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Question

What is the pH of a 1.0M solution of acetic acid? To what volume of one litre of this solution be diluted so that the pH of the resulting solution will be twice the original value? Given, Ka=1.8×105

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Solution

We know that degree of dissociation
α=KaC=1.8×1051=4.2426×103
[H+]=Cα=1×4.2426×103=4.2426×103molL1
pH=log[H+]=log4.2426×103=2.3724
so, pH of the acetic acid solution after dilution=2×2.3724
=4.7448
New [H+]=104.7448=1.8×105
Let the new concentration be C0
CH3COOHH++CH3COO
At equilibrium C01.8×105 1.8×105 1.8×105
Ka=[H+][CH3COO][CH3COOH]=1.8×105×1.8×105(C01.8×105)=1.8×105
so, C0=3.6×105
Let the new volume be V litre
1×1=3.6×105×V
V=13.6×105=2.78×104l

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