Trends in Solubility of Group 2 Hydroxides & Sulfates

Enthalpy of Solution ($\Delta H_{soln}$): The overall energy change when one mole of an ionic solid dissolves in water, determined by the balance between lattice enthalpy and hydration enthalpy.

Lattice Enthalpy ($\Delta H_{latt}$): The energy required to break the ionic lattice into gaseous ions. As cation size increases down Group 2, the attraction between ions weakens, and lattice enthalpy decreases.

Hydration Enthalpy ($\Delta H_{hyd}$): The energy released when gaseous ions are surrounded by water molecules. This also decreases down the group as the charge density of the $M^{2+}$ cation decreases.

The Governing Rule: Solubility increases if the lattice enthalpy decreases more rapidly than the hydration enthalpy. Conversely, if hydration enthalpy drops faster than lattice enthalpy, solubility decreases.

Trend Direction: Solubility increases down the group from Magnesium to Barium.

Observations: Magnesium hydroxide, $Mg(OH)_2$, is sparingly soluble and forms a weakly alkaline suspension (pH approx 10). Barium hydroxide, $Ba(OH)_2$, is much more soluble and forms a strongly alkaline solution.

Reasoning: The hydroxide ion ($OH^-$) is relatively small. As the cation size increases down the group, the lattice enthalpy decreases more significantly than the hydration enthalpy, making the dissolution process more energetically favorable.

Trend Direction: Solubility decreases down the group from Magnesium to Barium.

Observations: Magnesium sulfate, $MgSO_4$, is highly soluble. Barium sulfate, $BaSO_4$, is virtually insoluble and forms a thick white precipitate.

Reasoning: The sulfate ion ($SO_4^{2-}$) is very large. Because the anion is so large, the change in cation size has a minimal effect on the lattice enthalpy. However, the hydration enthalpy of the cation decreases significantly as it gets larger, making the overall dissolution less favorable.

The 'Opposite' Rule: Always remember that the trends for hydroxides and sulfates are opposites. If you remember that $BaSO_4$ is an insoluble 'barium meal,' you can deduce that sulfate solubility decreases and hydroxide solubility must therefore increase.

State Symbols: In exam questions regarding precipitates, always include $(s)$ for the insoluble product and $(aq)$ for the reactants to secure full marks.

Alkalinity Connection: Since hydroxide solubility increases down the group, the resulting solutions become more alkaline (higher pH) as you move from Magnesium to Barium.