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Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 5 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula
CHAPTER Simple mixtures Mixtures are an essential part of chemistry, either in their own right or as starting materials for chemical reactions This group of Topics deals with the rich physical properties of mixtures and shows how to express them in terms of thermodynamic quantities 5A The thermodynamic description of mixtures The first Topic in this chapter develops the concept of chemical potential as an example of a partial molar quantity and explores how to use the chemical potential of a substance to describe the physical properties of mixtures The underlying principle to keep in mind is that at equilibrium the chemical potential of a species is the same in every phase We see, by making use of the experimental observations known as Raoult’s and Henry’s laws, how to express the chemical potential of a substance in terms of its mole fraction in a mixture 5B The properties of solutions In this Topic, the concept of chemical potential is applied to the discussion of the effect of a solute on certain thermodynamic properties of a solution These properties include the lowering of vapour pressure of the solvent, the elevation of its boiling point, the depression of its freezing point, and the origin of osmotic pressure We see that it is possible to construct a model of a certain class of real solutions called ‘regular solutions’, and see how they have properties that diverge from those of ideal solutions shall see how the phase diagram for the system summarizes empirical observations on the conditions under which the various phases of the system are stable 5D Phase diagrams of ternary systems Many modern materials (and ancient ones too) have more than two components In this Topic we show how phase diagrams are extended to the description of systems of three components and how to interpret triangular phase diagrams 5E Activities The extension of the concept of chemical potential to real solutions involves introducing an effective concentration called an ‘activity’ We see how the activity may be defined and measured We shall also see how, in certain cases, the activity may be interpreted in terms of intermolecular interactions 5F The activities of ions One of the most important types of mixtures encountered in chemistry is an electrolyte solution Such solutions often deviate considerably from ideal behaviour on account of the strong, long-range interactions between ions In this Topic we show how a model can be used to estimate the deviations from ideal behaviour when the solution is very dilute, and how to extend the resulting expressions to more concentrated solutions 5C Phase diagrams of binary systems One widely used device used to summarize the equilibrium properties of mixtures is the phase diagram We see how to construct and interpret these diagrams The Topic introduces systems of gradually increasing complexity In each case we What is the impact of this material? We consider just two applications of this material, one from biology and the other from materials science, from among the 5 Simple mixtures huge number that could be chosen for this centrally important field In Impact I5.1, we see how the phenomenon of osmosis contributes to the ability of biological cells to maintain their shapes In Impact I5.2, we see how phase diagrams are used to describe the properties of the technologically important liquid crystals 179 To read more about the impact of this material, scan the QR code, or go to bcs.whfreeman.com/webpub/chemistry/ pchem10e/impact/pchem-5-1.html 5A The thermodynamic description of mixtures ➤➤ What you need to know already? Contents 5A.1 Partial molar quantities Partial molar volume Example 5A.1: Determining a partial molar volume (b) Partial molar Gibbs energies (c) The wider significance of the chemical potential (d) The Gibbs–Duhem equation Brief illustration 5A.1: The Gibbs–Duhem equation Example 5A.2: Using the Gibbs–Duhem equation (a) 5A.2 The thermodynamics of mixing The Gibbs energy of mixing of perfect gases Example 5A.3: Calculating a Gibbs energy of mixing (b) Other thermodynamic mixing functions Brief illustration 5A.2: The entropy of mixing (a) 5A.3 The chemical potentials of liquids Ideal solutions Brief illustration 5A.3: Raoult’s law (b) Ideal–dilute solutions Example 5A.4: Investigating the validity of Raoult’s and Henry’s laws Brief illustration 5A.4: Henry’s law and gas solubility (a) Checklist of concepts Checklist of equations 180 181 182 182 183 183 184 184 184 185 185 186 186 187 187 188 188 189 190 190 190 ➤➤ Why you need to know this material? Chemistry deals with a wide variety of mixtures, including mixtures of substances that can react together Therefore, it is important to generalize the concepts introduced in Chapter to deal with substances that are mingled together This Topic also introduces the fundamental equation of chemical thermodynamics on which many of the applications of thermodynamics to chemistry are based ➤➤ What is the key idea? The chemical potential of a substance in a mixture is a logarithmic function of its concentration This Topic extends the concept of chemical potential to substances in mixtures by building on the concept introduced in the context of pure substances (Topic 4A) It makes use of the relation between entropy and the temperature dependence of the Gibbs energy (Topic 3D) and the concept of partial pressure (Topic 1A) It uses the notation of partial derivatives (Mathematical background 2) but does not draw on their advanced properties As a first step towards dealing with chemical reactions (which are treated in Topic 6A), here we consider mixtures of substances that not react together At this stage we deal mainly with binary mixtures, which are mixtures of two components, A and B We shall therefore often be able to simplify equations by making use of the relation xA + xB = 1 In Topic 1A it is established that the partial pressure, which is the contribution of one component to the total pressure, is used to discuss the properties of mixtures of gases For a more general description of the thermodynamics of mixtures we need to introduce other analogous ‘partial’ properties One preliminary remark is in order Throughout this and related Topics we need to refer to various measures of concentration of a solute in a solution The molar concentration (colloquially, the ‘molarity’, [J] or cJ) is the amount of solute divided by the volume of the solution and is usually expressed in moles per cubic decimetre (mol dm−3; more informally, mol L−1) We write c