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Solution Manual for General Chemistry: Principles and Modern Applications, Loose Leaf Version 11th edition by Ralph H Petrucci, F Geoffrey Herring, Jeffry D Madura and Carey Bissonnette ATOMS AND THE ATOMIC THEORY CHAPTER OBJECTIVES State and apply the laws of conservation of mass and definite composition State the basic assumptions of Dalton’s atomic theory List some of the characteristic properties of cathode rays and of canal (anode) rays Describe the production of X-rays, the phenomenon of radioactivity, and the characteristics of α , β , and γ radiation Describe Thompson’s m/e experiment, Millikan’s oil drop experiment (to measure the charge on the electron), and Rutherford’s gold foil experiment (to establish the existence of the atomic nucleus) State the features of Rutherford’s nuclear atom and how it differs from Thompson’s model of the atom Perform calculations involving the masses and charges of the proton, neutron, and electron List the numbers of protons, neutrons, and electrons present in atoms and ions, using the A symbolism Z E Describe how atomic mass ratios are determined by mass spectrometry and use these ratios to determine relative atomic masses 10 Calculate the atomic mass of an element from the known masses and relative abundances of its naturally occurring isotopes 11 Use the periodic table in fundamental ways, including locating elements with certain properties and predicting the charges of ions of representative elements 12 Obtain and use relationships between the mole, the Avogadro constant (Avogadro’s number), and the molar mass of an element NOTES 1-1 Some Alternatives for Presenting Chapter For students with good backgrounds in high school chemistry, it may be possible to omit most of Chapter 2, or at least to assign it for self-study In this way the pace through the first two chapters of the text can be quickened The topics that are most important to discuss in this accelerated approach are isotopic masses, atomic masses, the Avogadro constant and the concept of the mole, and calculations involving the mole concept 2-1 Early Chemical Discoveries and the Atomic Theory Instructors who wish to de-emphasize historical topics may restrict their coverage of Section 2-1 to statements of the laws of conservation of mass and constant composition and to the assumptions of Dalton’s theory If a more complete treatment of the chemical basis of atomic theory is desired at this point, appropriate exercises can be brought forward from Chapter The laws of chemical combination are also illustrated through numerous drill problems and sample quizzes in the Student Study Guide 2-2 Electrons and Other Discoveries in Atomic Physics Experiments with cathode ray tubes produced an understanding of atomic structure The electron was recognized as a fundamental particle and its charge and mass were determined Mass-to-charge ratios of atomic ions led to the discovery of isotopes There are two reasons for a brief mention of radioactivity in this section The discovery of radioactivity was a direct consequence of cathode ray and X-ray research, and some knowledge of the nature of alpha particles is required in presenting Rutherford’s model of the nuclear atom Some instructors may prefer to expand the treatment of radioactivity in this chapter, especially if a later separate treatment of nuclear chemistry is not planned Sections 25-1 through 25-4 can serve this purpose 2-3 The Nuclear Atom Here is the story of Rutherford’s discovery of the nuclear atom The model of the atom is developed to the point where it consists of protons, neutrons, and electrons, a picture adequate for the study of chemistry The relative charges and masses of the three fundamental particles are presented 2-4 Chemical Elements The symbolism for designating a nuclide is developed in this section This enables one to specify the number of protons, neutrons, and electrons in a given species The concept of relative abundance is introduced and mass spectrometry is described as the manner of determining masses of individual atoms 2-5 Atomic Mass The expression is developed for determining average atomic mass from isotopic masses and percent abundances In discussing expression (2.3) it helps to emphasize that the equation can be used to solve for any one quantity—an atomic mass, a fractional abundance, an isotopic mass This emphasis is explored in several exercises 2-6 Introduction to the Periodic Table The items presented in this section include that groups in the periodic table contain elements of similar properties, there are four types of elements (metals, nonmetals, noble gases, and metalloids), the chemistries of main-group elements are very similar within a group, and one can predict the charge of the common ion of a main group element This is indeed an introduction 2-7 The Concept of the Mole and the Avogadro Constant The approach in the text is to define the mole and the Avogadro constant (Avogadro’s number) in terms of exactly 12 g of carbon-12, move on to one mole of a pure isotopic species, and then to consider mixtures of isotopes The mole concept is used in problem solving through the expressions: 23 mol = 6.02214 × 10 atoms = molar mass in grams Some of the illustrative examples and the Summarizing Example also