Zumdahl’s Chapter 13

1. Zumdahl’s Chapter 13 Chemical Equilibrium

2. Equilibrium’s Hallmarks The Equilibrium Constant, KC Expressions for Pressure Equilibria, KP Heterogeneous Equilibria Applications Reaction Quotient, Q Extent of Reaction,  Finding Equilibrium Extreme Equilibria Le Châtlier’s Principle Varying concentration Varying pressure Varying temperature Chapter Contents

3. Equilibrium’s Hallmarks • When bulk concentrations of all species no longer change with time. [species]eq = fixed • But reaction and unreaction still proceed (at equal rates), equilibrium is dynamic not static. • Same arrival point whether the initial conditions are reactants or products! • Rateforward = Ratereverse for A+B  C+D • I.e., kf [A]eq [B]eq = kr [C]eq [D]eq from kinetics

4. The Equilibrium Constant • aA + bB  cC + dD for this elementary reaction at equilibrium, Ratef = Rater is • kf [A]eqa [B]eqb = kr [C]eqc [D]eqd & becomes • K = kf / kr = [C]eqc [D]eqd / [A]eqa [B]eqb • Scaling reaction by factor ±n scales all exponents and thus Knew = Kold±n • Negative exponents denote reversed reactions. • This Law of Mass Action holds whether the reaction is elementary or not!

5. Pressure Equilibria Expressions • If aA + bB  cC + dD involves gases, instead of KC we have KP where • KP = ( PCc PDd ) / ( PAa PBb ) with partial pressures in place of concentrations. • Of course [A] = nA / V = PA / RT by ideal gas law so PAa = [A]a (RT)a or KP = KC (RT)n = c+d–(a+b) • Although it appears as if both KC and KP have dimensions (if n0), neither do!

6. Heterogeneous Equilibrium • Greek: heteros- “other” and –genos “kind” • Chemistry: more than one physical phase. • While gases appear as partial pressures and solutes appear as concentrations, pure liquids and solids vanish from K. • Because densities of solutes and gases vary but those of pure condensed phases do not! • Same reasoning eliminates [ H2O ] (fixed at 55.5 M)

7. Reaction Quotient, Q • While KC uses concentration at equilibrium exclusively, we can construct another mass action expression away from equilibrium. • Q = [C]c [D]d/ [A]a [B]b (arbitrary concentrations) • Is Q = K ? We’re at equilibrium! Rejoice? • Is Q < K ? Rxn. runs forward to equilibrium. • Is Q > K ? Rxn. runs backward to equilibrium.

8. Extent of Reaction,  • As reaction proceeds,  varies from 0 to 1. • But common practice dictates a simpler x indicating a change in [A] or PA. Each such change must obey reaction stoichiometry. • Example: 2 NOCl(g)  2 NO(g) + Cl2(g) from an intial PNOCl = 0.5 atm gives, at equilibrium: • KP = P(NO)2 P(Cl2) / P(NOCl)2 • KP = (x)2 (½ x) / ( 0.5 – x )2 = 1.610–5 at 35ºC

9. Finding Equilibrium • Solve the extent of reaction expression that renders Q = K. Try 2 NOCl  2 NO + Cl2 • For (x)2 (½ x) / ( 0.5 – x )2 = 1.610–5 find x • ½ x3 = 1.610–5 (0.5 – x)2 is a (painful) cubic • While cubics are solvable, we hope the small K will yield a small enoughx so 0.5 – x  0.5, whereupon • ½ x3  410–6 or x3  810–6 or x  0.02 Is it OK? • Test: (0.02)2 (½ 0.02) / (0.50 – 0.02)2 = 1.710–5 K • OK! Equil. Pressures are 0.48, 0.02, and 0.01 atm

10. Extreme Equilibria • For very small K, equilibrium lies virtually with the reactants with negligible products • As it was with the NOCl decomposition. • For very large K, equilibrium lies virtually with the products with negligible reactants. • Start with products, and move back by x. • At either extreme, x can be presumed tiny, and equilibrium algebra simplifies.

11. Le Châtlier’s Principle • “Equilibrium shifts to minimize its perturbation.” • In other words, if you impose a change, you render QK, and the equilibrium shifts to restore Q=K. • E.g., removing a product drives rxn forward • And increasing pressure drives rxn to the side with fewer gaseous molecules, relieving Ptotal. • Heating an exothermic rxn drives it backwards!