CHAPTER 6 CHEMICAL EQUILIBRIUM

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Bertram Cobb
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1 CHAPTER 6 CHEMICAL EQUILIBRIUM Spontaneous process involving a reactive mixture of gases Two new state functions A: criterion for determining if a reaction mixture will evolve towards the reactants or products at const V and T G: criterion for determining if a reaction mixture will evolve towards the reactants or products at const P and T Gibbs Energy and Helmholtz Energy Spontaneous process: S + S surroundings > 0 Spontaneity and equilibrium defined using only properties of the system rather than the combination of system and surroundings Clausius inequality Isolated system: du = 0 and w = 0 1

2 Systems Interacting with Environment For isothermal processes, dt = 0, so TdS = d(ts) Helmholtz free energy, A = U TS Maximum work a system can do on the surrounding in an isothermal process Helmholtz Free Energy At const V, dv = 0, so 0 If nonexpansion work is not possible in the transformation, 0 Definition of spontaneity and equilibrium For processes taking place at const V and T 2

3 Gibbs Free Energy Reactions at const P and T, PdV = d(pv) and TdS = d(ts) Gibbs free energy, G = H - TS Maximum nonexpansion work If nonexpansion work is not possible Spontaneity Criterion Clausius inequality, A and G only use macroscopic variables of the system A: maximum work done on the surroundings at constant T and V G: maximum nonexpansion work done on the surroundings at constant T and P 3

4 Implication on Heat Engine vs Fuel Cell Heat engine: conversion of heat to work at an efficiency < 100% (second law) Fuel cell: nonexpansion work from G, could reach 100%; no heat is involved in the conversion Direction of a Chemical Reaction At const T and P, The entropic contribution to G R is greater at higher temperature A chemical transformation is always spontaneous if H R < 0 (exothermal) and S R > 0 A chemical transformation is never spontaneous if H R > 0 (endothermal) and S R < 0 For all other cases, the relative magnitudes of H R and S R determine if the chemical transformation is spontaneous. If a chemical reaction is not spontaneous, then the reverse process is. If G R = 0, the reaction mixture is at an equilibrium, and neither direction of change is spontaneous. 4

5 Helmholtz Free Energy At constant V and T, and no nonexpansion work, da < 0 In a chemical transformation at constant T and V Differential Forms of U, H, A, and G U and H: changes in energy for a process A and G: direction of the change and the maximum work allowed 5

6 U = U(S, V) H = H(S, P) A = A(T, V) G = G(T, P) 6

7 Maxwell Relations U is a state function, so,, Dependence of G and A on P, V, and T Dependence on P P = 1 bar Solids or liquids Ideal gases 7

8 Dependence on T Gibbs-Helmholtz equation 8

9 Example 6.4 The value of for Fe(g) is 370kJ/mol at 298K, and for fe(g) is kj/mol at the same temperature. Assuming is constant in the interval K, calculate for Fe(g) at 400K. Gibbs Energy of a Reaction Mixture Chemical potential 9

Chemical Potential At constant T and P, Transport will occur spontaneously from a region of high chemical potential to another of low chemical potentials (extraction, phase transition, etc) At

10 Chemical Potential At constant T and P, Transport will occur spontaneously from a region of high chemical potential to another of low chemical potentials (extraction, phase transition, etc) At equilibrium, the chemical potential of each species is the same throughout a mixture Gibbs Energy of a Gas in a Mixture < Mixing of the two subsystems is spontaneous if not separated by the membrane 10

11 Calculating G mixing Mixing of Two Gases 11

12 Calculating G R for a Chemical Reaction for a pure element in its standard reference state Equilibrium Constant for a Mixture of Ideal Gases 12

13 Reaction Quotient of Pressures (Q P ) Chemical Equilibrium At equilibrium, G R = 0, and Q P = K P 13

14 Variation of K P with Temperature Gibbs-Helmholtz equation) H R independe nt of T Equilibrium Involving Ideal Gases and Solid or Liquid Phases 14

15 Expressing Equilibrium Constant in Terms of Mole Fraction Expressing Equilibrium Constant in Terms of Molarity PV=nRT, so c = n/v = P/RT 15

16 Dependence of the Extent of Reaction on T and P Extent of reaction If G R < 0, the reaction proceeds spontaneously as written If G R > 0, the reaction proceeds spontaneously in the opposite direction If G R = 0, the reaction system is at equilibrium and there is no direction of change. 16

The Standard Gibbs Energy Change, G

The Standard Gibbs Energy Change, G S univ = S surr + S sys S univ = H sys + S sys T S univ = H sys TS sys G sys = H sys TS sys Spontaneous reaction: S univ >0 G sys < 0 More observations on G and Gº I.