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Chapter 6 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 6 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 6 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 6 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula Chapter 6 Atkins Physical Chemistry (10th Edition) Peter Atkins and Julio de Paula
CHAPTER Chemical equilibrium Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products are present but have no further tendency to undergo net change In some cases, the concentration of products in the equilibrium mixture is so much greater than that of the unchanged reactants that for all practical purposes the reaction is ‘complete’ However, in many important cases the equilibrium mixture has significant concentrations of both reactants and products 6A The equilibrium constant This Topic develops the concept of chemical potential and shows how it is used to account for the equilibrium composition of chemical reactions The equilibrium composition corresponds to a minimum in the Gibbs energy plotted against the extent of reaction By locating this minimum we establish the relation between the equilibrium constant and the standard Gibbs energy of reaction 6B The response of equilibria to the conditions The thermodynamic formulation of equilibrium enables us to establish the quantitative effects of changes in the conditions One very important aspect of equilibrium is the control that can be exercised by varying the conditions, such as the pressure or temperature 6C Electrochemical cells Because many reactions involve the transfer of electrons, they can be studied (and utilized) by allowing them to take place in a cell equipped with electrodes, with the spontaneous reaction forcing electrons through an external circuit We shall see that the electric potential of the cell is related to the reaction Gibbs energy, so providing an electrical procedure for the determination of thermodynamic quantities 6D Electrode potentials Electrochemistry is in part a major application of thermodynamic concepts to chemical equilibria as well as being of great technological importance As elsewhere in thermodynamics, we see how to report electrochemical data in a compact form and apply it to problems of real chemical significance, especially to the prediction of the spontaneous direction of reactions and the calculation of equilibrium constants What is the impact of this material? The thermodynamic description of spontaneous reactions has numerous practical and theoretical applications We highlight two applications One is to the discussion of biochemical processes, where one reaction drives another (Impact I6.1) That, ultimately, is why we have to eat, for we see that the reaction that takes place when one substance is oxidized can drive nonspontaneous reactions, such as protein synthesis, forward Another makes use of the great sensitivity of electrochemical processes to the concentration of electroactive materials, and we see how specially designed electrodes are used in analysis (Impact I6.2) To read more about the impact of this material, scan the QR code, or go to bcs.whfreeman.com/webpub/chemistry/ pchem10e/impact/pchem-6-1.html 6A The equilibrium constant Contents 6A.1 The Gibbs energy minimum The reaction Gibbs energy Brief illustration 6A.1: The extent of reaction (b) Exergonic and endergonic reactions Brief illustration 6A.2: Exergonic and endergonic reactions (a) 6A.2 245 245 245 246 247 The description of equilibrium 247 Perfect gas equilibria 247 Brief illustration 6A.3: The equilibrium constant 247 (b) The general case of a reaction 248 Brief illustration 6A.4: The reaction quotient 248 Brief illustration 6A.5: The equilibrium constant 249 Example 6A.1: Calculating an equilibrium constant 249 Example 6A.2: Estimating the degree of dissociation at equilibrium 250 (c) The relation between equilibrium constants 251 Brief illustration 6A.6: The relation between equilibrium constants 251 (d) Molecular interpretation of the equilibrium constant 251 Brief illustration 6A.7: Contributions to K 252 (a) Checklist of concepts Checklist of equations 252 252 ➤➤ Why you need to know this material? Equilibrium constants lie at the heart of chemistry and are a key point of contact between thermodynamics and laboratory chemistry The material in this Topic shows how they arise and explains the thermodynamic properties that determine their values ➤➤ What is the key idea? The composition of a reaction mixture tends to change until the Gibbs energy is a minimum ➤➤ What you need to know already? Underlying the whole discussion is the expression of the direction of spontaneous change in terms of the Gibbs energy of a system (Topic 3C).This material draws on the concept of chemical potential and its dependence on the concentration or