Question

What volume of $0.1M$ sodium formate solution should be added to 50 mL of $0.05M$ formic acid to produce a buffer solution of $pH=4.0$?
$(p{K}_a$ of formic acid $=3.80)$
(antilog 1.59 =39.62)

• A. 3.96 mL
• B. 39.6 mL
• C. 45 mL
• D. 35.6 mL

Answer 1

The correct option is B 39.6 mL

Suppose $VmL$ of $0.1MHCOONa$ $\text{is mixed to 50 mL of}(0.05MHCOOH$
$\left[\text{Molarity}\right]=\frac{\text{Total millimole}}{\text{Total volume}}$
In mixture $\left[HCOONa\right]=\frac{0.1\times V}{(V+50)}$
$\left[HCOOH\right]=\frac{50\times 0.05}{V+50}$
By Henderson hasselbalch equation,
$pH=-\text{log}{K}_a+\text{log}\frac{\text{[Salt]}}{\text{[Acid]}}$
$4.0=3.80+{\text{log}}_{10}\frac{\frac{0.1\times V}{(V+50)}}{\frac{2.5}{(V+50)}}$
$V=39.62\text{mL}$