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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.
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