Question

what is the solubility of mgco₃ in water? (ksp of mgco₃ is 3.5 × 10⁻⁸)

Explanation:

Step1: Write the dissolution equation

$$\ce{MgCO3(s) <=> Mg^{2+}(aq) + CO3^{2-}(aq)}$$
Let the solubility of $\ce{MgCO3}$ be $s$. Then $[\ce{Mg^{2+}}]=s$ and $[\ce{CO3^{2-}}]=s$.

Step2: Write the solubility - product expression

$$K_{sp}=[\ce{Mg^{2+}}][\ce{CO3^{2-}}]$$
Substitute $[\ce{Mg^{2+}}]=s$ and $[\ce{CO3^{2-}}]=s$ into the $K_{sp}$ expression:
$$K_{sp}=s\times s=s^{2}$$

Step3: Solve for $s$

Given $K_{sp} = 3.5\times10^{-8}$, then $s^{2}=3.5\times10^{-8}$.
Take the square root of both sides:
$$s=\sqrt{3.5\times 10^{-8}}$$
$$s = 1.87\times10^{-4}\space mol/L$$

Answer:

The solubility of $\ce{MgCO3}$ in water is $1.87\times 10^{-4}\space mol/L$.