Enthalpies of solution and hydration — practice questions

Step 1: Identify the components of the Hess's Law cycle. The equation is $\Delta H_{\text{sol}}^{\ominus} = -\Delta H_{\text{latt}}^{\ominus} + \sum \Delta H_{\text{hyd}}^{\ominus}$.

Step 2: Calculate the total enthalpy of hydration. We have one Mg²⁺ ion and two Cl⁻ ions. $\sum \Delta H_{\text{hyd}}^{\ominus} = \Delta H_{\text{hyd}}^{\ominus}(\text{Mg}^{2+}) + 2 \times \Delta H_{\text{hyd}}^{\ominus}(\text{Cl}^{-})$ $\sum \Delta H_{\text{hyd}}^{\ominus} = (-1920) + 2 \times (-364) = -1920 - 728 = -2648 \text{ kJ mol}^{-1}$.

Step 3: Substitute the values into the main equation. Remember to reverse the sign of the lattice enthalpy. $\Delta H_{\text{sol}}^{\ominus}(\text{MgCl}_2) = -(-2526) + (-2648)$ $\Delta H_{\text{sol}}^{\ominus}(\text{MgCl}_2) = +2526 - 2648$

Step 4: Calculate the final answer. $\Delta H_{\text{sol}}^{\ominus}(\text{MgCl}_2) = -152 \text{ kJ mol}^{-1}$.

This exothermic value suggests that magnesium chloride dissolves readily in water, releasing heat.

(a) Calculation of $\Delta H_{\text{sol}}^{\ominus}(\text{AgCl})$

Using the formula: $\Delta H_{\text{sol}}^{\ominus} = -\Delta H_{\text{latt}}^{\ominus} + \sum \Delta H_{\text{hyd}}^{\ominus}$

Substitute the given values: $\Delta H_{\text{sol}}^{\ominus}(\text{AgCl}) = -(-905) + (-851)$ $\Delta H_{\text{sol}}^{\ominus}(\text{AgCl}) = +905 - 851$ $\Delta H_{\text{sol}}^{\ominus}(\text{AgCl}) = +54 \text{ kJ mol}^{-1}$.

(b) Comparison of Solubility

The enthalpy of solution for AgCl is highly endothermic ($+54 \text{ kJ mol}^{-1}$), while for NaCl it is only slightly endothermic ($+3 \text{ kJ mol}^{-1}$). A highly endothermic enthalpy of solution means a large amount of energy is required from the surroundings for the dissolving process to occur. This makes the process energetically unfavourable.

Therefore, the large positive $\Delta H_{\text{sol}}^{\ominus}$ for AgCl explains why it is considered insoluble in water, whereas the small $\Delta H_{\text{sol}}^{\ominus}$ for NaCl allows it to dissolve readily (driven by the favourable entropy change).