Using data from Appendix \(\mathrm{C}\), write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free- energy change for these reactions at \(298 \mathrm{~K}:\) (a) $\mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g)$ (b) $2 \mathrm{HBr}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)+\mathrm{Br}_{2}(g)$ (c) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$

(a) For the reaction \(\mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g)\), the equilibrium constant is \(K = 2.49 \times 10^{-3}\), and the free energy change is \(\Delta G = 16.6 \,\mathrm{kJ/mol}\). (b) For the reaction \(2 \mathrm{HBr}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)+\mathrm{Br}_{2}(g)\), the equilibrium constant is \(K = 6.80 \times 10^{26}\), and the free energy change is \(\Delta G = -155.2 \,\mathrm{kJ/mol}\). (c) For the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\), the equilibrium constant is \(K = 1.24 \times 10^{18}\), and the free energy change is \(\Delta G = -140.4 \,\mathrm{kJ/mol}\).