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Calculate [H^(o+)] and [CHC1(2)COO^(Thet...

Calculate `[H^(o+)]` and `[CHC1_(2)COO^(Theta)]` in a solution that is `0.01M HC1` and `0.01M CHC1_(2)COOH. K_(a)` for `CHC1_(2)COOH` is `5 xx 10^(-3)`.

Text Solution

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`{:(CH_(2)CI_(2)COOHhArr,CH_(2)CI_(2)COO^(Theta)+,H^(o+),,),(C,0,0.01,,),(C(1-alpha),Calpha,Calpha+0.01,,):}`
`:. K_(a) = (C alpha xx (Calpha + 0.1))/(C(1-alpha)) = (alpha.(0.01alpha+0.01))/((1-alpha)) = 5 xx 10^(-2)`
or `(0.01alpha(1+alpha))/((1-alpha)) = 5 xx 10^(-2) or alpha^(2) + 6 alpha - 5 = 0`
`:. alpha = 0.7416`
`:. [ChCI_(2)COO^(Theta)] = 0.01 xx 0.7416 = 7.416 xx 10^(-3)M`
`[H^(o+)] = 7.416 xx 10^(-3) + 0.01 = 0.0174 M`
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