The `K_(a)` value of formic acid and acetic acid are respectively, `1.77 xx 10^(-4) " and 1.75 xx 10^(-5)`. The ratio of the acid strength of 0.1 N acids is

Options

A. 10
B. 3.178
C. 0.3
D. 0.1

Answer

B

Explanation

`HA hArr H^(+) + A^(-), K_(a) = ([H^(+)][A^(-)])/([HA])`
Let `C mol L^(-1)` be the conc. and `alpha` its degree of dissociation
`:. K_(a) = (C alpha xx C alpha)/(C (1 - alpha)) = C alpha^(2)` (where `alpha` is very small)
`:. alpha = sqrt((K_(a))/(C))` where C is constant, `[H^(+)] prop alpha`
`:. (alpha_(1))/(alpha_(2)) = sqrt((K_(a_(1)))/(K_(a_(2)))) = sqrt((1.77 xx 10^(-4))/(1.75 xx 10^(-5)))`
`= sqrt(10) = 3.178`