Phosphorus pentachloride splits on heating: PCl₅(g) → PCl₃(g) + Cl₂(g)…

(a) Enthalpy. $\Delta H^\circ = -287.0 + 0 - (-374.9) = +87.9\ \text{kJ mol}^{-1}$.

(b) Entropy. $\Delta S^\circ = 311.8 + 223.1 - 364.6 = +170.3\ \text{J K}^{-1}\ \text{mol}^{-1}$: one mole of gas becomes two.

(c) Gibbs energy at 298 K. $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ = 87.9 - 298 \times \dfrac{170.3}{1000} = 87.9 - 50.75 = +37.2\ \text{kJ mol}^{-1}$.

(d) K at 298 K. $\log K = -\dfrac{\Delta G^\circ}{2.303RT} = -\dfrac{37.2 \times 1000}{2.303 \times 8.314 \times 298} = -6.511$, so $K = 3.1 \times 10^{-7}$. Very little $\text{PCl}_5$ splits at room temperature.

(e) The changeover. $\Delta G^\circ = 0$ at $T = \dfrac{87.9 \times 1000}{170.3}\ \text{K} = 516\ \text{K}$. Above it, $T\Delta S^\circ$ wins and $K > 1$.

(f) K at 600 K. $\Delta G^\circ = 87.9 - 102.18 = -14.28\ \text{kJ mol}^{-1}$, so $\log K = 1.243$ and $K = 17.5$.