The factor by which the degree of ionisation of `200mL` of `0.1M` benzoic acid solution `(K_(a) = 4 xx 10^(-5))` changes on addition of `100mL` of `0.2M HC1` is:

Options

A. `0.02`
B. `0.03`
C. `33.33`
D. None

Answer

B

Explanation

`HA hArr H^(o+) + A^(Theta)`
For `W_(A):`
`alpha = sqrt((K_(a))/(c)) = sqrt((4xx10^(-5))/(0.1)) = 2xx10^(-2)`
When `HC1` is added, due to common ion `(H^(o+)` ion), superssion of ionisation of `HA` occurs.
Total volume `= 200 + 100 =300 mL`
`M_(1)V_(2) = M_(2)V_(2) ("for" HC1)`
`100 xx 0.2 = M_(2) xx300`
`M_(2) = (0.2)/(3)`
`alpha' = (K_(a))/(M)`
(M = Concentration of common ion added)
`:. alpha' = (4 xx 10^(-5))/(0.2//3) = 6 xx 10^(-4)`
Change in `alpha` (factor) :
`(alpha')/(alpha) = (6 xx 10^(-4))/(2xx10^(-2)) = 0.03`