Chapter 17, Problem 6STP

Interpretation Introduction

Interpretation: The value of $K_{sp}$ for $Ca{F}_2$ needs to be determined.

Concept introduction: The solubility product constant ( $K_{sp}$ ) represents equilibrium constant between a solid substance and its constituent ions in a solution.

Answer to Problem 6STP

B is the correct option.

Explanation of Solution

  $Ca{F}_2$ dissociates in aqueous solution as follows,

  $\begin{array}{l}Ca{F}_2(s)\rightleftharpoons C{a}^{2+}\left(aq\right)+2F^{-}\left(aq\right)\\ s\text{ 2}s\\ \text{Where }s=\text{ solubility of }Ca{F}_2.\end{array}$

Expression for $K_{sp}$

  $\text{= }[C{a}^{2+}]{[F^{-}]}^2$ …...(1)

Putting the solubility values in equation (1) we get,

  $\begin{array}{}$ K_{sp}=s\times {(2s)}^2$$ =4s^3$$ =4\times {(2.15\times {10}^{-4})}^3$$ =4\times (9.93\times {10}^{-12})$$ =3.98\times {10}^{-11}$\end{array}$

Conclusion

Therefore, B is the correct option.