in volume, favoring the reverse reaction and resulting in the formation of more O2.

Nitric Acid (HN O 3 )

Laboratory preparation of HN O 3

Nitric acid is prepared in the laboratory by the action of concentratedH2SO4 on a nitrate.

Industrial preparation of HN O 3

The industrial preparation of nitric acid involves the catalytic oxidation of am- monia (N H3) and is known as theOstwald Process:

• A stream of pureN H3 and filtered air are passed over heated platinum gauze which is a contact catalyst This occurs at about 800 o C as the reaction is very slow at room temperature.

TheN H3 is obtained whenN H4OH is heated and decomposes releasing

(NOTE TO SELF: triangle on arrow below)

TheN H3 then mixes withO2and the reaction proceeds.

• TheN Oformed acts with the excess of atmospheric oxygen to formN O2

• The gases are cooled and led to absorption towers where theN O2reacts withH2O.

Reactions of Nitric Acid

Nitric acid is thermally unstable and heating causes it to decompose forming reddish brownN O2.

(NOTE TO SELF: triangle on arrow below)

At room temperature, nitric acid reacts slowly, resulting in its characteristic yellow-brown color To prevent decomposition caused by sunlight, nitric acid is stored in brown bottles in laboratories, as the dark glass effectively blocks light exposure.

Reactions with Copper a React copper with concentrated nitric acid

Cu+ 4HN O3→Cu(N O3)2+ 2H2O+N O2 b React copper with dilute nitric acid (HG only)

3Cu+ 8HN O3→3Cu(N O3)2+ 4H2O+ 2N O The colourlessN Oturns brown on contact with air

In both these reactions with copperHN O3 is acting as an oxidizing agent.

Uses of Nitric Acid

• Preparation of explosives, for example T.N.T (trinitro-toluene) and nitro- glycerine.

• Preparation of fertilizers, for example ammonium nitrate (N H4N O3).

• In the plastics industry nitric acid is used for the manafacture of basic materials for the preparation of plastic articles.

• Preparation of nitrates for medicinal and industrial use.

Nitrates

• All nitrates are soluble in water.

• Nitrates decompose on heating to form a nitrite and oxygen nitrate + heat → nitrite + O2

• composition and interaction with other global systems

• Ions in aqueous solution: their interaction and effects

– Electrolytes and extent of ionisation as measured by conductivity– Precipitation reactions

Exploiting the Earth’s crust (Grade 11)

• Mining and mineral processing gold, iron, phosphate (South Africa’s strengths), environmental impact of these activities

• Energy resources and their use

• Global warming and the environmental impact of population growth

The Chemical Industry: Resources, Needs and the Chemical Connection

Dean Govender is a process engineer at Sasol, specializing in Operations, Profitability, and Improvement He holds a Bachelor of Science degree (with honours) in Chemical Engineering from the University of Natal, South Africa In his role, he focuses on business innovation, technology optimization, and engineering support Additionally, Dean is pursuing a Bachelor of Physiology and Biochemistry degree to further enhance his expertise.

Scientists worldwide are continuously exploring and developing compounds that enhance our daily lives, with synthetic polymers playing a pivotal role in modern society and contributing to a multibillion-rand industry These man-made materials are found in a variety of everyday items, including pens, plastic bottles, food wraps, clothing, photographic film, and toys A polymer is a large macromolecule formed by linking numerous identical smaller units called monomers through a process known as polymerization For instance, polyethylene, a widely used plastic, consists of repeating units derived from the monomer ethylene (CH2=CH2), represented as [-CH2-CH2-]n, where "n" indicates the number of repetitions.

The applications of polymers are endless and you can probably see these ap- plications by exploring your house or shopping mall Some of these applications are listed below:

Polyethylene, poly(vinyl chloride), and polypropylene are widely used polymers in everyday products like films, squeeze bottles, and toys Additionally, polystyrene is utilized for packaging, food containers, and hot drink cups, while Teflon offers non-stick surfaces for cookware and textiles Synthetic polymers also play a significant role in producing carpets, blankets, and clothing.

In addition to artificial joints, heart valves and surgical gowns synthetic poly- mers have also played a major role in tissue engineering.

