Question

pH of a mixture of 1 M benzoic acid $(p{K}_a=4.20)$ and 1 M sodium benzoate is 4.5. In 300 mL of buffer solution , volume of benzoic acid solution is

• A. 200 mL
• B. 150 mL
• C. 100 mL
• D. 50 mL

Answer 1

Answer: (C)

$pH=p{K}_a+log\frac{\text{[Salt]}}{\text{Acid}}$
$4.5=4.2+log\frac{\text{[Salt]}}{\text{[Acid]}}$
$0.3=log\frac{\text{[Salt]}}{\text{[Acid]}}$
$\frac{\text{[Salt]}}{\text{[Acid]}}$ =antilog $0.3=2$
Let $\upsilon mL$ of $1M$ benzoic acid is mixed with $\left(300-\upsilon \right)$ mL of $1M$ sodium benzoate
$\therefore \frac{300-\upsilon }{\upsilon }=2$
$300-\upsilon =2\upsilon$
$\upsilon =100mL$