What is the `pH` of `1M` solution of acetic acid. To what volume one litre of this solution be diluted so that `pH` of the resulting solution will be twice of the original value. `K_(a) = 1.8 xx 10^(-5)`

Explanation

`CH_(3)COOH rarr CH_(3)COO^(-) + H^(+)`
When concentration of `CH_(3)COOH` is 1.0 M, `'alpha'` is negligible.
`[H^(+)] = sqrt(K_(a)C) = 4.24 xx 10^(-3)M`
`pH = -log(424 xx 10^(-3))M = 2.37`
Now, let us assume that solution is diluted to a volume where concentration of `CH_(3)COOH` (without considering ionisation) is x
`CH_(3)COOH underset("x(1-alpha)") rarr CH_(3)COO^(-)underset("xalpha") + H^(+)underset("xalpha")`
`K_(a) = xalpha^(2)/1-alpha`
Also, desired pH = 2 xx 2.37 = 4.74
`[H^(+)] = 1.8 xx 10^(-5) = xalpha`
`K_(a) = 1.8 xx 10^(-5) =1.8 xx 10^(-5)alpha/1-alpha`
`alpha = 0.5 and x = 3.6 xx 10^(-5)M`
Volume(final) `= 1//3.6 xx 10^(-5) = 27.78 xx 10^(3)L`