Chapter 17, Problem 86A

Interpretation Introduction

Interpretation:

The compound precipitating first in the given scenario needs to be determined.

Concept introduction:

Le Chatelier principle states that a system at equilibrium when subjected to changes in the system adjusts it self to attain the equilibrium state again.

Answer to Problem 86A

Magnesium fluoride will precipitate first due to its lower K_sp.

Explanation of Solution

Solubility of magnesium fluoride:

$Mg{F}_2\to M{g}^{2+}+2F^{-}$

$K_{sp}=[M{g}^{2+}]{[F^{-}]}^2$

$K_{sp}=\frac{so\mathrm{lub}ility}{molarmass}$

$\begin{array}{l}{K}_{sp}=\frac{0.13}{62.30}\\ K_{sp}=0.00208\end{array}$

Solubility of barium fluoride,

$Ba{F}_2\to B{a}^{2+}+2F^{-}$

$K_{sp}=[B{a}^{2+}]{[F^{-}]}^2$

$\begin{array}{l}{K}_{sp}=\frac{so\mathrm{lub}ility}{molarmass}\\ K_{sp}=\frac{1.1}{175.33}\\ K_{sp}=0.00627\end{array}$

This shows that barium fluoride is more soluble and on addition of sodium fluoride MgF₂ will precipitate first.

Conclusion

MgF₂ will precipitate earlier than BaF₂ due to its lower solubility product.