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Conductivity of an aqueous solution of 0...

Conductivity of an aqueous solution of `0.1M HX` (a weak mono-protic acid) is `5 xx 10^(-4) Sm^(-1)`
Given: `^^_(m)^(oo) [H^(+)] = 0.04 Sm^(2) mol^(-1): ^^_(m)^(oo) [X^(-)] = 0.01 Sm^(2)mol^(-1)`
Find `pK_(a)[HX]`

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Verified by Experts

The correct Answer is:
9
`HX hArr H^(+) +X^(-)`
`0.1(1-alpha) 0.1 alpha 0.1 alpha`
`K_(a) = (0.1alpha^(2))/(1-alpha)`
`alpha =(^^_(m))/(^^_(m)^(oo)) = 0.05`
`^^_(m) = (K)/(M) = (5 xx 10^(-4)Sm^(-1))/((0.1mol)/(10^(-3)m^(3)))`
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