Question #44052

The standard enthalpy of ionization of a weak monoprotic acid \ce{HA} is $\Delta H^\circ_{\text{ion}} = 54.45 \text{ kJ mol}^{-1}$ and is assumed to be independent of temperature. At $298 \text{ K}$, the acid dissociation constant is $K_a = 1.0 \times 10^{-5}$. The ionic product of water at $318 \text{ K}$ is $K_w = 2.5 \times 10^{-14}$. Calculate the pH of a $0.1 \text{ M}$ aqueous solution of the sodium salt \ce{NaA} at $318 \text{ K}$.

(Given: $R = 8.314 \text{ J K}^{-1} \text{ mol}^{-1}$, $2.303 \times R = 19.15 \text{ J K}^{-1} \text{ mol}^{-1}$, $\log 2.5 = 0.4$)