Question

$\text{The pH of an aqueous solution containing 1 M benzoic acid (} pK_a = 4.20 \text{) and 1 M sodium benzoate is 4.5.}$
\(\text{The volume of benzoic acid solution in 300 mL of this buffer solution is \_\_\_\_\_\_ mL.}\)

Answer 1

Correct Answer: 100

Solution: The volume of benzoic acid in the buffer is determined using the Henderson-Hasselbalch equation:

\[ \text{pH} = pK_a + \log \left( \frac{[A^-]}{[HA]} \right) \]

Where: \([A^-]\) denotes the concentration of the conjugate base (sodium benzoate) and \([HA]\) denotes the concentration of the weak acid (benzoic acid).

Given Information: pH = 4.5

\[ pK_a = 4.20, \quad [A^-] = 1 \, M \text{ (sodium benzoate)} \]

The total volume of the buffer solution is 300 mL.

Calculate the ratio of base to acid:

\[ 4.5 = 4.20 + \log \left( \frac{[A^-]}{[HA]} \right) \]

\[ 0.30 = \log \left( \frac{1}{[HA]} \right) \]

\[ 10^{0.30} = \frac{1}{[HA]} \implies [HA] = \frac{1}{10^{0.30}} \approx 0.50 \, M \]

Calculate the volume of benzoic acid: Let \(V_a\) be the volume of 1M benzoic acid. The concentration in the total 300 mL buffer solution is:

\[ [HA] = \frac{V_a}{200} \]

Equating the concentrations yields:

\[ 0.50 = \frac{V_a}{200} \implies V_a = 0.50 \times 200 = 100 \, mL \]

Total volume of benzoic acid solution: The total volume of benzoic acid required to achieve the specified pH is:

\[ V_a = 100 \, mL \quad \text{(rounded from calculations)} \]

Therefore, the volume of benzoic acid solution in 300 mL of the buffer solution is: 100 mL