Question

What is the maximum concentration of equimolar solutions of ferrous sulphateand sodium sulphide so that when mixed in equal volumes, there is no precipitation of iron sulphide? (For iron sulphide, $K_{sp}=6.3\times {10}^{-18}$).

Answer 1

Let x M be the concentration of both $FeS{O}_4$ solution and $N{a}_{2}S$ solution.
When equal volumes of two solutions are mixed,
$\left[FeS{O}_4\right]=\left[N{a}_{2}S\right]=\left[F{e}^{2+}\right]=\left[S^{2-}\right]=\frac{x}{2}M$
$FeS\rightleftharpoons F{e}^{2+}+S^{2-}$
$K_{sp}=\left[F{e}^{2+}\right]\left[S^{2-}\right]$
$6.3\times {10}^{-18}=\frac{x}{2}\times \frac{x}{2}$
$x=5.02\times {10}^{-9}M$
This is the maximum concentration of $FeS{O}_4$ and $N{a}_{2}S$ which will not precipitate iron sulphide.