High School

Calculate the pH of a buffer solution prepared by dissolving 23.8 g of benzoic acid (HC₇H₅O₂) and 35.9 g of sodium benzoate in 201.0 mL of solution.

Answer :

The pH of the buffer solution is approximately 4.30.

To calculate the pH of a buffer solution, we can use the Henderson-Hasselbalch equation:

[tex]pH = pKa + \log \left( \frac{[A^-]}{[HA]} \right)[/tex]

where:

  • [tex][A^-][/tex] is the concentration of the conjugate base (sodium benzoate)
  • [tex][HA][/tex] is the concentration of the weak acid (benzoic acid)
  • [tex]pKa[/tex] is the acid dissociation constant of the weak acid

First, we need to find the molar mass of benzoic acid (HC₇H₅O₂) and sodium benzoate (NaC₇H₅O₂):

  • Molar mass of benzoic acid (HC₇H₅O₂) = 122.12 g/mol
  • Molar mass of sodium benzoate (NaC₇H₅O₂) = 144.11 g/mol

Next, we calculate the number of moles of each component:

  • Moles of benzoic acid (HC₇H₅O₂) = [tex]\frac{23.8 \text{ g}}{122.12 \text{ g/mol}} \approx 0.195 \text{ mol}[/tex]
  • Moles of sodium benzoate (NaC₇H₅O₂) = [tex]\frac{35.9 \text{ g}}{144.11 \text{ g/mol}} \approx 0.249 \text{ mol}[/tex]

Now, we find the concentrations of each species in the 201.0 mL solution (0.201 L):

  • Concentration of benzoic acid (HC₇H₅O₂) = [tex]\frac{0.195 \text{ mol}}{0.201 \text{ L}} \approx 0.970 \text{ M}[/tex]
  • Concentration of sodium benzoate (NaC₇H₅O₂) = [tex]\frac{0.249 \text{ mol}}{0.201 \text{ L}} \approx 1.239 \text{ M}[/tex]

We also need the [tex]pKa[/tex] value for benzoic acid, which is approximately 4.20.

Using the Henderson-Hasselbalch equation, we can now calculate the pH:

[tex]pH = 4.20 + \log \left( \frac{1.239 \text{ M}}{0.970 \text{ M}} \right)[/tex]

[tex]pH = 4.20 + \log(1.278)[/tex]

[tex]pH = 4.20 + 0.106[/tex]

[tex]pH \approx 4.30[/tex]

Therefore, the pH of the buffer solution is approximately 4.30.