Question

To a $50$ mL of $0.05$M formic acid how much volume of $0.10$M sodium formate must be added to get a buffer solution of pH$=4.0$? (p$K_a$ of the acid is $3.7$)

• A. $40$ mL
• B. $4$ mL
• C. $50$ mL
• D. $100$ mL

Answer 1

Answer: (C)

$50$ mL

We have, if $V$ ml be the volume of $0.1MHCOONa$ be mixed to 50ml of 0.05M $HCOOH$,
$\left[Molarity\right]=\frac{Totalmilimole}{Totalvolume}$
$Inmixture\left[HCOONa\right]=\frac{(0.1\times V)}{(V+50)}$
$\left[HCOOH\right]=\frac{(50\times 0.05)}{(V+50)}$
As $pH=-log{(K}_a)+log\left(\frac{\left[Salt\right]}{\left[Acid\right]}\right)$
$\therefore 4.0=3.70+log\left(\frac{\left[\frac{(0.1\times V)}{(V+50)}\right]}{\left[\frac{\left(2.5\right)}{(V+50)}\right]}\right)$
Thus, $V=49.88approx=50ml$

Conclusion: Hence, the option $\left(C\right)$ is correct.