Q36 / 180 · KCET 2010 · Chemistry
A buffer solution contains $0.1$ mole of sodium acetate in $1000 \mathrm{~cm}^{3}$ of $0.1 \mathrm{M}$ acetic acid. To the above buffer solution, $0.1$ mole of sodium acetate is further added and dissolved. The $\mathrm{pH}$ of the resulting buffer is equal to
- A$\mathrm{pK}_{\mathrm{a}}-\log 2$
- B$\mathrm{pK}_{\mathrm{a}}$
- C$\mathrm{pK}_{\mathrm{a}}+2$
- Correct answerD$\mathrm{pK}_{\mathrm{a}}+\log 2$
Solution
Initially $\left[\mathrm{CH}_{3} \mathrm{COONa}\right]=0.1 \mathrm{~mol}$
$\left[\mathrm{CH}_{2} \mathrm{COOH}\right]=0.1 \mathrm{~mol}$
when $0.1 \mathrm{~mol} \mathrm{CH}_{3} \mathrm{COONa}$ is added.
$$
\begin{aligned}
{\left[\mathrm{CH}_{3} \mathrm{COONa}\right] } &=0.1+0.1=0.2 \mathrm{~mol} \\
\mathrm{pH} &=\mathrm{pK}_{\mathrm{a}}+\log \frac{\text { [salt }]}{\text { [acid] }} \\
&=\mathrm{pK}_{\mathrm{a}}+\log \frac{0.2}{0.1} \\
&=\mathrm{pK}_{\mathrm{a}}+\log 2
\end{aligned}
$$
Hence, the correct answer is option: 'D'.