Problem 51 - A Complete Resource Book in Chemistry for JEE Main

Question

Which among the following is the least soluble? (a) \(\mathrm{MnS}\left(\mathrm{K}_{\mathrm{sp}}=7 \times 10^{-16}\right)\) (b) \(\mathrm{FeS}\left(\mathrm{K}_{\mathrm{sp}}=4 \times 10^{-19}\right)\) (c) \(\mathrm{PtS}\left(\mathrm{K}_{\mathrm{sp}}^{\mathrm{m}}=8 \times 10^{-73}\right)\) (d) \(\mathrm{NiS}\left(\mathrm{K}_{\mathrm{sp}}^{3}=3 \times 10^{-12}\right)\)

Step-by-Step Solution

Answer

\( \mathrm{PtS} \) is the least soluble compound because it has the smallest \( K_{sp} \) value of \( 8 \times 10^{-73} \).

Step 1: Understand Solubility Product Constant

The solubility product constant, denoted as \( K_{sp} \), is a measure of the solubility of a compound. The smaller the \( K_{sp} \), the less soluble the compound is in water. Therefore, we need to identify which compound has the smallest \( K_{sp} \) value.

Step 2: Compare \( K_{sp} \) Values

List the given \( K_{sp} \) values for each compound: - \( \mathrm{MnS}, K_{sp} = 7 \times 10^{-16} \) - \( \mathrm{FeS}, K_{sp} = 4 \times 10^{-19} \) - \( \mathrm{PtS}, K_{sp} = 8 \times 10^{-73} \) - \( \mathrm{NiS}, K_{sp} = 3 \times 10^{-12} \). Identify the smallest \( K_{sp} \) value from these compounds.

Step 3: Select the Least Soluble Compound

After comparing the \( K_{sp} \) values:- \( \mathrm{PtS} \) has the smallest \( K_{sp} = 8 \times 10^{-73} \), indicating it is the least soluble among the given options.

Key Concepts

Ksp value comparison

When determining the solubility of a compound, the solubility product constant, or \( K_{sp} \), plays a crucial role. It measures a compound's ability to dissolve in a solution. You could think of \( K_{sp} \) as a numerical representation of solubility.
The process of comparing \( K_{sp} \) values involves looking at numbers. The smaller the \( K_{sp} \), the less soluble the compound is. This means that compounds with lower \( K_{sp} \) values dissolve less in water. To compare, you organize the \( K_{sp} \) values from least to greatest.
Here's a quick checklist for comparison:

• List out each compound's \( K_{sp} \).
• Identify the smallest \( K_{sp} \) value.
• Recognize that the smallest value indicates the least solubility.

Understanding \( K_{sp} \) values helps us efficiently determine solubility ranks among multiple compounds.

Least soluble compound

Finding the least soluble compound among a group requires focusing on their respective \( K_{sp} \) values. "Least soluble" means the compound hardly dissolves in water.
In our example list, consider the \( K_{sp} \) value of each compound given:

• \( \mathrm{MnS}, K_{sp} = 7 \times 10^{-16} \)
• \( \mathrm{FeS}, K_{sp} = 4 \times 10^{-19} \)
• \( \mathrm{PtS}, K_{sp} = 8 \times 10^{-73} \)
• \( \mathrm{NiS}, K_{sp} = 3 \times 10^{-12} \)

The compound \( \mathrm{PtS} \) stands out with its incredibly small \( K_{sp} \) of \( 8 \times 10^{-73} \). This minute number shows it hardly dissolves in water, making it the least soluble among the choices. Identifying such compounds relies heavily on reading and understanding the magnitude of \( K_{sp} \) values.

Solubility measurement

Solubility measurement explains how much of a compound can dissolve in a given solvent until it reaches a saturation point. In basic terms, it's like asking "How much sugar can I stir into my tea before it can't dissolve anymore?"
The measurement is based on the amount of dissolved substance at equilibrium. To connect this with \( K_{sp} \), consider it as controlling the outcome: a lower \( K_{sp} \) results in a lower power of solubility meaningless of the compound can dissolve. The relationship between solution concentration and \( K_{sp} \) is direct and mathematical.
To understand solubility measurement, keep these in mind:

• It is determined at equilibrium.
• Low \( K_{sp} \) means less soluble.
• Always relates to specific concentration and conditions.

These concepts help encapsulate the foundation of how compounds behave in solutions, making it easier for one to analyze and interpret solubility data.