`K_(a)` for ascorbic acid `(HASc)` is `5 xx 10^(-5)`. Calculate the `[H^(o+)]` in an aqueous solution in which the concentration of `Asc^(Theta)` ions is `0.02M`.

Options

A. `2 xx 10^(-6)`
B. `2 xx 10^(-7)`
C. `5 xx 10^(-9)`
D. `5 xx 10^(-10)`

Answer

C

Explanation

`Asc^(Theta) + H_(2)O hArr HASc^(Theta) + overset(Theta)OH`
`[overset(Theta)OH] = Ch = C sqrt(((Kh)/(C))) = sqrt(K_(h)C)`
` = sqrt((K_(w).C)/(K_(a))) = ((10^(-14)xx0.02)/(5xx10^(-5)))^((1)/(2)`
`[H_(3)O^(o+)] = (K_(w))/([overset(Theta)OH]) = (10^(-14))/(2xx10^(-16)) = 5 xx 10^(-9)`