The `pH` of `0.1 M` solution of cyanic acid `(HCNO)` is `2.34`. Calculate the ionization constant of the acid and its degree of ionisation in the solution.

Answer

`K_(a) = 2.09 xx 10^(-4)` and degree of ionization `= 0.0457`

Explanation

`c = 0.1 M`
`pH = 2.34`
`-"log" [H^(+)] = pH`
`-"log" [H^(+)] = 2.34`
`[H^(+)] = 4.5 xx 10^(-3)`
Also,
`[H^(+)] = calpha`
`4.5 xx 10^(-3) = 0.1 xx alpha`
`(4.5 xx 10^(-3))/(0.1) = alpha`
`alpha = 45 xx 10^(-3) = .045`
Then,
`K_(a) = calpha^(2)`
`0.1 xx (45 xx 10^(-3))^(2)`
`= 202.5 xx 10^(-6)`
`= 2.02 xx 10^(-4)`