Acidity or alkalinity of a solution depend upon the concentration of hydrogen ion relative to that of hydroxyl ions. The product of hydrogen ion & hydroxyl ion concentration is given by
`K_(w) = [H^(+)][OH^(-)]`
the value of which depends only on the temperature & not on the individual ionic concentration. If the concentratoin of hydrogen ions exceeds that of the hydroxyl ions, the solution is said to be acidic, whereas, if concentrations of hydroxyl ion exceeds that of the hydrogen ions, the solution is said to be alkaline. The pH corresponding to the acidic and alkaline solutions at `25^(@)C` will be less than and greter than seven, respectively. To confirm the above facts `0.5 M CH_(3)COOH` is taken fro the experiments.
[Given : `K_(a)` of acetic acid `= 1.8 xx 10^(-5)`]
If `pH` of solution is double what will be the concentration of acetic acid-

Options

A. `1.8 xx 10^(-5) M`
B. `1.0 M`
C. `4.6 xx 10^(-6) M`
D. `1.25 xx 10^(-3) M`

Answer

C

Explanation

`P^(H) = 5.04 :'` It is doubled
`:. [H^(+)] = 9.120 xx 10^(-6)`
`:. [H^(+)] = sqrt(K_(a).C) , :. C = 4.6 xx 10^(-6)`