Question
The solubility product of a salt having general formula $$M{X_2},$$ in water is : $$4 \times {10^{ - 12}}.$$ The concentration of $${M^{2 + }}$$ ions in the aqueous solution of the salt is
A.
$$4.0 \times {10^{ - 10}}\,M$$
B.
$$1.6 \times {10^{ - 4}}\,M$$
C.
$$1.0 \times {10^{ - 4}}\,M$$
D.
$$2.0 \times {10^{ - 6}}\,M$$
Answer :
$$1.0 \times {10^{ - 4}}\,M$$
Solution :
\[M{{X}_{2}}\rightleftharpoons {{\underset{s}{\mathop{M}}\,}^{++}}+{{\underset{2s}{\mathop{2X}}\,}^{-}}\]
$${\text{Where s is the solubility of }}M{X_2}$$
$${\text{then}}\,\,{K_{sp}} = 4{s^3};\,s \times {\left( {2s} \right)^2} = 4 \times {10^{ - 12}}$$ $$ = 4{s^3};s = 1 \times {10^{ - 4}}$$
$$\therefore \left[ {{M^{ + + }}} \right] = s = 1\left[ {{M^{ + + }}} \right] = 10 \times {10^{ - 4}}$$