Atkins’ Physical Chemistry Eighth Edition Chapter 7 – Lecture 1 Chemical Equilibrium Copyright © 2006 by Peter Atkins and Julio de Paula Peter Atkins Julio de Paula Sections only

Homework Set #7 Atkins & de Paula, 8e Chap 7 Exercises: all part (b) unless noted: 2, 3, 4, 5, 7, 9, 10, 12

Objectives: Further develop the concept of chemical potential, μ Apply μ to account for equilibrium composition of a chemical reaction Establish relationship between Gibbs energy and the equilibrium constant, K Establish the quantitative effects of pressure and temperature on K

Equilibrium - state in which there are no observable changes with time Chemical equilibrium - achieved when: rates of the forward and reverse reactions are equal and concentrations of the reactants and products remain constant dynamic equilibriumdynamic equilibrium Physical equilibrium H 2 O (l) Chemical equilibrium N2O4 (g)N2O4 (g) H 2 O (g) 2NO 2 (g) colorlessred-brown

dG = VdP - SdT “spontaneous” ⇒ G → min Fig 3.18 Gibbs energy tends to minimum at ΔT = 0, ΔP =0

Fig 7.1 Plot of Gibbs energy vs. extent of reaction, ξ ξ pronounced zi Reaction Gibbs energy: For equilibrium A ⇌ B Therefore ΔG r = μ B - μ A

Exergonic and endergonic reactions At constant temperature and pressure: ΔG rxn < 0 forward rxn spontaneous (Exergonic) ΔG rxn > 0 reverse rxn spontaneous (Endergonic) ΔG rxn = 0 rxn at equilibrium (Neither)

Fig 7.2 A strongly exergonic process can drive a weaker endergonic process Nonspontaneous, but!!.....

Description of Equilibrium For perfect gases: A ⇌ B At equilibrium: ΔG rxn = 0

N 2 O 4 (g) 2NO 2 (g) = 4.63 x at 25 °C K = [NO 2 ] 2 [N 2 O 4 ] aA + bB cC + dD K = [C] c [D] d [A] a [B] b Law of Mass Action K > 1 K < 1 Lie to the rightFavor products Lie to the leftFavor reactants Equilibrium will: Must be caps Equilibrium constant

Fig 7.3 Plot of Gibbs energy vs. extent of reaction Hypothetical rxn A (g) → B (g) Molecular interpretation of tendency for ΔG r = 0 (i) slope = ΔG r at all times (ii) from Eqn. 5.18: (iii) curve has minimum corresponding to equilibrium composition

Ways of Expressing Equilibrium Constants Concentration of products and reactants may be expressed in different units, so: Heterogeneous equilibria Homogeneous equilibria K = [C] c [D] d [A] a [B] b Law of Mass Action

Heterogenous equilibrium applies to reactions in which reactants and products are in different phases CaCO 3 (s) ⇌ CaO (s) + CO 2 (g) K c = [CaO][CO 2 ] [CaCO 3 ] [CaCO 3 ] = constant [CaO] = constant K c = [CO 2 ] orK p = P CO 2 The concentration of solids and pure liquids are not included in the expression for the equilibrium constant

P CO 2 = K p P CO 2 does not depend on the amount of CaCO 3 or CaO CaCO 3 (s) ⇌ CaO (s) + CO 2 (g)

Homogenous equilibrium applies to reactions in which all reacting species are in the same phase N 2 O 4 (g) ⇌ 2NO 2 (g) K c = [NO 2 ] 2 [N 2 O 4 ] K p = NO 2 P2P2 N2O4N2O4 P In most cases K c  K p aA (g) + bB (g) ⇌ cC (g) + dD (g) K p = K c (RT)  n  n = moles of gaseous products – moles of gaseous reactants = (c + d) – (a + b)

Fig 7.4 Boltzmann distribution of populations of A and B For endothermic reaction A → B Bulk of population is species A Therefore: A is dominant species at equilibrium Assumption: Similar densities of E-levels

Fig 7.5 Plot of energy levels vs. population For endothermic reaction A → B Assumption: Density of E-levels of B >> density of E-levels of A Bulk of population is species B Therefore: B is dominant species at equilibrium