Thermodynamics: Practice Questions

For a chemical reaction to be feasible (spontaneous) at all temperatures, what must be the signs of the enthalpy change (\( \Delta H \)) and the entropy change (\( \Delta S \))?

Calculate the enthalpy of solution for sodium chloride given the following data:
Lattice enthalpy of formation for \( \text{NaCl(s)} = -787 \text{ kJ mol}^{-1} \)
Enthalpy of hydration for \( \text{Na}^+(g) = -406 \text{ kJ mol}^{-1} \)
Enthalpy of hydration for \( \text{Cl}^-(g) = -364 \text{ kJ mol}^{-1} \)

Calculate the lattice enthalpy of formation for magnesium oxide (\( \text{MgO} \)) using the following Born-Haber cycle data (all in \( \text{kJ mol}^{-1} \)):
Enthalpy of formation of \( \text{MgO(s)} = -602 \)
Enthalpy of atomisation of \( \text{Mg(s)} = +148 \)
First ionisation energy of \( \text{Mg(g)} = +738 \)
Second ionisation energy of \( \text{Mg(g)} = +1451 \)
Enthalpy of atomisation of \( \text{O}_2(g) = +249 \)
First electron affinity of \( \text{O(g)} = -141 \)
Second electron affinity of \( \text{O(g)} = +798 \)

A reaction has an enthalpy change (\( \Delta H \)) of \( +45 \text{ kJ mol}^{-1} \) and an entropy change (\( \Delta S \)) of \( +120 \text{ J K}^{-1} \text{ mol}^{-1} \). What is the minimum temperature required for this reaction to become feasible?

The experimental lattice enthalpy of silver iodide (\( \text{AgI} \)) is found to be significantly more exothermic than the value calculated using the perfect ionic model. Which statement best explains this observation?

Calculate the standard entropy change (\(\Delta S^\theta\)) for a reaction that becomes feasible at temperatures above \(500\) K, given \(\Delta H^\theta = +60\) kJ mol\(^{-1}\).

Explain why the lattice formation enthalpy of magnesium oxide (\(MgO\)) is significantly more exothermic than that of sodium chloride (\(NaCl\)).

Calculate the minimum temperature at which the decomposition of magnesium carbonate becomes feasible.
\(\text{MgCO}_3(s) \rightarrow \text{MgO}(s) + \text{CO}_2(g)\)
Use the following standard thermodynamic data:
\(\Delta H_f^\circ\): \(\text{MgCO}_3(s) = -1096 \text{ kJ mol}^{-1}\); \(\text{MgO}(s) = -602 \text{ kJ mol}^{-1}\); \(\text{CO}_2(g) = -394 \text{ kJ mol}^{-1}\).
\(S^\circ\): \(\text{MgCO}_3(s) = 65.9 \text{ J K}^{-1} \text{ mol}^{-1}\); \(\text{MgO}(s) = 26.9 \text{ J K}^{-1} \text{ mol}^{-1}\); \(\text{CO}_2(g) = 213.6 \text{ J K}^{-1} \text{ mol}^{-1}\).