Question #44225

One mole of liquid \ce{X2} at $500\text{ K}$ and $1\text{ atm}$ is placed in an insulated, constant-pressure chamber. A catalyst is introduced, triggering the endothermic decomposition and phase change: $\ce{X2(l) -> 2X(g)}$ The reaction proceeds via a highly reactive steady-state intermediate \ce{X^*(g)}, ensuring the process is strictly irreversible. The reaction goes to completion. Given the following thermodynamic parameters at $500\text{ K}$: $\Delta H^\circ_{\text{rxn}} = 10.0\text{ kJ mol}^{-1}$ $S^\circ_{m}(\ce{X2}, l) = 100\text{ J K}^{-1}\text{mol}^{-1}$ $S^\circ_{m}(\ce{X}, g) = 100\text{ J K}^{-1}\text{mol}^{-1}$ $C_{p,m}(\ce{X}, g) = 25\text{ J K}^{-1}\text{mol}^{-1}$ (assumed independent of temperature) Assume the heat capacity of the chamber is negligible. What is the total entropy change of the universe ($\Delta S_{\text{univ}}$) for this process? (Take $\ln(0.6) = -0.51$)