A materials chemist is investigating the widely varying aqueous solubilities of the Group 2 metal sulfates. Thermodynamic data applicable at 25 °C are provided below.
Salt
Ionic radius of M²⁺ (pm)
ΔHₗₐₜₜᵢcₑ (kJ mol⁻¹, + endothermic)
ΔHₕyₑdᵣₐₜᵢₒₙ of M²⁺ (kJ mol⁻¹, – exothermic)
MgSO₄
72
+3000
–1920
CaSO₄
100
+2600
–1575
SrSO₄
118
+2450
–1430
BaSO₄
135
+2300
–1305
Assume the hydration enthalpy of the sulfate ion is –1000 kJ mol⁻¹ for all four salts and that the entropy of dissolution is approximately +10 J mol⁻¹ K⁻¹, temperature-independent.
(a) For each salt, calculate the molar enthalpy of solution, ΔH°₍soln₎, by combining the lattice enthalpy with the hydration enthalpies of both ions.
(b) Using the entropy value given, determine the standard free-energy change, ΔG°₍soln₎, for dissolution of each salt at 298 K.
(c) Rank the four salts by predicted solubility and compare your ranking with the experimentally observed order MgSO₄ > CaSO₄ > SrSO₄ > BaSO₄. Identify any discrepancies.
(d) Propose a quantitative adjustment or an additional energetic consideration that could reconcile your calculated trend with the observed solubility of MgSO₄ being greater than that of CaSO₄, even though MgSO₄ has the more endothermic ΔH°₍soln₎.