Three sparingly soluble salts have same solubility products are given below:

• I. A₂X
• II. AX
• III. Aₓ₃

Their solubility in a standard solution will be such that:

• A: III > II > I
• B: III > I > II
• C: II > III > I
• D: II > I > III

To determine the solubility of the three salts A₂X, AX, and Aₓ₃, we need to analyze their dissociation in water and how their solubility products (Ksp) relate to their solubility.

Understanding the Salts

Each salt dissociates into ions in solution:

• A₂X: Dissociates into 2A⁺ and X^2-
• AX: Dissociates into A⁺ and X^2-
• Aₓ₃: Dissociates into A³⁺ and 3X^2-

Calculating Solubility

The solubility product (Ksp) is related to the concentration of the ions in solution:

• For A₂X: Ksp = [A⁺]² * [X^2-]
• For AX: Ksp = [A⁺] * [X^2-]
• For Aₓ₃: Ksp = [A³⁺] * [X^2-]³

Comparing Solubility

Since all salts have the same Ksp, we can compare their solubility:

• A₂X produces more A⁺ ions, leading to lower solubility.
• AX has a moderate solubility.
• Aₓ₃ produces fewer A⁺ ions due to its higher charge, resulting in higher solubility.

Final Ranking

Based on this analysis, the order of solubility from highest to lowest is:

Aₓ₃ > AX > A₂X

Thus, the correct answer is:

A: III > II > I