How many times a 0.1 M strong monobasic solution should be diluted so that the pH of the resulting solution is tripled ?

Options

A. 20 times
B. 200 times
C. `5.55 xx 10^(2)` times
D. `5.55xx10^(4) ` times

Answer

D

Explanation

pH of a weak acid `=(1)/(2)[pK_(a)-log c]`
`:.x=(1)/(2) [ pK_(a)-log 1] = (1)/(2) pK_(a)`
and `2x=(1)/(2)[pK_(a)-log c]`
or `pK_(a)=(1)/(2) pK_(a)-(1)/(2)log c (.:' 2x=pK_(a)]`
or `(1)/(2) log c = - (1)/(2) pK_(a)`
or `log c = -pK_(a)=log K_(a)`
or `c=K_(a)=1.8xx10^(-5)`
`:.` Dilution `=(1)/(1.8xx10^(-5))=5.55xx10^(4)` times