Problem 16 - 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) \(\mathrm{Be}(\mathrm{OH})_{2}\)

Step-by-Step Solution

Answer

\(\mathrm{Be(OH)}_2\) has the lowest \(K_{sp}\).

Step 1: Understanding Solubility Product (\(K_{sp}\))

The solubility product constant, \(K_{sp}\), indicates how soluble a compound is in water. A lower \(K_{sp}\) value means the compound is less soluble.

Step 2: Evaluating Given Compounds

We need to consider \(K_{sp}\) values of the hydroxides: \(\text{Mg(OH)}_2\), \(\text{Ca(OH)}_2\), \(\text{Ba(OH)}_2\), and \(\text{Be(OH)}_2\). Typically, as we go down a group in the periodic table, solubility tends to increase, indicating higher \(K_{sp}\) values.

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

While \(K_{sp}\) values for individual compounds may not be directly given in the problem, chemical data indicate that \(\text{Be(OH)}_2\) is less soluble due to its low solubility in solution, resulting in the smallest \(K_{sp}\) value among the listed compounds.

Step 4: Concluding the Compound with Lowest \(K_{sp}\)

Based on comparative \(K_{sp}\) values and periodic trends, \(\text{Be(OH)}_2\) has the lowest \(K_{sp}\) value among the given options, as beryllium compounds tend to be less soluble compared to those of calcium, magnesium, and barium.

Key Concepts

Solubility Trends in Hydroxides

When discussing the solubility trends of hydroxides, one can investigate the behavior of alkaline earth metals, such as the ones in this exercise: magnesium (Mg), calcium (Ca), barium (Ba), and beryllium (Be). Hydroxides of these metals show a specific pattern of solubility as we move down the periodic table.
Hydroxides generally become more soluble as we move from the top of a group to the bottom. This means that beryllium hydroxide, \( \text{Be(OH)}_2 \), being at the top, is less soluble than magnesium hydroxide, \( \text{Mg(OH)}_2 \), calcium hydroxide, \( \text{Ca(OH)}_2 \), and barium hydroxide, \( \text{Ba(OH)}_2 \). The reason is related to lattice energies and the size of the ions.
- **Higher Lattice Energy:** Beryllium, smaller and with a higher charge density, has stronger lattice forces, making it harder for the hydroxide to dissociate in water.
- **Larger Ions:** As ions increase in size down the group, their lattice energies decrease, making these compounds more soluble in water.
Consequently, \( \text{Be(OH)}_2 \) has the lowest value of \( K_{sp} \) among these hydroxides.

Periodic Table Group Trends

In the periodic table, elements are organized in a way that predicts chemical behavior by their positioning. Group trends involve those properties that change in a predictable manner for elements in the same group as you move down the group.
One such trend observed in alkaline earth metals (Group 2 elements) is their increasing solubility of hydroxides as we descend the group from beryllium to barium. This trend is a critical concept when analyzing chemical behaviors like solubility.
- **Increasing Atomic Size:** As we move down the group, the atomic radius of the elements increases. This increase in size affects properties such as electronegativity and ionization energy.
- **Decreasing Lattice Energy:** Larger atoms form weaker ionic lattices, implying that less energy is required to break the bonds and dissolve the substance in water.
These factors combined lead to more soluble hydroxides and is reflected by the increasing \( K_{sp} \) values from \( \text{Be(OH)}_2 \) to \( \text{Ba(OH)}_2 \). Recognizing periodic trends is essential for predicting the behavior of compounds formed by these elements.

Chemical Solubility Concepts

Understanding chemical solubility is pivotal for grasping how compounds behave in solutions. Solubility is often expressed using the solubility product constant, \( K_{sp} \), which provides insight into the extent to which a compound will dissolve in water.
- **The Role of \( K_{sp} \):** The value of the solubility product gives a direct indication of how much of a particular compound can dissolve in a solution before it reaches saturation. A lower \( K_{sp} \) indicates a compound with lower solubility.
- **Temperature Influence:** \( K_{sp} \) values are temperature-dependent. At higher temperatures, many salts become more soluble, although this can vary with different types of compounds.
- **Comparative Analysis:** By comparing the \( K_{sp} \) values of similar compounds, like the hydroxides in our exercise, it becomes easier to predict solubility behavior.
These solubility concepts not only help deduce the behavior of compounds in solution but are essential for various practical applications in chemistry like extraction and purification processes.