At `25^(@)C` , the molar conductance of 0.007 M hydrofluoric acid is 150 `"mho cm^(2) mol^(-1)` and `^^ _(@) = 500 "mho" cm^(2) mol^(-1)`. The value of the dissociation constant of the acid at the given concentration at `25^(@) C` is _________.

Options

A. `7 xx 10^(-4) M`
B. `7 xx 10^(-5) M`
C. `9 xx 10^(-3) M`
D. `9 xx 10^(-4) M`

Answer

D

Explanation

`alpha = (Lambda_(m)^(@))/(Lambda_(m)^(@)) = (150)/(500) = 0.3`
`K_(a) = (c alpha^(2))/(1 - alpha) = (0.007 (0.3)^(2))/((1- 0.3))`
`= (0.007 xx 0.09)/(0.7) = 9 xx 10^(-4) M`