Chemical and Ionic Equilibrium - Result Question 126
####69. What is the $pH$ of a $1.0 M$ solution of acetic acid? To what volume must one litre of this solution be diluted so that the $pH$ of the resulting solution will be twice the original value? Given, $K _a=1.8 \times 10^{-5}$
$(1990,4 M)$
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Solution:
- $CH _3 COOH \rightleftharpoons CH _3 COO^{-}+H^{+}$
When concentration of $CH _3 COOH$ is $1.0 M$, ’ $\alpha$ ’ is negligible,
$$ \begin{aligned} {\left[H^{+}\right] } & =\sqrt{K _a C}=4.24 \times 10^{-3} M \ pH & =-\log \left(4.24 \times 10^{-3}\right)=2.37 \end{aligned} $$
Now, let us assume that solution is diluted to a volume where concentration of $CH _3 COOH$ (without considering ionisation) is $x$.
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Also, desired $pH=2 \times 2.37=4.74$
$$ \left[H^{+}\right]=1.8 \times 10^{-5}=x \alpha $$
$$ \begin{aligned} K _a & =1.8 \times 10^{-5}=\frac{1.8 \times 10^{-5} \alpha}{1-\alpha} \ \alpha & =0.5 \text { and } x=3.6 \times 10^{-5} M \ \text { Volume (final) } & =1 / 3.6 \times 10^{-5}=27.78 \times 10^{3} L \end{aligned} $$
