Three sparingly soluble salts `M_(2)X`, `MX` and `MX_(3)` have the same solubility product. Their solubilities will be in the order

Options

A. `MX_(3) gt MX gt M_(2)X`
B. `MX gt MX_(3) gt M_(2)X`
C. `MX gt M_(2) X gt MX_(3)`
D. `MX_(3) gt M_(2) X gt MX`

Answer

D

Explanation

Let solubility of `M_(2)X `is `S_(1), MX ` is `S_(2)` and `MX_(3)` is `S_(3)`
`S_(1)=(K_(sp)//4)^(-(1)/(3)),S_(2)=(K_(sp))^(1//2)`
`S_(3)=(K_(sp)//27)^(1//4)`
As `K_(sp)` is generally of the order of `10^(-12)` (say ) . In that case
`S_(1)=(1)/(3) sqrt(4), S_(2)=10^(-6) ` and `S_(3) =(1)/(3) sqrt(3)" "10^(-3)`
Clearly `S_(3) gt S_(1) gt S_(2)`
`:. `The correct order of solubilities is
`MX_(3) gt M_(2) X gt M_(1) X `