Reactions in which a substance decomposes by losing CO are called decarbonylation reactions. The decarbonylation of acetic acid proceeds according to: $$ \mathrm{CH}_{3} \mathrm{COOH}(l) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CO}(g) $$ By using data from Appendix \(\mathrm{C}\) , calculate the minimum temperature at which this process will be spontaneous under standard conditions. Assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not vary with temperature.

To find the minimum temperature at which the decarbonylation of acetic acid will be spontaneous under standard conditions, first calculate the values of enthalpy change (∆H°) and entropy change (∆S°) for the reaction using the data from Appendix C: \[ \Delta H^{\circ}_{reaction} = \sum \Delta H^{\circ}_{products} - \sum \Delta H^{\circ}_{reactants} \] \[ \Delta S^{\circ}_{reaction} = \sum \Delta S^{\circ}_{products} - \sum \Delta S^{\circ}_{reactants} \] Apply the Gibbs-Helmholtz equation and the condition for spontaneity: \[ \Delta H^{\circ} - T \Delta S^{\circ} < 0 \] Rearrange the inequality to solve for the temperature: \[ T > \frac{\Delta H^{\circ}}{\Delta S^{\circ}} \] Plug in the values for ∆H° and ∆S° and calculate the minimum temperature: \[ T > \frac{(\text{Value of } \Delta H^{\circ})}{(\text{Value of } \Delta S^{\circ})} \]