Question

use the references to access important values if needed for this question.
the solubility product constant for chromium(iii) phosphate is 2.4×10 - 23.
if chromium(iii) phosphate is dissolved in water you can say that the equilibrium concentrations of chromium(iii) and phosphate
ions are:
a. high
b. moderate
c. low
the solubility of chromium(iii) phosphate in water is:
a. high
b. moderate
c. low

Explanation:

First Sub - Question (Equilibrium Concentrations of Ions)

Step 1: Recall \(K_{sp}\) and Solubility Relationship

The solubility product constant (\(K_{sp}\)) for a compound \(A_xB_y\) is given by \(K_{sp}=[A^{y +}]^x[B^{x -}]^y\). A very small \(K_{sp}\) value (like \(2.4\times10^{-23}\) for chromium(III) phosphate, \(\ce{CrPO_4}\) or \(\ce{Cr(PO_4)_x}\) depending on formula, but generally for sparingly soluble salts) implies that the concentrations of the ions in equilibrium with the solid are very low.

Step 2: Relate \(K_{sp}\) to Ion Concentrations

Since \(K_{sp}=2.4\times10^{-23}\), which is a very small number (much less than 1), when the salt dissolves \(\ce{Cr^{3+}}\) and \(\ce{PO_4^{3 -}}\) (or relevant phosphate ion) concentrations will be low because the product of their concentrations (raised to appropriate powers) is very small. So the equilibrium concentrations of chromium(III) and phosphate ions are low.

Step 1: Recall \(K_{sp}\) and Solubility

The solubility of a salt is related to its \(K_{sp}\). A low \(K_{sp}\) value ( \(2.4\times10^{-23}\) is very small) means that very little of the salt dissolves in water to form ions. Salts with very small \(K_{sp}\) values are considered to have low solubility.

Step 2: Determine Solubility Category

Since the \(K_{sp}\) is \(2.4\times10^{-23}\), the amount of chromium(III) phosphate that dissolves in water is very small, so its solubility is low.

Answer:

C. Low

Second Sub - Question (Solubility of Chromium(III) Phosphate in Water)