(a) Predict and explain the variation in enthalpy change of hydration for the ions \(Na^+\), \(Mg^{2+}\) and \(Al^{3+}\).
(b) Fig. 2.1 shows an incomplete energy cycle.
(i) Complete line C on Fig. 2.1. Include state symbols.
(ii) Use both words and symbols to identify change 2 on Fig. 2.1. Use changes 1 and 3 as examples of how this should be done.
(iii) Calculate a value for the lattice energy of magnesium chloride, \(\Delta H_{latt}\) MgCl₂(s), by selecting and using appropriate data from Table 2.1.
(c) Define entropy.
(d) At 25°C the enthalpy change of solution of compound Z is +26 kJ mol⁻¹. The entropy change of solution of Z at the same temperature is \(+52JK^{–1}mol^{–1}\). Calculate the value of the Gibbs free energy change, ΔG, for the solution of Z at 25°C.
(e) (i) Use your answer to (d) to predict whether or not Z is soluble in water at 25°C. Explain your answer.
(ii) Predict whether Z becomes more or less soluble as the water is heated from 25°C to 95°C. Explain your answer.
▶️ Answer/Explanation
(a) \(\Delta H_{hyd}\) becomes more negative from \(Na^+\) to \(Al^{3+}\) due to increasing charge density. Higher charge (\(Al^{3+} > Mg^{2+} > Na^+\)) and smaller ionic radius enhance attraction to water molecules, releasing more energy.
(b)(i) \(Mg^{2+} (aq) + 2Cl^–(aq)\)
Explanation: Line C represents the hydrated ions in solution, so state symbols \((aq)\) are included.
(b)(ii) Enthalpy change of hydration of magnesium ions and chloride ions
\(\Delta H_{hyd} Mg^{2+} + 2\Delta H_{hyd}Cl^–\)
Explanation: Change 2 corresponds to the hydration of gaseous ions into aqueous ions, analogous to changes 1 and 3.
(b)(iii) \(-2493 \text{ kJ mol}^{-1}\)
Explanation: Using Hess’s Law: \(\Delta H_{latt} = \Delta H_{f} – \Delta H_{hyd} – \Delta H_{at}\). Substituting values: \(-155 – (-1920) – 2(364) = -2493 \text{ kJ mol}^{-1}\).
(c) Entropy is a measure of the number of ways energy and particles can be distributed in a system, reflecting disorder or randomness.
(d) \(\Delta G = +10.5 \text{ kJ mol}^{-1}\)
Explanation: Using \(\Delta G = \Delta H – T\Delta S\), with \(T = 298 \text{ K}\):
\(\Delta G = 26 – (298 \times 0.052) = +10.5 \text{ kJ mol}^{-1}\).
(e)(i) No, Z is not soluble at 25°C because \(\Delta G > 0\).
Explanation: A positive \(\Delta G\) indicates the process is non-spontaneous.
(e)(ii) Z becomes more soluble as temperature increases.
Explanation: Since \(\Delta S > 0\), increasing \(T\) makes \(\Delta G\) more negative (or less positive), favoring solubility.