What is the solubility of [tex]$MgCO_3$[/tex] in water?

( [tex]\left( K_{sp} \text{ of } MgCO_3 \text{ is } 3.5 \times 10^{-8}\right)[/tex])



Answer :

To determine the solubility of magnesium carbonate ([tex]\( \text{MgCO}_3 \)[/tex]) in water, we will follow these steps:

1. Write the Dissociation Equation:
[tex]\[ \text{MgCO}_3 \rightleftharpoons \text{Mg}^{2+} + \text{CO}_3^{2-} \][/tex]

2. Establish the Solubility Product Expression:
The solubility product constant ([tex]\( K_{sp} \)[/tex]) is given by the expression:
[tex]\[ K_{sp} = [\text{Mg}^{2+}][\text{CO}_3^{2-}] \][/tex]

3. Relate Ion Concentrations to Solubility:
If we let the solubility of [tex]\( \text{MgCO}_3 \)[/tex] be [tex]\( s \)[/tex] moles per liter, then at equilibrium, the concentrations of the ions will be:
[tex]\[ [\text{Mg}^{2+}] = s \quad \text{and} \quad [\text{CO}_3^{2-}] = s \][/tex]
Thus, the solubility product expression becomes:
[tex]\[ K_{sp} = s \cdot s = s^2 \][/tex]

4. Substitute the Given [tex]\( K_{sp} \)[/tex] and Solve for [tex]\( s \)[/tex]:
We are given that [tex]\( K_{sp} = 3.5 \times 10^{-8} \)[/tex]. Therefore, we have:
[tex]\[ 3.5 \times 10^{-8} = s^2 \][/tex]

To find [tex]\( s \)[/tex], take the square root of both sides:
[tex]\[ s = \sqrt{3.5 \times 10^{-8}} \][/tex]

5. Calculate the Solubility:
Using a calculator to find the square root:
[tex]\[ s = 0.00018708286933869707 \][/tex]

6. Final Answer:
The solubility of [tex]\( \text{MgCO}_3 \)[/tex] in water is approximately [tex]\( 0.000187 \)[/tex] moles per liter (or [tex]\( 1.87 \times 10^{-4} \)[/tex] M).