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Chemical equilibrium
Exercises
7.1 At 2257 K and 1.00 atm total pressure, water is 1.77 per cent dissociated at equilibrium by way of the reaction 2H2O(g) = 2H¬2,(g) + O2,(g). Calculate (a) K, (b) ∆G , and (c) ∆G at this temperature.
K= 2.85 x 10-6; (b) ∆G = +240 kJ.mol-1 (c) ∆G = 0 (the system is at quilibrium).
7.2 Dinitrogen tetroxide is 18.46 per cent dissociated at 25°C and 1.00 bar in the quilibrium N2O4(g) = 2NO2(g). Calculate (a) K at 25°C, (b) ∆G , (c) K at 100°C given that ∆H = +57.2 kJ.mol-1 over the temperature range.
(a) K = 0.1411; (b) ∆G = +4.855 kJ.mol-1 (c) K (l00°C) = 14.556.
7.3 From information in the Data section, calculate the standard Gibbs energy and the equilibrium constant at (a) 298 K and (b) 400K for the reaction PbO(s) + CO(g) = Pb(s) + CO2(g). Assume that the reaction enthalpy is independent of temperature.
(a) ∆G =-68.26 kJ.mol-1, K= 9.2 x l011;
(b) K (400K) = 1.3 x 109, ∆G (400K) = -69.7 kJ.mol-1.
7.4 In the gas-phase reaction 2A + B = 3C + 2D, it was found that, when 1.00 mol A, 2.00 mol B, and 1.00 mol D were mixed and allowed to come to equilibrium at 25°C, the resulting mixture contained 0.90 mol C at a total pressure of 1.00 bar. Calculate (a) the mole fractions of each species at equilibrium, (b) Kx, (c) K, and (d) ∆G .
(a) Mole fractions: A: 0.087, B: 0.370, C: 0.196, D: 0.348, Total: 1.000;
(b) Kx = 0.33; (c) Kp = 0.33; (d) ∆G =+2.8 x 103 Jmol-1.
7.5 The standard reaction enthalpy of Zn(s) + H2O(g) → ZnO(s) + H2(g) is approximately constant at +224 kJ.mol-1 from 920K up to 1280K. The standard reaction Gibbs energy is +33 kJ.mol-1 at 1280K. Estimate the temperature at which the equilibrium constant becomes greater than 1.
T = 1500 K.
7.6 The equilibrium constant of the reaction 2C3H6(g) = C2H4(g) + C4H8(g) is found to fit the expression lnK =A + B/T + C/T2 between 300 K and 600 K, with A = -1.04, B = -1088 K, and C= 1.51 x 105 K2. Calculate the standard reaction enthalpy and standard reaction entropy at 400K.
∆H = +2.77 kJ. mol-1, ∆S = -16.5 J.K-1.mol-1,
7.7 The standard reaction Gibbs energy of the isomerization of borneol (C10H17OH) to isoborneol in the gas phase at 503 K is +9.4 kJ.mol-1. Calculate the reaction Gibbs energy in a mixture consisting of 0.15 mol of borneol and 0.30 mol of isoborneol when the total pressure is 600 Torr.
∆Go =+12.3 kJ.mol-1
7.8 Calculate the percentage change in Kx for the reaction H2CO(g) = CO(g) + H2(g) when the total pressure is increased from 1.0 bar to 2.0 bar at constant temperature.
50 per cent.
7.9 The equilibrium constant for the gas-phase isomerization of borneol (C10H17OH) to isoborneol at 503 K is 0.106. A mixture consisting of 7.50 g of borneol and 14.0 g of isoborneol in a container of volume 5.0 dm3 is heated to 503 K and allowed to come to equilibrium. Calculate the mole fractions of the two substances at equilibrium.
= xB=0.904, x1 =0.096.
7.10 What is the standard enthalpy of a reaction for which the equilibrium constant is (a) doubled, (b) halved when the temperature is increased by 10 K at 298 K?
(a) ∆H = +53 kJ.mol-1; (b) ∆H = -53 kJ.mol-1.
7.11 The standard Gibbs energy of formation of NH3(g) is -16.5 kJ.mol-1 at 298 K. What is the reaction Gibbs energy when the partial pressures of the N2, H2, and NH3 (treated as perfect gases) are 3.0 bar, 1.0 bar, and 4.0 bar, respectively? What is the spontaneous direction of the reaction in this case?
∆G = -14.38 kJ.mol-1, spontaneous direction of reaction is towards products.
7.12 Estimate the temperature at which CaCO3(calcite) decomposes.
T= 1110K.

7.13 For CaF2(s) = Ca2+(aq) + 2F-(aq), K = 3.9x10-11 at 25°C and the standard Gibbs energy of formation of CaF2(s) is -1167 kJ.mol-1, Calculate the standard Gibbs energy of formation of CaF2(aq).
∆G = -1108 kJ.mol-1.
Equilibrium electrochemistry

Exercises
7.14 Write the cell reaction and electrode half-reactions and calculate the standard emf of each of the following cells:
(a) Zn│ZnSO4(aq)││AgNO3(aq) │Ag
(b) Cd│CdCl2(aq) ││ HNO3(aq) │H2(g) │Pt
(c) Pt│K3[Fe(CN)6](aq),K4[Fe(CN)6] (aq) ││CrCl3(aq) │Cr

7.15 Devise cells in which the following are the reactions and calculate the standard emf in each case:
(a) Zn(s) + CuSO4(aq) → ZnSO4(aq) + Cu(s)
(b) 2AgCl(s) + H2(g) → 2HCl(aq) + 2Ag(s)
(c) 2H2(g) + O2(g) → 2H2O(l)
7.16 Use the Debye-Huckel limiting law and the Nernst equation to estimate the potential of the cell
Ag│AgBr(s)│KBr(aq, 0.050 mol kg-1) ││Cd(NO3)2(aq, 0.010 mol kg-1) │Cd
at 25°C.
E=-0.62V.
7.17 Calculate the equilibrium constants of the following reactions at 25°C from standard potential data:
(a) Sn(s) + Sn4+(aq) → 2Sn2+(aq)
(b) Sn(s) + 2 AgCl(s) → SnCl2(aq) + 2Ag(s)
(a)K = 6.5x 109; (b) K = 1.5 x 1012.
7.18 The emf of the cell Ag│AgI(s) │AgI(aq) │Ag is +0.9509V at 25°C. Calculate (a) the solubility product of AgI and (b) its solubility.
(a) 9.2 x 10-9 M, (b) 8.5 x 10-17 M.


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