Chapter 17, Problem 5STP

Interpretation Introduction

Interpretation:

The solubility of magnesium carbonate is to be calculated.

Concept introduction

Solubility is the concentration of the solute dissolved in a given solvent . The equilibrium constant is the ratio of concentration of the products to the concentration of reactants.

${\text{K}}_{\text{sp}}\text{= }{\left[{\text{Mg}}^{\text{+2}}\right]}^{}\left[{\text{CO}}_{\text{3}}{}^{\text{2-}}\right]\begin{array}{l}\hfill \end{array}$

${\left[{\text{Mg}}^{\text{+2}}\right]}^{}\left[{\text{CO}}_{\text{3}}{}^{\text{2-}}\right]$ = concentration of the reactants

Answer to Problem 5STP

The solubility product is $\text{ 2}{\text{.24×10}}^{\text{-11}}$. So, the option A is correct.

Explanation of Solution

Given information :

Initial concentration of magnesium ion $\text{= 0}\text{.0000 M}$

Initial concentration of carbonate ion $\text{= 0}\text{.00400 M}$

Equilibrium concentration of magnesium and carbonate ion is $\text{5}{\text{.60×10}}^{\text{-9}}$ and $\text{4}{\text{.00×10}}^{\text{-3}}$ respectively.

Solubility is the concentration of solute which dissolved in a given solvent. So, the given reaction is

${\text{MgCO}}_{\text{3}}{}_{}\underset{}{\rightleftharpoons }{\text{Mg}}^{\text{2+}}{\text{+CO}}_{\text{3}}{}^{\text{2-}}$

I $\text{= 0}\text{.0000 0}\text{.00400 }$ (initial concentration)

C $\text{= +x +x }$ (change in concentration or change in amount from initial state to equilibrium)

E $\text{= 5}{\text{.60×10}}^{\text{-9}}\text{ 4}{\text{.00×10}}^{\text{-3}}$ (equilibrium concentration)

The solubility product is given as

$\text{KSP = }\left[{\text{mg}}^{\text{2+}}\right]\text{ × }\left[{\text{CO}}_{\text{3}}{}^{\text{2-}}\right]$

$\begin{array}{l}\text{= ( 5}{\text{.60×10}}^{\text{-9)}}\text{ × ( 4}{\text{.00×10}}^{\text{-3)}}\hfill \\ \text{ = 2}{\text{.24 ×10}}^{\text{-11}}\hfill \end{array}$

Conclusion

The solubility product of magnesium carbonate is $\text{2}{\text{.24 ×10}}^{\text{-11}}$. All options are incorrect because in these options solubility product is different.