The measured freezing point depression for a 0.1 m aqueous `CH_(3)COOH` solution is `0.19^(@)C`. The acid dissociation constant `K_(a)` at this concentration will be (Given `K_(f)`, the moala cryoscopic constant = 1.86 K Kg `mol^(-1))`

Options

A. `4.76xx10^(-5)`
B. `4xx10^(-5)`
C. `8xx10^(-5)`
D. `2xx10^(-5)`

Answer

B

Explanation

`DeltaT_(f)=ixxk_(f)xxm`
`i=(0.19)/(1.86xx0.1)=1.02`
`alpha=(i-1)/(n-1)=(0.02)/(1)=2xx10^(-2)`
`k_(a)=calpha^(2)=1xx10^(-1)xx(2xx10^(-2))^(2)=4xx10^(-5)`.