Ionic Equilibrium Question 6
Question 6 - 2024 (30 Jan Shift 2)
The $\mathrm{pH}$ of an aqueous solution containing $1 \mathrm{M}$ benzoic acid $\left(\mathrm{pK}_{\mathrm{a}}=4.20\right)$ and $1 \mathrm{M}$ sodium benzoate is 4.5 . The volume of benzoic acid solution in $300 \mathrm{~mL}$ of this buffer solution is __________ $\mathrm{mL}$.
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Answer (100)
Solution
| $1 \mathrm{M}$ Benzoic acid | $+1 \mathrm{M}$ Sodium Benzoate | |
|---|---|---|
| Milimole | $\left(\mathrm{V}_{\mathrm{a}} \mathrm{ml}\right)$ | $\left(\mathrm{V}_{\mathrm{s}} \mathrm{ml}\right)$ |
| $\mathrm{V}_{\mathrm{a}} \times 1$ | $\mathrm{~V}_{\mathrm{s}} \times 1$ |
$\mathrm{pH}=4.5$
$\mathrm{pH}=\mathrm{pka}+\log \frac{[\text { salt }]}{[\text { acid }]}$
$4.5=4.2+\log \left(\frac{\mathrm{V}{\mathrm{s}}}{\mathrm{V}{\mathrm{a}}}\right)$
$\frac{\mathrm{V}{\mathrm{s}}}{\mathrm{V}{\mathrm{a}}}=2$
$\mathrm{V}{\mathrm{s}}+\mathrm{V}{\mathrm{a}}=300$
$\mathrm{V}_{\mathrm{a}}=100 \mathrm{ml}$
