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Q.
What concentration of acetic acid is needed to give a hydrogen ion concentration of $3.5 \times 10^{-4} M$ ? $\left(K_{a}=1.8 \times\right.$ $\left.10^{-5}\right)$
Equilibrium
Solution:
$\underset{C-C\alpha}{CH _{3} COOH} \rightleftharpoons \underset{C \alpha}{CH _{3} COO ^{-}}+ \underset{C \alpha}{H^{+}}$ Let the concentration of acetic acid be 'C'.
$K_{a}=1.8 \times 10^{-5}=\frac{C \alpha \cdot C \alpha}{C(1-\alpha)}=C \alpha^{2}$
Now $\alpha^{2}=\frac{K_{a}}{C}$ or $\alpha=\sqrt{\frac{K_{a}}{C}}$ or $C \alpha=\sqrt{K_{a} . C}$
$C \alpha=\left[ H ^{+}\right]=3.5 \times 10^{-4} M$
$ \therefore 3.5 \times 10^{-4}=\sqrt{1.8 \times 10^{-5} C }$
Or $\sqrt{C}=\frac{3.5 \times 10^{-4}}{\sqrt{1.8 \times 10^{-5}}}$ or $C=\frac{\left(3.5 \times 10^{-4}\right)^{2}}{1.8 \times 10^{-5}}$