What is the `[CO_(3)^(2-)]` in a 0.001M `Na_(2)CO_(3)` solution after the hydrolysis reactions have come to an equilibrium? `K_(a) (HCO_(3)^(-))=4.7 xx 10^(-11)`

Explanation

The first step of hydrolysis of `CO_(3)^(2-)` ions is predominant.
`" 0.001 "`
`underset(0.001-x)(CO_(3)^(2-))+H_(2)O Leftrightarrow underset(x) (HCO_(3)^(-))+underset(x)(OH^(-))`
`K_(h)=(x^2)/((0.001-x))=(K_(w))/(K_(2))=(1 xx 10^(-14))/(4.7 xx 10^(-11)`
or `x=3.7 xx 10^(-4)`
`[CO_(3)^(2-)]=0.001-0.00037=0.00063M`