pressure of the substance (Topic 5A) You need to know how to express the total Gibbs energy of a mixture in terms of the chemical potentials of its components (Topic 5A) As explained in Topic 3C, the direction of spontaneous change at constant temperature and pressure is towards lower values of the Gibbs energy, G The idea is entirely general, and in this Topic we apply it to the discussion of chemical reactions There is a tendency of a mixture of reactants to undergo reaction until the Gibbs energy of the mixture has reached a minimum: that state corresponds to a state of chemical equilibrium The equilibrium is dynamic in the sense that the forward and reverse reactions continue, but at matching rates As always in the application of thermodynamics, spontaneity is a tendency: there might be kinetic reasons why that tendency is not realized 6A.1 The Gibbs energy minimum We locate the equilibrium composition of a reaction mixture by calculating the Gibbs energy of the reaction mixture and identifying the composition that corresponds to minimum G Here we proceed in two steps: first, we consider a very simple equilibrium, and then we generalize it (a) The reaction Gibbs energy Consider the equilibrium A ⇌ B Even though this reaction looks trivial, there are many examples of it, such as the isomerization of pentane to 2-methylbutane and the conversion of l-alanine to d-alanine Suppose an infinitesimal amount dξ of A turns into B, then the change in the amount of A present is dnA = −dξ and the change in the amount of B present is dnB = +dξ The quantity ξ (xi) is called the extent of reaction; it has the dimensions of amount of substance and is reported in moles When the extent of reaction changes by a measurable amount Δξ, the amount of A present changes from nA,0 to nA,0 − Δξ and the amount of B changes from nB,0 to nB,0 + Δξ In general, the amount of a component J changes by νJΔξ, where νJ is the stoichiometric number of the species J (positive for products, negative for reactants) Brief illustration 6A.1 The extent of reaction If initially 2.0 mol A is present and we wait until Δξ = +1.5 mol, then the amount of A remaining will be 0.5 mol The amount of B formed will be 1.5 mol 246 6 Chemical equilibrium Self-test 6A.1 Suppose the reaction is A → 2 B and that ini- Answer: 1.0 mol A, 1.0 mol B The reaction Gibbs energy, ΔrG, is defined as the slope of the graph of the Gibbs energy plotted against the extent of reaction: ∂G ∆rG = ∂ξ p ,T Definition Reaction Gibbs energy (6A.1) Although Δ normally signifies a difference in values, here it signifies a derivative, the slope of G with respect to ξ However, to see that there is a close relationship with the normal usage, suppose the reaction advances by dξ The corresponding change in Gibbs energy is Figure 6A.1 As the reaction advances (represented by motion from left to right along the horizontal axis) the slope of the Gibbs energy changes Equilibrium corresponds to zero slope at the foot of the valley The spontaneity of a reaction at constant temperature and pressure can be expressed in terms of the reaction Gibbs energy: This equation can be reorganized into • If ΔrG 0, the reverse reaction is spontaneous • If ΔrG = 0, the reaction is at equilibrium That is, (6A.2) We see that ΔrG can also be interpreted as the difference between the chemical potentials (the partial molar Gibbs energies) of the reactants and products at the current composition of the reaction mixture Because chemical potentials vary with composition, the slope of the plot of Gibbs energy against extent of reaction, and therefore the reaction Gibbs energy, changes as the reaction proceeds The spontaneous direction of reaction lies in the direction of decreasing G (that is, down the slope of G plotted against ξ) Thus we see from eqn 6A.2 that the reaction A → B is spontaneous when μA > μ B, whereas the reverse reaction is spontaneous when μ B > μA The slope is zero, and the reaction is at equilibrium and spontaneous in neither direction, when ∆rG = ΔrG = (b) Exergonic and endergonic reactions dG = µ A dnA + µB dnB = − µ A dξ + µB dξ = (µB − µ A )dξ ∆ r G = μB − μ A ΔrG > Extent of reaction, ξ ∂G ∂ξ = µB − µ A p ,T ΔrG < Gibbs energy, G tially 2.5 mol A is present What is the composition when Δξ = +0.5 mol? A reaction for which ΔrG 0 is called endergonic (signifying work consuming) The reaction can be made to occur only by doing work on it, such as electrolysing water to reverse its spontaneous formation reaction reactions The standard Gibbs energy of the reaction H2 (g) + 12 O2 (g ) → H2O(l) at 298 K is −237 kJ mol−1, so the reaction is exergonic and in a suitable device (a fuel cell, for instance) operating at constant temperature and pressure could produce 237 kJ of electrical work for each mole of H2 molecules that react The reverse reaction, for which ΔrG