At T (K), the molar conductivity of 0.04 M acetic acid is 7.8 S `cm^(2) mol^(-1)`. If the limiting molar conductivities of `H^(+)` and `CH_(3)COO^(-)` at T (K) are 349 and 41 S `cm^(2) mol^(-1)` repsectively, the dissociation constant of acetic acid is :

Options

A. `1.63xx10^(-5)`
B. `8.33xx10^(-5)`
C. `1.63xx10^(-4)`
D. `8.33xx10^(-4)`

Answer

A

Explanation

`Lambda_(m)^(@)=CH_(3)COOH=lambda_(CH_(3)COO^(-))^(@)+lambda_(H^(+))^(@)`
`=349+41=390" S cm"^(2)mol^(-1)`
`alpha=Lambda_(m)/Lambda_(m)^(@)=7.8/390=0.02`
`K_(a)=(C alpha^(2))/((1-alpha))=(0.04xx(0.02)^(2))/((1-0.02))`
`=1.63xx10^(-5)`