Problem 44 - A Complete Resource Book in Chemistry for JEE Main

Question

Amongst the following hydroxides, the one which has the lowest value of \(\mathrm{K}_{\mathrm{sp}}\) at ordinary temperature (about \(25^{\circ} \mathrm{C}\) ) is (a) \(\mathrm{Mg}(\mathrm{OH})_{2}\) (b) \(\mathrm{Ca}(\mathrm{OH})_{2}\) (c) \(\mathrm{Ba}(\mathrm{OH})_{2}\) (d) \(\mathrm{Be}(\mathrm{OH})_{2}\)

Step-by-Step Solution

Answer

Be(OH)₂ has the lowest K_{sp} and is the least soluble hydroxide at 25°C.

Step 1: Understand Solubility Product Constant ( K_{sp})

The solubility product constant (K_{sp}) is a measure of the solubility of a compound, specifically how much of the solid will dissolve in water. A lower K_{sp} value indicates lower solubility.

Step 2: Examine The K_{sp} Values For Each Hydroxide

Find the known K_{sp} values at ordinary temperature (about 25°C) for each hydroxide: Mg(OH)_{2}, Ca(OH)_{2}, Ba(OH)_{2}, and Be(OH)_{2}. Common reference data includes: - K_{sp} for Mg(OH)_{2}: Approximately 5.61 × 10^{-12} - K_{sp} for Ca(OH)_{2}: Approximately 6.5 × 10^{-6} - K_{sp} for Ba(OH)_{2}: Approximately 1.67 × 10^{-5} - K_{sp} for Be(OH)_{2}: Very low, indicating very low solubility, often considered nearly insoluble.

Step 3: Compare The K_{sp} Values

Compare the K_{sp} values obtained from reference data. It is evident that Be(OH)_{2} has the lowest K_{sp} value among the given hydroxides, indicating it is the least soluble.

Step 4: Conclusion

After comparing the K_{sp} values, the hydroxide with the lowest K_{sp} is Be(OH)_{2}. This means Be(OH)_{2} is the least soluble of the options at 25°C.

Key Concepts

Understanding Ksp Comparison

The solubility product constant, denoted as \(K_{sp}\), is essential in understanding the solubility levels of compounds. It represents a specific equilibrium constant for a solid substance dissolving in a solvent. The formula generally used is the product of the concentrations of its constituent ions, each raised to its coefficient in the balanced equation. A lower \(K_{sp}\) indicates a substance that does not dissolve easily, suggesting very low solubility.

When comparing \(K_{sp}\) values, it's crucial to view them as indicators of just how soluble different substances are. For hydroxides like \(Mg(OH)_2\), \(Ca(OH)_2\), \(Ba(OH)_2\), and \(Be(OH)_2\), the \(K_{sp}\) values vary significantly:

• \(Mg(OH)_2\): \(5.61 \times 10^{-12}\)
• \(Ca(OH)_2\): \(6.5 \times 10^{-6}\)
• \(Ba(OH)_2\): \(1.67 \times 10^{-5}\)
• \(Be(OH)_2\): Extremely low, signifying almost insolubility

These values show how differently each compound dissolves and inform which among them is the least or most soluble.

Hydroxide Solubility Explained

Hydroxide solubility refers to how well hydroxide compounds can dissolve in water. The solubility of a compound is essential in many chemical processes and applications. Various factors affect solubility, such as temperature, pressure, and the nature of the solute and solvent. At a given temperature, often 25°C for standard conditions, comparing the \(K_{sp}\) values provides a clear picture of their solubility.

In our case, we are looking at hydroxides of magnesium, calcium, barium, and beryllium. Each one has a distinct \(K_{sp}\) value, revealing distinct levels of solubility:

• **Magnesium Hydroxide** \(\text{(Mg(OH)}_2\)): With a \(K_{sp}\) of \(5.61 \times 10^{-12}\), it is relatively low, implying it doesn't dissolve easily.
• **Calcium Hydroxide** \(\text{(Ca(OH)}_2\)): A higher \(K_{sp}\) of \(6.5 \times 10^{-6}\) indicates more solubility compared to \(Mg(OH)_2\).
• **Barium Hydroxide** \(\text{(Ba(OH)}_2\)): With \(1.67 \times 10^{-5}\) as its \(K_{sp}\), it is even more soluble than both magnesium and calcium hydroxides.
• **Beryllium Hydroxide** \(\text{(Be(OH)}_2\)): Known to have a very low \(K_{sp}\), suggesting it's almost insoluble.

Each hydroxide's solubility determines its usage and role in different chemical scenarios.

Identifying the Least Soluble Hydroxide

When determining the least soluble among the hydroxides, we must consider their \(K_{sp}\) values at similar conditions, such as at room temperature (25°C). The one with the lowest \(K_{sp}\) will be least soluble, meaning it hardly dissolves in water at all, compared to others.

Among the hydroxides:

• \(Mg(OH)_2\)
• \(Ca(OH)_2\)
• \(Ba(OH)_2\)
• \(Be(OH)_2\)

we find that \(Be(OH)_2\) stands out with an exceptionally low \(K_{sp}\) value. This indicates that it has incredibly low solubility in water. Thus, \(Be(OH)_2\) is identified as the least soluble hydroxide. This knowledge is pivotal in fields such as chemistry and environmental science, where the solubility of compounds can affect everything from product formulation to environmental impacts.