`A_(3)B_(2)` is a sparingly soluble salt with molar mass `M(gmol^(-1))` and solubility `x` gm `litre^(-1)`, the ratio of the molar concentration of `B^(3-)` to the solubilty product of the salt is `:-`

Options

A. `108(x^(5))/(M^(5))`
B. `(1)/(108)(x^(5))/(M^(5))`
C. `(1)/(54)(M^(4))/(x^(4))`
D. `54(M^(4))/(x^(4))`

Answer

C

Explanation

`S=(X)/(M)`
`{:(A_(3)B_(2)hArr," ",3A^(+2)," ",+2B^(-3)),(," ",3S," ",2S):}`
`[B^(-3)]=2S=2((X)/(M))`
`K_(sp)=[A^(+2)]^(3)[B^(-3)]^(2)`
`K_(sp)=108S^(5)=108((X)/(M))^(5)`
`K_(sp)=54((X)/(M))^(4)((2X)/(M))`
`K_(sp)=54((X)/(M))^(4)[B^-3]`