Synthetic polymers play a crucial role in the automotive and aerospace industries, with many truck and car parts manufactured from these materials Poly(vinyl chloride) is widely utilized in industrial piping, while polymers are also integral to the construction of space shuttle nose cones and various aircraft components.

Synthetic polymers are renowned for their exceptional strength and heat resistance, making them essential in the production of various sporting equipment, including tennis racquets and advanced bicycles Nylon, widely recognized in the clothing industry, also serves vital roles in creating fishing lines and ropes Additionally, Kevlar is specifically utilized in the manufacturing of skis, showcasing the versatility of these materials in sports.

In addition, the strength of Kevlar is greater than steel and is used in bullet- proof vests, flame-resistant clothing and helmets.

Sir Isaac Newton famously stated, "If I have seen further it is by standing on the shoulders of giants," highlighting the importance of foundational work in science The pioneers of polymer chemistry laid the groundwork for future innovations, enabling scientists to achieve remarkable discoveries and inventions Today, polymer chemistry has evolved into a sophisticated field focused on designing macromolecules for a wide array of applications.

Lets look at some of the major developments of polymer chemistry:

In 1839, Charles Goodyear made a serendipitous discovery of the vulcanization process when he accidentally spilled a mixture of rubber and sulfur on a stove This fortuitous event led to the creation of a material with enhanced properties compared to natural rubber Goodyear named this transformative process after Vulcan, the Roman god of fire, highlighting its significance in the advancement of rubber technology.

• 1887: Rayon, the first synthetic fibre, was developed by Count Hilaire de Chardonnet.

• 1909: Leo Baekeland becomes the first person to develop the first syn- thetic plastic called Bakelite.

In 1920, Hermann Staudinger introduced the groundbreaking concept that polymers consist of long chains formed by repeating units, a discovery that later earned him the Nobel Prize His research was further validated by X-ray crystallography, which confirmed that these polymers are composed of smaller units known as monomers.

• 1920: During the late 1920s Wallace Carothers and a team of scientists at the Du Pont company in America began to synthesise many polymers including nylon.

• 1939: The industrial production of polyethylene began.

• 1971: The production of Kevlar began.

In today's world, the focus on creating larger and more advanced polymers is prevalent, yet many scientists are prioritizing the reduction of environmental pollution A significant initiative in this area involves developing polymers designed to degrade naturally over time when exposed to ultraviolet light or when disposed of in soil.

The polymer industry is a significant contributor to the economy in various countries, including South Africa, where Sasol Polymers stands out as the leading producer of monomers and polymers By 2006, the company is projected to produce over 1.5 million tons of polymers annually, catering to an expanding customer base across Africa, Europe, and Asia Sasol's primary production facilities are located in Sasolburg and Secunda, specializing in the manufacture of essential products such as ethylene, propylene, low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE), polypropylene, vinyl chloride

Sasol Polymers, in collaboration with joint venture partners, oversees significant investments in two major plants in Malaysia and is currently developing an integrated ethylene and polyethylene production facility in Iran To maintain cost competitiveness and reliability, Sasol Polymers has made substantial investments in upgrading technologies, including catalysts and polymerization reactor modifications The establishment of the Polymers Technology Centre is pivotal for showcasing Sasol Polymers' commitment to continuous improvement in product and service output This centre conducts various tests on polymers to assess their suitability for specific end-products and conversion processes, while also enhancing plant technology, operational efficiencies, and new product development.

Sasol Polymers stands out as an exceptional company, providing a diverse range of products used in numerous applications, including woven cloth, furniture, automotive parts, and domestic ware Their materials are essential for cable sheathing in electrical, electronic, and telecommunication sectors, as well as cling wrap, personal-care items, floor tiles, piping, credit cards, smart cards, computer housings, footwear, wallpaper, and medical supplies like blood and transfusion sets.

The future of polymer chemistry is very promising Perhaps one day you will become a famous scientist that discovers a new material that will revolutionise our lives!

• SASOL, fuels, monomers and polymers, polymerisation

• the Chloralkali industry (soap, PVC, etc)

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