Thermodynamics

 66) T = 298 K          R = 8.314 J/mol•K

       (a) NaHCO₃(s) NaOH(s) + CO₂(g)

             K_eq = P_CO2

             K_eq = e^-ΔG°/RT

             ΔG°_rxn = ΣΔG_f°(products) - ΣΔG_f°(reactants)

             ΔG°_rxn = [ΔG_f°(NaOH(s)) + ΔG_f°(CO₂(g))] - [ΔG_f°(NaHCO₃(s))]

             ΔG°_rxn = [1 mol NaOH(s) x -379.5 kJ/1 mol NaOH(s) + 1 mol CO₂(g) x -394.4 kJ/1 mol CO₂(g)] - [1 mol NaHCO₃(s) x -851.8 kJ/1 mol NaHCO₃(s)]

             ΔG°_rxn = 77.9 kJ

             -ΔG°/RT = -(77.9 kJ x 10³ J/kJ)/(8.314 J/mol•K x 298 K) = -31.4 kJ

             K_eq = e^-ΔG°/RT = e^-31.4 = 2 x 10^-14

       (b) 2HBr(g) + Cl₂(g) 2HCl(g) + Br₂(g)

            K_eq = P_CO2

             K_eq = e^-ΔG°/RT

             ΔG°_rxn = ΣΔG_f°(products) - ΣΔG_f°(reactants)

             ΔG°_rxn = [2ΔG_f°(HCl(g)) + ΔG_f°(Br₂(g))] - [2ΔG_f°(HBr(g)) + ΔG_f°(Cl₂(g))]

             ΔG°_rxn = [2 mol HCl(g) x -95.27 kJ/1 mol HCl(g) + 1 mol Br₂(g) x 3.14 kJ/1 mol Br₂(g)] - [2 mol HBr(g) x -53.22 kJ/1 mol HBr(g) + 0]

             ΔG°_rxn = -80.96 kJ

             -ΔG°/RT = -(-80.96 kJ x 10³ J/kJ)/(8.314 J/mol•K x 298 K) = 32.7 kJ

             K_eq = e^-ΔG°/RT = e^32.7 = 2 x 10¹⁴

       (c) 2SO₂(g) + O₂(g) 2SO₃(g)

            K_eq = P_CO2

             K_eq = e^-ΔG°/RT

             ΔG°_rxn = ΣΔG_f°(products) - ΣΔG_f°(reactants)

             ΔG°_rxn = [2ΔG_f°(SO₃(g))] - [2ΔG_f°(SO₂(g)) + ΔG_f°(O₂(g))]

             ΔG°_rxn = [2 mol SO₃(g) x -370.4 kJ/1 mol SO₃(g)] - [2 mol SO₂(g) x -300.4 kJ/1 mol SO₂(g) + 0]

             ΔG°_rxn = -140.0 kJ

             -ΔG°/RT = -(-140.0 kJ x 10³ J/kJ)/(8.314 J/mol•K x 298 K) = 56.5 kJ

             K_eq = e^-ΔG°/RT = e^56.5 = 3 x 10²⁴