The Behavior of Gases and Liquids

Chapter 1: The Behavior of Gases and Liquids PRINCIPAL FACTS AND IDEAS The principal goal of physical chemistry is to understand the properties and behavior of material systems and to apply this understanding in useful ways The state of a system is specified by giving the values of a certain number of independent variables (state variables) In an equilibrium one-phase fluid system of one substance, three macroscopic variables such as temperature, volume, and amount of substance can be independent variables and can be used to specify the macroscopic equilibrium state of the system At least one of the variables used to specify the state of the system must be proportional to the size of the system (be extensive) Other macroscopic variables are mathematical functions of the independent variables The intensive state, which includes only intensive variables (variables that are independent of the size of the system), is specified by only two variables in the case of an equilibrium one-phase fluid system of one substance Nonideal gases and liquids are described mathematically by various equations of state The coexistence of phases can be described mathematically The liquid–gas coexistence curve terminates at the critical point, beyond which there is no distinction between liquid and gas phases The law of corresponding states asserts that in terms of reduced variables, all substances obey the same equation of state 1.1 Introduction - Antoine Laurent Lavoisier, 1743–1794, was a great French chemist who was called the “father of modern chemistry” because of his discovery of the law of conservation of mass - Physics has been defined as the study of the properties of matter that are shared by all substances, whereas chemistry has been defined as the study of the properties of individual substances - Dalton proposed his atomic theory in 1803, as well as announcing the law of multiple proportions With this theory, chemistry could evolve into a molecular science, with properties of substances tied to their molecular structures Systems We call any object that we wish to study our system A large system containing many atoms or molecules is called a macroscopic system, and a system consisting of a single atom or molecule is called a microscopic system We consider two principal types of properties of systems - Macroscopic properties such as temperature and pressure apply only to a macroscopic system and are properties of the whole system - Microscopic properties such as kinetic energy and momentum They apply to either macroscopic or microscopic systems Mathematics in Physical Chemistry The study of any physical chemistry topics requires mathematics Galileo once wrote, “The book of nature is written in the language of mathematics.” We will use mathematics in two different ways -First, we will use it to describe the behavior of systems without explaining the origin of the behavior - Second, we will use it to develop theories that explain why certain behaviors occur Mathematical Functions A mathematical function involves two kinds of variables: An independent variable and a dependent variable Consider the ideal gas law: P = nRT/V We represent such a function by P = f(T , V, n) Units of Measurement The official set of units that physicists and chemists use is the International System of Units, or SI units The unit of length is the meter (m) The unit of mass is the kilogram (kg) The unit of time is the second (s) The unit of temperature is the kelvin (K) The unit of electric current is the ampere (A) The unit of luminous intensity is the candela (cd) The unit of force: N =1 kgms−2 The unit of pressure:1 Pa =1Nm−2 = kgm−1s−2 A force exerted through a distance is equivalent to an amount of work, which is a form of energy: J = Nm = kgm2s−2 We will also use some non-SI units The calorie (cal), which cal = 4.184 J We will use several non-SI units of pressure; the atmosphere (atm), the torr, and the bar atm = 101325 Pa 760 torr = atm bar = 100000 Pa The angstrom (Å, equal to 10−10m or 10−8 cm) has been a favorite unit of length Picometers are nearly as convenient, with 100 pm equal to Å Chemists are also reluctant to abandon the liter (L), which is the same as 0.001m3 or dm3 • degree C = degree F * 100 / 180 = degree F * / • we can convert from the temperature on the Fahrenheit scale (TF) to the temperature on the Celsius scale (TC) by using this equation: TF = 32 + (9 / 5) * TC • Of course, you can have temperatures below the freezing point of water and these are assigned negative numbers When scientists began to study the coldest possible temperature, they determined an absolute zero at which molecular kinetic energy is a minimum (but not strictly zero!) They found this value to be at -273.16 degrees C Using this point as the new zero point we can define another temperature scale called the absolute temperature If we keep the size of a single degree to be the same as the Celsius scale, we get a temperature scale which has been named after Lord Kelvin and designated with a K Then: K = C + 273.16 • There is a similar absolute temperature corresponding to the Fahrenheit degree It is named after the scientist Rankine and designated with an R: R = F + 459.69 The Clausius–Clapeyron Equation The Clausius–Clapeyron equation is obtained by integrating the Clapeyron equation in the case that one of the two phases is a vapor (gas) and the other is a condensed phase (liquid or solid) We make two approximations: (1) that the vapor is an ideal gas, and (2) that the molar volume of the condensed phase is negligible compared with that of the vapor (gas) phase These are both good approximations - For a liquid–vapor transition with our approximations The same approximation holds for a solid–vapor transition From Eqs (5.3-8) and (5.3-12) we obtain the derivative form of the Clausius–Clapeyron equation For a liquid–vapor transition - For sublimation (a solid–vapor transition), ∆vapHm is replaced by ∆subHm, the molar enthalpy change of sublimation.To obtain a representation of P as a function of T , we need to integrate Eq (5.3-13).We multiply by dT and divide by P: Carrying out a definite integration with the assumption that ∆Hm is constant gives the integral form of the Clausius–Clapeyron equation: If the enthalpy change of a particular substance is not known We have a modified version of the Clausius– Clapeyron equation can be derived using the assumption that ∆CP,m is constant: 5.4 The Gibbs Energy and Phase Transitions We ask the following question: Why is water a liquid with a molar volume of 18mLmol−1at 1atm and 373.14 K, but a vapor with a molar volume of 30 L mol−1 at 1atm and 373.16K? Why should such a small change in temperature make such a large change in structure? The thermodynamic answer to this question comes from the fact that at equilibrium at constant T and P, the Gibbs energy of the system must be at a minimum we have used Eq (4.2-20): The molar entropy of the water vapor is greater than the molar entropy of the liquid water, so that the tangent to the vapor curve in Figure 5.5 has a more negative slope than that of the liquid curve Figure 5.6 shows schematically the molar Gibbs energy of liquid and gaseous water as a function of pressure at constant temperature The two curves intersect at the equilibrium pressure for the phase transition at this temperature The slope of the tangent to the curve is given by Eq (4.2-21): The Critical Point of a Liquid–Vapor Transition -The tangents to the two curves in Figure 5.6 represent the molar volumes In the case of a liquid– vapor transition the two molar volumes become more and more nearly equal to each other as the temperature is increased toward the critical temperature The tangents to the curves approach each other more and more closely until there is only one curve at the critical temperature - At the critical point, the two curves representing Sm in Figure 5.8 also merge into a single curve The molar entropy of the liquid and the molar entropy of the gas phase approach each other The Temperature Dependence of the Gibbs Energy Change The temperature derivative of the Gibbs energy is given by Eq (4.2-20): However, we cannot use this equation to calculate a value of ∆G for a temperature change because the value of the entropy can always have an arbitrary constant added to it without any physical effect We can write an analogous equation for the temperature dependence of ∆G for an isothermal process: A useful version of this equation can be written We can use this equation to calculate ∆G for an isothermal process at temperature T2 from its value at temperature T1.We multiply by dT and integrate from T1 to T2: If ∆H is temperature-independent, Part Thermodynamics and the Macroscopic Description of Physical Systems Chapter The Behavior of Gases and Liquids 1.1 Introduction 1.2 Systems and States in Physical Chemistry 1.3 Real Gases 1.4 The Coexistence of Phases and the Critical Point Chapter Work, Heat, and Energy: The First Law of Thermodynamics 2.1 Work and the State of a System 2.2 Heat 2.3 Internal Energy: The First Law of Thermodynamics 2.4 Calculation of amounts of Heat and Energy Changes 2.5 Enthalpy 2.6 Calculation of Enthalpy Changes of Processes without Chemical Reactions 2.7 Calculation of Enthalpy Changes of a Class of Chemical Reactions 2.8 Calculation of Energy Changes of Chemical Reactions Chapter The Second and Third Laws of Thermodynamics: Entropy 3.1 The Second Law of Thermodynamics and the Carnot Heat Engine 3.2 The Mathematical Statement of the Second Law: Entropy 3.3 The Calculation of Entropy Changes 3.4 Statistical Entropy 3.5 The Third Law of Thermodynamics and Absolute Entropies Chapter The Thermodynamics of Real Systems 4.1 Criteria for Spontaneous Processes and for Equilibrium: The Gibbs and Helmholtz Energies 4.2 Fundamental Relations for Closed Simple Systems 4.3 Additional Useful Thermodynamic Identities 4.4 Gibbs Energy Calculations 4.5 Multicomponent Systems 4.6 Euler’s Theorem and the Gibbs–Duhem Relation Chapter Phase Equilibrium 5.1 The Fundamental Fact of Phase Equilibrium 5.2 The Gibbs Phase Rule 5.3 Phase Equilibria in One-Component Systems 5.4 The Gibbs Energy and Phase Transitions 5.5 Surfaces in One-Component Systems 5.6 Surfaces in Multicomponent Systems Chapter The Thermodynamics of Solutions 6.1 Ideal Solutions 6.2 Henry’s Law and Dilute Nonelectrolyte Solutions 6.3 Activity and Activity Coefficients 6.4 The Activities of nonvolatile Solutes 6.5 Thermodynamic Functions of nonideal Solutions 6.6 Phase Diagrams of nonideal Mixtures 6.7 Colligative Properties Chapter Chemical Equilibrium 7.1 Gibbs Energy Changes and the Equilibrium Constant 7.2 Reactions involving Gases and Pure Solids or Liquids 7.3 Chemical Equilibrium in Solutions 7.4 Equilibria in Solutions of Strong Electrolytes 7.5 Buffer Solutions 7.6 The Temperature Dependence of Chemical Equilibrium The Principle of Le Châtelier 7.7 Chemical Equilibrium and Biological Systems Chapter The Thermodynamics of Electrochemical Systems 8.1 The Chemical Potential and the Electric Potential 8.2 Electrochemical Cells 8.3 Half-Cell Potentials and Cell Potentials 8.4 The Determination of Activities and Activity Coefficients of Electrolytes 8.5 Thermodynamic Information from Electrochemistry ... physicists and chemists use is the International System of Units, or SI units The unit of length is the meter (m) The unit of mass is the kilogram (kg) The unit of time is the second (s) The unit of. .. all of the (3) continents; 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