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The conductivity of 0.01 M aqueous aceti...

The conductivity of 0.01 M aqueous acetic acid measured with a conductivity cell of cell constant of `0.5cm^(-1)` at 298 K is `3.12xx10^(-4)` S. If the limiting conductivities of `H^(+)andCH_(3)COO^(-)` at the same temperature are 349, and 41 S `cm^(2)mol^(-1)` respectively, the dissociation constant of acetic acid is

A

`1.67xx10^(-4)`

B

`1.67xx10^(-5)`

C

`1.67xx10^(-3)`

D

`1.67xx10^(-6)`

Text Solution

Verified by Experts

The correct Answer is:
B
Conductivity = `3.12xx10^(-4)xx0.5Scm^(-1)`
= `1.56xx10^(-4)Scm^(-1)`
Molar conductivity = `(1.56xx10^(-4))/(0.01)=Scm^(3)mol^(-1)`
= `1.56xx10^(-2)Scm^(3)mol^(-1)=1.56Scm^(3)mol^(-1)`
Degree of dissociation d = `(1.56)/(390)=0.004=4xx10^(-3)`
Dissociation constant = `((4xx10^(-3))^(2))/(1-(4xx10^(-3)))`
= `(16xx10^(-6))/(1-0.004)=(16xx10^(-6))/(0.996)=16.0xx10^(-6)=1.60xx10^(-5)`
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