Question

what is the solubility of la(io₃)₃ in a solution that contains 0.300 m io₃⁻ ions? (ksp of la(io₃)₃ is 7.5 × 10⁻¹²)

Explanation:

Step1: Write the dissolution equation

$$\text{La(IO}_3\text{)}_3(s) ightleftharpoons\text{La}^{3 +}(aq)+3\text{IO}_3^-(aq)$$

Let the solubility of $\text{La(IO}_3\text{)}_3$ be $s$. Then $[\text{La}^{3 +}]=s$ and $[\text{IO}_3^-]=3s + 0.300$. Since $s$ is very small (common - ion effect), $3s\ll0.300$, so $[\text{IO}_3^-]\approx0.300\ M$.

Step2: Write the $K_{sp}$ expression

$$K_{sp}=[\text{La}^{3 +}][\text{IO}_3^-]^3$$
Substitute $K_{sp}=7.5\times 10^{-12}$, $[\text{La}^{3 +}]=s$ and $[\text{IO}_3^-]=0.300$ into the $K_{sp}$ expression:
$$7.5\times 10^{-12}=s\times(0.300)^3$$

Step3: Solve for $s$

$$s=\frac{7.5\times 10^{-12}}{(0.300)^3}$$
$$s=\frac{7.5\times 10^{-12}}{0.027}$$
$$s = 2.78\times 10^{-10}\ M$$

Answer:

The solubility of $\text{La(IO}_3\text{)}_3$ is $2.78\times 10^{-10}\ M$.