Consider the following reaction: $\mathrm{H}_{2} \mathrm{O}(g)+\mathrm{Cl}_{2} \mathrm{O}(g) \rightleftharpoons 2 \mathrm{HOCl}(g) \quad K_{298}=0.090$
For $\mathrm{Cl}_{2} \mathrm{O}(g)$,
$\Delta G_{\mathrm{f}}^{\circ}=97.9 \mathrm{~kJ} / \mathrm{mol}$
$\Delta H_{\mathrm{f}}^{\circ}=80.3 \mathrm{~kJ} / \mathrm{mol}$
$S^{\circ}=266.1 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}$
a. Calculate $\Delta G^{\circ}$ for the reaction using the equation $\Delta G^{\circ}=$ $-R T \ln (K)$
b. Use bond energy values (Table 8.4) to estimate $\Delta H^{\circ}$ for the reaction.
c. Use the results from parts a and $b$ to estimate $\Delta S^{\circ}$ for the reaction.
d. Estimate $\Delta H_{\mathrm{f}}^{\circ}$ and $S^{\circ}$ for $\mathrm{HOCl}(g)$.
e. Estimate the value of $K$ at $500 . \mathrm{K}$.
f. Calculate $\Delta G$ at $25^{\circ} \mathrm{C}$ when $P_{\mathrm{H}_{2} \mathrm{O}}=18$ torr, $P_{\mathrm{Cl}_{2} \mathrm{O}}=2.0$ torr, and $P_{\mathrm{HOCl}}=0.10$ torr.