The `K_(a)` value of `CaCO_(3)` and `CaC_(2)O_(4)` in water are `4.7 xx 10^(-9)` and `1.3 xx 10^(-9)`, respectively, at `25^(@)C`. If a miaxture of two is washed with `H_(2)O`, what is `Ca^(2+)` ion concentration in water?

Options

A. `5.831 xx 10^(-5)M`
B. `6.856 xx 10^(-5)M`
C. `3.606 xx 10^(-5) M`
D. `7.746 xx 10^(-5) M`

Answer

D

Explanation

`CaCO_(3) rarr underset(x)(Ca^(2+)) + underset(x)(CO_(3))^(2-)`
`CaC_(2)O_(4) rarr underset(y)(Ca^(2+)) + underset(y)(C_(2)O_(4))^(2-)`
Now, `[Ca^(2+)] = x + y`
and `x(x+y) = 4.7 xx 10^(-9)`
`y(x+y) = 1.3 xx 10^(-9)`
On solving we get
`[Ca^(2+)] = 7.746 xx 10^(-5)M`.