# Trends in Solubility of Group 2 Hydroxides and Sulfates This section explores the solubility trends of Group 2 hydroxides and sulfates, explaining them in terms of hydration enthalpy and lattice energy. ### 5.5 Trends in Solubility of the Group 2 Hydroxides and Sulphate #### (a) Solubility of Hydroxides of Group 2 Elements The solubility of Group 2 hydroxides generally increases as we move down the group. This trend is due to the interplay of lattice energy and hydration enthalpy. The order of solubility for Group 2 hydroxides is: $$\mathrm{Mg(OH)_2} < \mathrm{Ca(OH)_2} < \mathrm{Sr(OH)_2} < \mathrm{Ba(OH)_2}$$ Barium hydroxide ($\mathrm{Ba(OH)_2}$) is notably highly soluble in water. **Table 5.3 Solubilities in water of some Group 2 hydroxides.** | Group 2 hydroxide | Solubility at 298 K (mol/100 g of water) | | :---------------- | :--------------------------------------- | | $\mathrm{Mg(OH)_2}$ | $2 \times 10^{-5}$ | | $\mathrm{Ca(OH)_2}$ | $1.5 \times 10^{-3}$ | | $\mathrm{Sr(OH)_2}$ | $3.4 \times 10^{-3}$ | | $\mathrm{Ba(OH)_2}$ | $1.5 \times 10^{-2}$ | #### (b) Change in Hydration Enthalpy Down the Group **Definition:** Hydration enthalpy refers to the enthalpy change when one mole of gaseous ions dissolves in sufficient water to give an infinitely dilute solution. **Factors:** Hydration enthalpy is directly proportional to the charge on the ion and inversely proportional to the size of the ion. Smaller ions (with the same charge) have greater (more exothermic or negative) enthalpy changes of hydration. **Trend:** As we move down Group 2, the ionic radius of the $\mathrm{M^{2+}}$ cation increases. Consequently, the enthalpy change of hydration decreases (becomes less exothermic) in the order: $$\mathrm{Mg^{2+}} > \mathrm{Ca^{2+}} > \mathrm{Sr^{2+}} > \mathrm{Ba^{2+}}$$ This decrease is relatively small down the group, as it primarily depends on the increasing size of the cation, while the anion ($\mathrm{OH^{-}}$) remains constant. #### (c) Change in Lattice Energy Down the Group **Definition:** Lattice energy is the enthalpy change when one mole of an ionic compound is formed from its gaseous ions. **Factors:** Lattice energy is greater if the ions forming the lattice are small and highly charged. It is inversely proportional to the sum of the radii of the anion and cation. **Trend:** As the size of the $\mathrm{M^{2+}}$ cation increases down Group 2, the lattice energy decreases (becomes less exothermic, or the lattice dissociation enthalpy becomes less endothermic). $$\mathrm{Mg^{2+}} > \mathrm{Ca^{2+}} > \mathrm{Sr^{2+}} > \mathrm{Ba^{2+}}$$ The decrease in lattice energy is relatively large down the group because it is more significantly determined by the increasing size of the large cation ($\mathrm{M^{2+}}$) compared to the smaller hydroxide ion ($\mathrm{OH^{-}}$). #### (d) Difference in Enthalpy Change of Solution of Group 2 Hydroxide The enthalpy change of solution ($\Delta H_{sol}$) is related to the lattice energy ($\Delta H_{LE}$ and hydration enthalpy ($\Delta H_{hyd}$) by the equation: $$\Delta H_{sol} = \Delta H_{LE} + \Delta H_{hyd}$$ (Note: $\Delta H_{LE}$ here is usually represented as the lattice dissociation enthalpy, which is positive, while $\Delta H_{hyd}$ is negative for exothermic hydration). Substances with very high solubility in water are generally associated with a highly negative (exothermic) enthalpy of solution. A more negative value for $\Delta H_{sol}$ typically indicates higher solubility. **Conclusion: Solubility Trend of Group 2 Hydroxides** - **Lattice energy** of the hydroxides decreases by relatively higher values down the group (becomes less exothermic). - **Enthalpy changes of hydration** decrease (become less exothermic) by relatively lower values down the group. - The overall effect is that the **enthalpy of solution ($\Delta H_{sol}$)** gets more exothermic (more negative) down the group. - Therefore, the **solubility of the Group 2 hydroxides increases** down the group. A compound is likely to be soluble in water if its enthalpy of solution is negative or has a small positive value. #### (e) Solubility of Sulfates of Group 2 Elements In contrast to hydroxides, the solubility of Group 2 sulfates decreases as we move down the group. Barium sulfate ($\mathrm{BaSO_4}$) is well-known for its insolubility in water. The order of solubility for Group 2 sulfates is: $$\mathrm{MgSO_4} > \mathrm{CaSO_4} > \mathrm{SrSO_4} > \mathrm{BaSO_4}$$ **Table 5.4 Solubilities in water of some Group 2 sulfates.** | Group 2 Sulphates | Solubility at 298 K (mol/dm³) | | :---------------- | :---------------------------- | | $\mathrm{MgSO_4}$ | 1.83 | | $\mathrm{CaSO_4}$ | $4.66 \times 10^{-2}$ | | $\mathrm{SrSO_4}$ | $7.11 \times 10^{-4}$ | | $\mathrm{BaSO_4}$ | $9.43 \times 10^{-6}$ | **Explanation: Solubility Trend of Group 2 Sulfates** - When moving down the group, both the lattice dissociation enthalpy and hydration enthalpy decrease (become less endothermic/exothermic, respectively). - However, for sulfates, the **hydration enthalpy decreases more significantly** than the lattice dissociation enthalpy (or lattice energy becomes less exothermic at a slower rate than hydration enthalpy becomes less exothermic). This is because the sulfate ion ($\mathrm{SO_4^{2-}}$), being large, means the lattice energy is less sensitive to changes in the cation size compared to hydration enthalpy, which is highly sensitive to cation size. - As a result, the **enthalpy of solution ($\Delta H_{sol}$)** becomes more endothermic (more positive) down the group. - This increase in endothermicity of $\Delta H_{sol}$ leads to the **decrease in solubility** of Group 2 sulfates down the group. ### Significance/Application These solubility trends are important in various chemical applications, such as: - **Qualitative Analysis:** The insolubility of $\mathrm{BaSO_4}$ is used in gravimetric analysis to test for sulfate ions. - **Medical Applications:** Barium meal (a suspension of $\mathrm{BaSO_4}$) is used in X-ray imaging of the digestive system because of its insolubility and thus non-toxicity (despite $\mathrm{Ba^{2+}}$ being toxic). - **Water Treatment:** $\mathrm{Ca(OH)_2}$ (limewater) is used to treat acidic industrial waste.