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What is the value of pK(b)(CH(3)COO^(c-)...

What is the value of `pK_(b)(CH_(3)COO^(c-))` if `wedge^(@)._(m)=390 S cm^(-1) mol ^(-1)` and `wedge_(m)=7.8 S cm^(2) mol^(-1)` for `0.04 M` of `CH_(3)COOH` at `25^(@)C`?

A

`9.3`

B

`9.2`

C

`4.7`

D

`4.8`

Text Solution

Verified by Experts

The correct Answer is:
B
`alpha = (Lambda_(m))/(Lambda_(m)^(@)) = (7.8)/(390) = 0.02`
`K_(a) (CH_(3) COOH) = (e alpha xx e alpha)/(e - e alpha) = (e alpha^(2))/(1 - alpha)`
`= (0.04 xx (0.02)^(2))/(1 - 0.02) = 1.6 xx 10^(-5)`
`pK_(a) = 4.8`
Use , `pK_(a) + pK_(b) = p K_(w) = 14`
`implies K_(b) = 14 - pK_(a) = 14 - 4.8 = 9.2`
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