5.5 Solubility Trends of Group 2 Hydroxides and Sulphates

Key Concepts

The solubility of an ionic compound in water depends on the balance between two competing energy terms:

• Lattice Energy ($\Delta H_{latt}$): Energy required to break apart the ionic lattice (endothermic). Larger lattice energy → harder to dissolve.
• Enthalpy of Hydration ($\Delta H_{hyd}$): Energy released when ions are surrounded by water molecules (exothermic). Larger hydration energy → easier to dissolve.

Enthalpy of Solution

$\Delta H_{sol}=-(\Delta H_{latt})+\Delta H_{hyd}(\text{cation})+\Delta H_{hyd}(\text{anion})$

A compound is more soluble when $\Delta H_{sol}$ is negative (exothermic) or only slightly positive.

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Group 2 Hydroxides — Solubility Increases Down the Group

Explanation

The hydroxide ion ($O{H}^{-}$) is small. When the anion is small, the lattice energy is strongly dependent on the cation size — as the cation gets larger down the group, the lattice energy decreases steeply.

The hydration energy of the cation also decreases down the group, but more slowly than the lattice energy.

$\text{Decrease in }\Delta H_{latt}>\text{Decrease in }\Delta H_{hyd}(\text{cation})$

Therefore, $\Delta H_{sol}$ becomes more exothermic (or less endothermic) going down the group → solubility increases.

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Group 2 Sulphates — Solubility Decreases Down the Group

Explanation

The sulphate ion ($S{O}_4^{2-}$) is large. When the anion is large, the lattice energy is relatively insensitive to changes in cation size — the lattice energy decreases only slowly down the group.

However, the hydration energy of the cation still decreases significantly as the cation gets larger.

$\text{Decrease in }\Delta H_{hyd}(\text{cation})>\text{Decrease in }\Delta H_{latt}$

Therefore, $\Delta H_{sol}$ becomes more endothermic going down the group → solubility decreases.

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Summary: Why the Trends Are Opposite

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Enthalpy of Solution — Definition

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Applications

• $BaS{O}_4$ (Barium Meal): Used in X-ray imaging of the digestive tract. Its extreme insolubility means toxic $B{a}^{2+}$ ions are not released into the body. It is also opaque to X-rays.
• $Mg(OH{)}_2$ (Milk of Magnesia): Used as an antacid. Its low solubility means it acts slowly and safely in the stomach.
• $Ca(OH{)}_2$ (Slaked Lime): Used in agriculture to neutralise acidic soils.

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