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

Question

Amongst the following hydroxides, the one which has the lowest value of \(K_{s p}\) 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) \(\mathrm{Be}(\mathrm{OH})_{2}^{2}\)

Step-by-Step Solution

Answer

\(\mathrm{Be(OH)_{2}}\) has the lowest \(K_{sp}\) value.

Step 1: Understanding Solubility Product

The solubility product constant, denoted as \(K_{sp}\), is a measure of the solubility of a compound. For different hydroxides, the smaller the \(K_{sp}\), the less soluble the hydroxide is in water. A low \(K_{sp}\) value indicates that less of the substance can dissolve in solution, leading to a higher preference for the solid state.

Step 2: Identifying Hydroxides

We are considering four hydroxides: \(\mathrm{Mg(OH)_{2}}\), \(\mathrm{Ca(OH)_{2}}\), \(\mathrm{Ba(OH)_{2}}\), and \(\mathrm{Be(OH)_{2}}\). We need to compare their \(K_{sp}\) values to find the one with the smallest value.

Step 3: Comparing \(K_{sp}\) Values

Generally, \(\mathrm{Mg(OH)_{2}}\) has a \(K_{sp}\) value of approximately \(1.5 \times 10^{-11}\), while \(\mathrm{Ca(OH)_{2}}\) has a \(K_{sp}\) around \(6.5 \times 10^{-6}\). \(\mathrm{Ba(OH)_{2}}\) often has a \(K_{sp}\) around \(5 \times 10^{-3}\), and \(\mathrm{Be(OH)_{2}}\) has a remarkably low \(K_{sp}\) of \(6.92 \times 10^{-11}\).

Step 4: Conclusion

Among these, \(\mathrm{Be(OH)_{2}}\) has the smallest \(K_{sp}\) value, implying it is the least soluble amongst the given hydroxides and has a strong preference to remain in the solid state.

Key Concepts

Ksp values

The solubility product constant, abbreviated as \(K_{sp}\), is a crucial concept in predicting how well a compound can dissolve in water. It is the product of the molar concentrations of the constituent ions in a saturated solution, each raised to the power of their stoichiometric coefficients.

In simple terms, the \(K_{sp}\) value provides insight into the extent to which a compound can dissolve. A higher \(K_{sp}\) value suggests greater solubility, meaning the compound easily dissolves in water.

Conversely, a lower \(K_{sp}\) value indicates poor solubility, so the compound tends to remain in its solid state. This is particularly useful for determining the likelihood of precipitation in a solution.

Solubility of hydroxides

The solubility of hydroxides in water varies significantly based on their chemical composition and the specific ions involved. These hydroxides include compounds like

• \( \mathrm{Mg(OH)_{2}} \)
• \( \mathrm{Ca(OH)_{2}} \)
• \( \mathrm{Ba(OH)_{2}} \)
• \( \mathrm{Be(OH)_{2}} \)

Understanding their solubility is essential for applications ranging from industrial processes to environmental science.

These different hydroxides have distinct \(K_{sp}\) values, which help in predicting their behavior in aqueous environments. For instance,

1. \( \mathrm{Mg(OH)_{2}} \) has a \(K_{sp}\) of about \(1.5 \times 10^{-11}\)
2. \( \mathrm{Ca(OH)_{2}} \) approximately \(6.5 \times 10^{-6}\)
3. \( \mathrm{Ba(OH)_{2}} \) around \(5 \times 10^{-3}\)
4. \( \mathrm{Be(OH)_{2}} \) with the lowest \(K_{sp}\) of \(6.92 \times 10^{-11}\)

This indicates that \( \mathrm{Be(OH)_{2}} \) is the least soluble under ordinary conditions.

Chemical solubility concepts

Chemical solubility is a fundamental concept in chemistry, determining how substances interact with solvents. When discussing solubility, two main concepts come into play:

• The concentration at which a substance dissolves in a solvent until it reaches saturation.
• The balance between the dissolved ions and the solid form of a compound.

Solubility is not only influenced by \(K_{sp}\) but also by factors like temperature, pressure, and the common ion effect, which all contribute to how substances dissolve.

The concept of solubility is essential in various fields, including pharmaceuticals, where it affects drug delivery; environmental science, where it impacts pollutant spread; and industrial chemistry, where it influences product formation and processing.