20 mL of 0.1 M weak acid `HA(K_(a)=10^(-5))` is mixed with solution of 10 mL of 0.3 M HCl and 10 mL. of 0.1 M NaOH. Find the value of `[A^(-)]`//([HA]+[A^(-)])` in the resulting solution :

Options

A. `2 xx 10^(-4)`
B. `2 xx 10^(-5)`
C. `2 xx 10^(-3)`
D. `5 xx 10^(-2)`

Answer

A

Explanation

`[H^(+)] = (10 xx 0.3 - 10 xx 0.1)/(10 + 10 + 20) = 0.05`
`[HA] = (20 xx 0.1)/(20 + 20) = 0.05`
`{:underset(0.05-x)(HAhArr)underset(0.05+x x)(H^(+)+A^(-)):}`
Due to common ion effect neglect x w.r.t `0.05`
`K_(a) = ((0.5 + x)x)/((0.05-x))=x, :. x = 10^(-5)`
`:. ([A^(-)])/([HA]+[A^(-)]) = (x)/(x+0.05)`
`(x)/(0.05) = (10^(-5))/(5 xx 10^(-2)) = 2 xx 10^(-4)`