Question

A solution is saturated with respect to strontium fluoride and strontium carbonate. The fluoride ion concentration in the solution is found to be $3.7\times {10}^{-2}mol{L}^{-1}$. What is the value of $\left[{CO}_3^{2-}\right]$?
($K_{sp}:Sr{F}_2=7.9\times {10}^{-10};K_{sp}:Sr{CO}_3=7.0\times {10}^{-10}$)

Answer 1

A solution is saturated with $Sr{F}_2$ and $SrC{O}_3$.

$\left[F^{-}\right]=3.7\times {10}^{-2}M$

$\Rightarrow \left[F^{-}{]}^2\right[S{r}^{2+}]=K_{sp}=7.9\times {10}^{-10}$

$\therefore \left[S{r}^{2+}\right]=\frac{7.9\times {10}^{-10}}{(3.7\times {10}^{-2}{)}^2}=0.577\times {10}^{-6}$

Now, $\left[S{r}^{2+}\right]\left[C{O}_3^{2-}\right]=K_{sp}=7\times {10}^{-10}$

$\Rightarrow \left[C{O}_3^{2-}\right]=\frac{7\times {10}^{-10}}{0.577\times {10}^{-6}}=12.1\times {10}^{-4}M$