At a given temperature, specific conductance of 0.001(M) acetic acid solution is `5xx10^(-5)"S.cm"^(-1)` and equivalent conductivity at infinite dilution is `"390.5 S.cm"^(2).mol"^(-1)`. What is the value of dissociation constant of acetic acid at the same temperature.

Explanation

`Lambda_(m)=kappa xx(1000)/(M)=5xx10^(-5)xx(1000)/(0.001)="50 S.cm"^(2)."mol"^(-1)`
`alpha=(Lambda_(m))/(Lambda_(m)^(@))=(50)/(390.5)=0.128`
`K_(a)=(alpha^(2)c)/(1-alpha)=((0.128)^(2)xx0.001)/(1-0.128)=1.878xx10^(-5)`