Question

What is the correct representation of solubility product of \[{\text{A}}{{\text{g}}_{\text{2}}}{\text{Cr}}{{\text{O}}_{\text{4}}}\]
A. \[{\left[ {{\text{A}}{{\text{g}}^ + }} \right]^2}\left[ {{\text{CrO}}_4^{2 - }} \right]\]
B. \[\left[ {{\text{A}}{{\text{g}}^ + }} \right]\left[ {{\text{CrO}}_4^{2 - }} \right]\]
C. \[\left[ {{\text{2A}}{{\text{g}}^ + }} \right]\left[ {{\text{CrO}}_4^{2 - }} \right]\]
D. \[{\left[ {{\text{2A}}{{\text{g}}^ + }} \right]^2}\left[ {{\text{CrO}}_4^{2 - }} \right]\]

Answer 1

Hint:The solubility product constant expression, is an equilibrium constant expression for the dissociation of the sparingly soluble salt in aqueous medium. In the solubility product constant expression, the concentration terms are raised to appropriate stoichiometric coefficients.

Complete step by step solution:
The chemical formula \[{\text{A}}{{\text{g}}_{\text{2}}}{\text{Cr}}{{\text{O}}_{\text{4}}}\] represents the compound silver chromate. It is silver salt of chromic acid. The chemical formula of chromic acid is \[{{\text{H}}_{\text{2}}}{\text{Cr}}{{\text{O}}_{\text{4}}}\] .
In aqueous medium, one molecule of silver chromate dissociates to produce two silver cations and one chromate anion. Write a balanced chemical equation for the dissociation of silver chromate in water.
\[{\text{A}}{{\text{g}}_{\text{2}}}{\text{Cr}}{{\text{O}}_{\text{4}}} \rightleftharpoons 2{\text{A}}{{\text{g}}^ + }{\text{ + CrO}}_4^{2 - }\]
Write the equilibrium constant expression for the above dissociation reaction. The equilibrium constant for the dissociation of sparingly soluble salts is known as solubility product constant. You can write the symbol \[{K_{sp}}\] to denote the solubility product constant.
\[{K_{sp}} = {\left[ {{\text{A}}{{\text{g}}^ + }} \right]^2}\left[ {{\text{CrO}}_4^{2 - }} \right]\]
In the equilibrium constant expression (or in the expression for the solubility product constant), the concentration of solids (and pure liquids) is not written. Hence, the concentration of solid silver chromate will not appear in the expression for the solubility product constant.
In the expression for the solubility product constant of silver chromate, the concentration of silver ions is raised to power 2. This is because two silver ions are obtained from the dissociation of one molecule of silver chromate.
In the solubility product constant expression, the concentration terms are raised to appropriate stoichiometric coefficients.
The correct representation of solubility product of \[{\text{A}}{{\text{g}}_{\text{2}}}{\text{Cr}}{{\text{O}}_{\text{4}}}\] is \[{\left[ {{\text{A}}{{\text{g}}^ + }} \right]^2}\left[ {{\text{CrO}}_4^{2 - }} \right]\]

Hence, the correct option is the option A.

Note:
Let s be the molar solubility of silver chromate:
\[
\Rightarrow \left[ {{\text{A}}{{\text{g}}^ + }} \right] = 2s \\
\Rightarrow \left[ {{\text{CrO}}_4^{2 - }} \right] = s
 \]
\[
\Rightarrow {K_{sp}} = {\left[ {{\text{A}}{{\text{g}}^ + }} \right]^2}\left[ {{\text{CrO}}_4^{2 - }} \right] \\
\Rightarrow {K_{sp}} = {\left( {2s} \right)^2} \times s \\
\Rightarrow {K_{sp}} = 4{s^3}
 \]