require ideas from Chapter (e.g., percent mass and density) Students who have difficulty with the concept of the mole may be helped by Figure 2-17 and the analogies and photograph on page 54 Additional help can also be found in the Student Study Guide Finally, it should be helpful to explain to students why the mole concept is applied only to very small entities—protons, electrons, atoms, molecules, ions, … 2-8 Using the Mole Concept in Calculations The relationship between the mole, Avogadro’s number, and the molar mass are related and used to perform some fundamental calculations These calculations are combined with the relationships (density and percent composition) that were introduced in Chapter Focus on Occurrence and Abundances of the Elements There are several possibilities for dealing with this topic in addition to its placement here It can be considered as early as Chapter 1, in conjunction with the descriptive chemistry chapter (Chapter 20) If Chapter 26 on biochemistry is not covered in the course, students might be interested in learning of the elements occurring in living matter (Table 26-1) at the time that this Focus On feature is taken up ANCILLARY MATERIALS Transparencies OVERHEAD TEXT REFERENCE NUMBER Figure CAPTION Page T5 2.7 40 different cathode ray diagrams T6 2.10 42 Three types of radiation from radioactive materials T7 2.11 42 The scattering of alpha-particles by metal foil T8 2.12 43 Explaining the results of alpha-particle scattering experiments T9 2.14 T10 2.15 51 Periodic Table of the Elements T11 2.16 54 Distribution of isotopes in four elements A mass spectrometer and mass spectrum Animations, Demonstrations and Activities TYPE TITLE Animation Reactions with Oxygen Animation Multiple Proportions Simulation Coulomb’s Law Animation Millikan Oil Drop Experiment Animation Alpha, Beta, and Gamma Rays Animation Rutherford Experiment Simulation Mass Spectrometer Activity Isotopes of Hydrogen Activity Interactive Periodic Table CHAPTER – TEACHING TIPS Demonstration: Conservation of Mass Glue a vial onto the bottom of a flask Pipet into the vial some Fe(NO3)3 (aq) Pipet around this some NaOH (aq) Stopper the flask Weigh the setup using the most accurate balance available Tip the flask and allow the solutions to react Weigh again CD: Animation – Reactions with Oxygen Dalton’s Atomic Theory is an excellent example of the use of the scientific method: the distinction between laws and assumption and how these relate, and the importance of careful quantitative measurement A good topic for discussion, possibly at the end of this or the next chapter, is how each of Dalton’s assumptions has had to be modified in light of modern observations The Law of Multiple Proportions is probably the hardest concept in this chapter for students to grasp Emphasize that it is mass ratios, and the ratios of these ratios, that matter Give students some mass percentages and have them convert these into mass ratios CD: Animation – Multiple Proportions Mention here that we will use simple electrostatics (charge attractions and repulsions) to explain and understand many chemical properties CD: Simulation – Coulomb’s Law Demonstration: Cathode Ray Tube If available, show a CRT as in Figure 2-6 Try reversing the leads and see the effect Mention that this demonstrates ―Ben Franklin guessed wrong‖ We now know that the flow of charge in wires and in a CRT is by negative electrons moving from negative to + We still talk today, however, of current flowing from + to negative Also demonstrate the effect of a magnetic field Note that the electrons are not attracted or repelled but rather are deflected by a magnetic field 10 The effect of a magnetic field on a charge is somewhat of a surprise to many students, and is not intuitive Emphasize that the effect only works when a charge is moving, and results in a deflection, not an attraction or repulsion 11 The magnetic deflection effect can be used to identify the poles of a magnet With a cathode ray traveling from left to right, the deflection will be ―down‖ if the North pole is closer to the observer 12 CD: Animation – Millikan Oil-Drop Experiment 13 CD: Animation – Alpha, Beta and Gamma Rays 14 Discuss, possibly at the end of the next section, that beta particles result from the decay of a neutron into a proton and a high kinetic energy electron 15 CD: Animation – Rutherford Experiment 16 Rutherford’s interpretation was quite remarkable He proposed the nuclear atomic structure without observation of any direct form of imagery Atomic level scattering experiments became th important again in the latter half of the 20 century 17 The masses of the proton and neutron are slightly different has been clearly demonstrated The charges of the proton and electron, however, are believed to be exactly equal in magnitude (but opposite in sign) 18 The electron is believed to be truly fundamental Modern particle physics now considers the neutron and proton to be composed of other, more fundamental particles 19 Other atomic symbols not based on English names include Cu, Ag, Sn, Sb, Au, and Hg 20 Some elements only have one naturally-occurring isotope Common examples are beryllium-6, fluorine-19, sodium-23 and aluminum-27 21 CD: Activity – Isotopes of Hydrogen 22 Usually all the isotopes of an element share the same name