Question

Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298 K from their solubility product constants. Determine also the molarities of individual ions.
The solubility product constants are:
Silver chromate, $1.1\times {10}^{-12}$
Barium chromate, $1.2\times {10}^{-10}$
Ferric hydroxide, $1.0\times {10}^{-38}$
Lead dichloride, $1.6\times {10}^{-5}$
Mercurous iodide, $4.5\times {10}^{-29}$

Answer 1

(i) Silver chromate $A{g}_{2}Cr{O}_4\rightleftharpoons 2A{g}^{+}+Cr{O}_4^{2-}$
$\left[A{g}^{+}\right]=2s,Cr{O}_4^{2-}=s$
$K_{sp}=\left(2s{)}^2\right(s)=4s^3=1.1\times {10}^{-12}$
$s=6.5\times {10}^{-5}$
$\left[A{g}^{+}\right]=2s=1.30\times {10}^{-4}M$
$\left[Cr{O}_4^{2-}\right]=s=6.5\times {10}^{-5}M$
(ii) Barium chromate $BaCr{O}_4\rightleftharpoons B{a}^{2+}+Cr{O}_4^{2-}$
$\left[B{a}^{2+}\right]=\left[Cr{O}_4^{2-}\right]=s$
$K_{sp}=s\times s=s62=1.2\times {10}^{-10}M$
$\left[B{a}^{2+}\right]=\left[Cr{O}_4^{2-}\right]=s=1.09\times {10}^{-5}M$
(iii) Ferric hydroxide $Fe(OH{)}_3\rightleftharpoons F{e}^{3+}+3O{H}^{-}$
$\left[F{e}^{3+}\right]=s,\left[O{H}^{-}\right]=3s$
$K_{sp}=s(3s{)}^3=27s^4=1.0\times {10}^{-38}$
$\left[F{e}^{3+}\right]=s=1.38\times {10}^{-10}M$
$\left[O{H}^{-}\right]=3s=4.14\times {10}^{-10}M$
(iv)Lead dichloride $PbC{l}_2\rightleftharpoons P{b}^{2+}+2C{l}^{-}$
$\left[P{b}^{2+}\right]=s,\left[C{l}^{-}\right]=2s$
$K_{sp}=s\times (2s{)}^2=4s^3=1.6\times {10}^{-5}$
$\left[P{b}^{2+}\right]=s=0.0159M$
$\left[C{l}^{-}\right]=2s=0.0318M$M
(v) Mercurous iodide $H{g}_2{I}_2\rightleftharpoons 2H{g}^{+}+2I^{-}$
$\left[H{g}^{+}\right]=\left[I^{-}\right]=2s$
$K_{sp}=\left(2s{)}^2\right(2s{)}^2=16s^4=4.5\times {10}^{-29}$
$s=4.09\times {10}^{-8}M$
$\left[H{g}^{+}\right]=\left[I^{-}\right]=2s=8.18\times {10}^{-8}M$