MCQ
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____ $\mathrm{mL}$.
  • $100$
  • B
    $200$
  • C
    $300$
  • D
    $400$

Answer

Correct option: A.
$100$
a
                  $\text { 1M Benzoic acid }+1 \mathrm{M} \text { Sodium Benzoate }$

                           $\left(\mathrm{V}_{\mathrm{a}} \mathrm{ml}\right)$                        $\left(\mathrm{V}_{\mathrm{s}} \mathrm{ml}\right)$

Millimole            $\mathrm{V}_{\mathrm{a}} \times 1$                      $\mathrm{~V}_{\mathrm{s}} \times1$

$\mathrm{pH}=4.5$

$\mathrm{pH}=\mathrm{pka}+\log \frac{[\text { salt }]}{[\text { acid }]}$

$4.5=4.2+\log \left(\frac{\mathrm{V}_{\mathrm{s}}}{\mathrm{V}_{\mathrm{a}}}\right)$

$\frac{\mathrm{V}_{\mathrm{s}}}{\mathrm{V}_{\mathrm{a}}}=2$      $.....(1)$

$\mathrm{~V}_{\mathrm{s}}+\mathrm{V}_{\mathrm{a}}=300$        $....(2)$

$\mathrm{~V}_{\mathrm{a}}=100 \mathrm{ml}$

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