Concentration of the `Ag^(+) `ions in a saturated solution of `Ag_2C_2O_4` is ` 2.2 xx 10 ^(-4) " mol " L^(-1) ` , Solubility product of `Ag_2C_2O_4` is
(a)` 2.42 xx 10^(-8)`
(b)` 2.66 xx 10^(-12)`
(c)` 4.5 xx 10^(-11)`
(d)` 5.3 xx 10 ^(-12)`

Options

A. `2.42xx10^(-8)`
B. `2.66xx10^(-12)`
C. `4.5xx10^(-11)`
D. `5.3xx10^(-12)`

Answer

D

Explanation

Key concept - For a sparingly soluble salt, if S is the molar solubility,
`A_(x)B_(y)(s)+H_(2)O hArr xA^(y+)+yB^(x-)`
At saturation,
`K[A_(x)B_(y)]=[A^(y+)]^(x)xx[B^(x-)]^(y)=[xS]^(x)[yS]^(y)`
or `K_(sp)=x^(t).y^(y)S^(x+y)`
Where, the constant `K_(sp)` is called solubility product.
`Ag_(2)C_(2)O_(4)(s)hArr underset(2S)(2Ag^(+))+underset(S)(C_(2)O_(4)^(2-))`
`K_(sp)=[Ag^(+)]^(2)[C_(2)O_(4)^(2-)]=[2S]^(2)[S]`
Given, `2S=22xx10^(-4)` or `S=1.1xx10^(-4)M`
`therefore K_(sp)=[2.2xx10^(-4)]^(2)[1.1xx10^(-4)]`
`=5.3xx10^(-12)`