In aqueous solution the ionization constants for carbonic acid are:
`K_(1)=4.2xx10^(-7)and K_(2)=4.8xx10^(-11)`
Select the correct statement for a saturated `0.034M` solution of the carbonic acid.

Options

A. The concentration of `H^(+)` is double that of `CO_(3)^(2-)`
B. The concentration of `CO_(3)^(2-)` is `0.034M`
C. The concentration of `CO_(3)^(2-)` is greater than that of `HCO_(3)^(-)`
D. The concentration of `H^(+)` and `HCO_(3)^(-)` are approximately equal

Answer

D

Explanation

`H_(2)CO_(3)hArrH^(+)+HCO_(3)^(-)K_(1)=4.2xx10^(-7)`
`{:(C,,0,,0,,"Initial"),(C(1-alpha_(1)),,Calpha_(1),,Calpha_(1),,"Final"):}`
`[HCO_(3)^(-)]=Calpha_(1)=sqrt(K_(1).C)`
`{:(HCO_(3)^(-),,hArr,,H^(+),,+,,CO_(3)^(--),,K_(2)=4.8xx10^(-11)),(Calpha_(1),,,,0,,,,0,,"Initial"),(Calpha_(1)(1-alpha_(2)),,,,Calpha_(1)alpha_(2),,,,Calpha_(1)alpha_(2),,"Final"):}`
`[CO_(3)^(2-)]=Calpha_(1)alpha_(2)=sqrt(K_(2).Calpha_(1)`
So, `[HCO_(3)^(-)] gt [CO_(3)^(2-)]`
Value of `K_(2)` is very low so `H^(+)` ions from the dissociation `(Calpha_(1)alpha_(2))` is negligible
`[H^(+)]~~[HCO_(3)^(-)]=Calpha_(1)`.