and atomic symbol The exception is hydrogen Isotope H is called deuterium (symbol D) and H is tritium (T) o Demonstration: Heavy Water Exhibit stoppered test tubes of H2O and D2O, cooled to o C in an ice bath o 23 D2O melts at 3.8 C and will be a solid Hydrogen is unusual in that the different isotopes and their compounds have significantly different properties 24 Traces of naturally occurring radioactive isotopes appear in our ecosystem in carbon, hydrogen and potassium 25 CD: Simulation – Mass Spectrometer 26 The mass spectrometer depicted in Figure 2-14 uses electrostatic deflection to separate a beam of ions Other designs use an electrostatic deflection effect 27 The primary standard for atomic masses has evolved over time Dalton used H = l u as his original definition of atomic masses Later, chemists took naturally occurring oxygen as 16 u to be the definition of their atomic weight scale Concurrently, physicists defined just the oxygen-16 isotope as 16 u This resulted in conflicting values In 1971 the adoption of carbon12 as a universal standard resolved this disparity 28 Students frequently confuse the terms atomic number, mass number, isotopic mass and atomic mass 29 Point out that ―atomic mass‖ always means average or weighted atomic mass, unless the reference clearly applies to an isotope 30 One can easily review a table of atomic masses to find elements that must contain two or more isotopes each with appreciable (more than 1%) abundances Based on ―isotopic mass mass number,‖ elements like lithium (6.941 u) and boron (10.81 u) must be mixtures The other atomic masses on row 2, and many others, are nearly integral This suggests that these elements have a single predominant isotope Chromium (52.00 u), however, consists of ―appreciable‖ isotopes: 50, 52, 53, and 54 The abundances of these just happen to average close to an integer! 31 CD: Activity – Interactive Periodic Table 32 Demonstration: Sodium in Water This can be performed solely in miniature Use an evaporating dish with watch-glass cover on an overheard projector Cut a small corner off of a larger piece of sodium and blot to remove any oil Use tweezers to drop the sodium onto the water and cover quickly Note that the sodium melts due to the heat of reaction Complete and balance a net ionic equation for the reaction Repeat the experiment after adding phenolphthalein indicator to a fresh portion of water The point here is that all Group I metals this, with varying rates of reaction (Avoid using potassium This forms explosive peroxides and is not recommended.) 33 That elements in one group have similar properties is perhaps the most useful simplifying feature of atomic properties Significant differences in one group occur The manner and reason for such differences is much of what we try to discover in studying chemistry 34 An advantage of the older American number and letter system is that a single rule ―maximum charge = group number‖ applies to most main-group metals 35 Mendeleev’s arrangement of the elements in the original periodic table was based on observed chemical and physical properties of the elements and their compounds The arrangement of the elements in the modern periodic table is based on atomic numbers 36 Perhaps the most constant property of the elements in one group is their combining capacity, as indicated by the formula of their compounds Two compounds more dissimilar than CO2 and SiO2, in terms of their physical and chemical properties, probably cannot be found They have the same formula 37 The topic of stoichiometry is spread over chapters Chapter introduces the mole for elements Chapter continues with compounds Chapter applies mole concepts to reactions This provides valuable reinforcement of this important subject It also permits blending a largely mathematical procedure with chemical applications and some more qualitative topics 38 The value of Avogadro’s number is based on both a definition and a measurement A mole of carbon-12 is defined to be 12 g The mass of one carbon-12 atom is measured using a -23 mass spectrometer and found to be 1.99927 x 10 g The ratio of these two masses is th Avogadro’s number In the mid 20 century the value first fluctuated and then stabilized, as mass spectra methods were revised and improved 39 When rounding Avogadro’s number, or any other accurately known value, keep one more significant figure than that of the least accurate number in the calculation, to avoid rounding errors 40 The mole was purposely defined so that atomic masses (in u, per atom) and molar masses (in g/mol) would conveniently be the same number, with different units Some students require some time to understand this 41 The mole concept and Avogadro’s number are difficult for some students to understand Using quantities like a dozen and a gross to help explain these topics is helpful 42 Demonstration: Moles of Elements Display samples of mole of several elements such as C, S, Al, Cu, Zn, Pb, and Hg Note that mole is a convenient ―handful-sized‖ quantity While molar masses vary considerably, say from carbon to lead, the volume stays reasonably constant We shall discuss important atomic radius differences later, but many atoms have roughly the same size 43 The abundances of the elements in the earth’s atmosphere are given in Focus on section of Chapter