The equivalent conductance of `M//32` solution of a weak monobasic acid is `8.0 ` and at infinite dilution is `400 `. The dissociation constant of this acid is :

Options

A. `1.25xx10^(-5)`
B. `1.5xx10^(-6)`
C. `6.25xx10^(-4)`
D. `1.25xx10^(-4)`

Answer

A

Explanation

(a) Degree of dissociation, ` alpha=(Lambda^( C))/(Lambda^(oo))`
where, `Lambda^( C) and Lambda^(oo)` are equivalent conductances at a given concentration and at infinite dilution respectively.
`implies alpha=(8.0)/(400)=2xx10^(-2)`
From Ostwald's dilution law ( for weak monobasic acid ),
`K_( C )=(C alpha^(2))/((1-alpha))`
` or =C alpha^(2) " " ( :. 1 gt gt gt alpha)`
`=(1)/(32)(2xx10^(-2))^(2)`
`=1.25xx10^(-5)`