Question

$MY$ and $NY_3$, two nearly insoluble salts, have the same $K_{SP}$ values of $6.2 \times 10^{-13}$ at room temperature. Which statement would be true in regard to $MY$ and $NY_3$ ?

• A. The molar solubility of MY in water is less than that of $NY_3$
• B. The salts $MY$ and $NY_3$ are more soluble in 0.5 M KY than in pure water
• C. The addition of the salt of KY to solution of $MY$ and $NY_3$ will have no effect on their solubilities
• D. The molar solubilities of $MY$ and $NY_3$ in water are identical

Answer 1

Answer: (A)

For MY
$K_{SP} = S^{2}$
$ S= \sqrt{K_{SP}} $
$ = \sqrt{6.2 \times10^{-13}}$
$ = \sqrt{62 \times10^{-14}}$
$ \approx8 \times10^{-7} $
for $NY_3$,
$ K_{SP} = 27S^{4} $
$NY_3 \rightleftharpoons \underset{\text{ S}}{N^{+3} } + \underset{\text{ 3S}}{ 3Y^{-}}$
$ S = \left( \frac{6.2 \times 10^{-13}}{27}\right)^{1/4} = \left(0.2296 \times 10^{-13}\right)^{1/4}$
$ S = 3.89 \times10^{-4} $