The pH of an aqueous solution containing 1M benzoic acid and 1M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is ________ mL. (given: log 2 = 0.3)

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Solution

Q.
The pH of an aqueous solution containing 1M benzoic acid $({pK}_{a} = 4.20)$ and 1M sodium benzoate is 4.5. The volume of benzoic acid solution in 300 mL of this buffer solution is ________ mL. (given: log 2 = 0.3) [2024]

Ans.
(100)

As total volume of mixture is 300mL, let V mL of 1M benzoic acid is mixed with (300-V) mL of 1M sodium benzoate solution.

Moles of benzoic acid $(n_{a c i d})$ = Molarity $\times$ volume

= 1M $\times$ Vml = Vmmol

Moles of sodium benzoate $(n_{s a l t})$ = Molarity $\times$ volume = 1M $\times$ (300 - V)mL = (300 - V) mmol

A mixture of benzoic acid (weak acid) and sodium benzoate is an acidic buffer. For acidic buffer:

$pH = {pK}_{a} + \log \frac{[salt]}{[acid]} = {pK}_{a} + \log \frac{n_{salt}}{n_{acid}}$

$4.5 = 4.20 + \log \frac{300 - V}{V}$

$\log \frac{300 - V}{V} = 0.3$

$\frac{300 - V}{V} = 2$

$V = 100 mL$

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