How would you prepare a benzoic acid/benzoate buffer with a pH of 4.25, starting with 5.0L of .050M sodium benzoate (C6H5COONa solution and adding the solid acidic component (Ka of benzoic acid =6.3×10^-5)? How would you prepare a benzoic acid/benzoate buffer with a pH of 4.25, starting with 5.0L of .050M sodium benzoate (C6H5COONa solution and adding the solid acidic component (Ka of benzoic acid =6.3×10^-5)?
The Correct Answer and Explanation is :
To prepare a benzoic acid/benzoate buffer with a pH of 4.25, starting with 5.0 L of 0.050 M sodium benzoate (C₆H₅COONa) solution, follow these steps:
1. Calculate the pKa of Benzoic Acid:
The acid dissociation constant (Ka) for benzoic acid is 6.3 × 10⁻⁵. The pKa is calculated as:
pKa = -log(Ka) = -log(6.3 × 10⁻⁵) ≈ 4.20
2. Apply the Henderson-Hasselbalch Equation:
The Henderson-Hasselbalch equation relates pH, pKa, and the ratio of concentrations of the conjugate base (A⁻) and the acid (HA):
pH = pKa + log([A⁻]/[HA])
Rearranging to solve for the ratio of [A⁻] to [HA]:
[A⁻]/[HA] = 10^(pH – pKa)
Substitute the known values:
[A⁻]/[HA] = 10^(4.25 – 4.20) = 10^0.05 ≈ 1.12
3. Determine the Moles of Sodium Benzoate (A⁻):
The initial concentration of sodium benzoate is 0.050 M, and the volume is 5.0 L:
Moles of sodium benzoate = 0.050 mol/L × 5.0 L = 0.25 mol
4. Calculate the Required Moles of Benzoic Acid (HA):
Using the ratio from the Henderson-Hasselbalch equation:
Moles of benzoic acid = Moles of sodium benzoate / 1.12 ≈ 0.25 mol / 1.12 ≈ 0.223 mol
5. Calculate the Mass of Benzoic Acid Needed:
The molar mass of benzoic acid (C₆H₅COOH) is approximately 122.12 g/mol:
Mass of benzoic acid = 0.223 mol × 122.12 g/mol ≈ 27.2 g
6. Prepare the Buffer Solution:
- Weigh out approximately 27.2 g of solid benzoic acid.
- Add the benzoic acid to the 5.0 L of 0.050 M sodium benzoate solution.
- Stir the mixture until the benzoic acid is completely dissolved.
This preparation will yield a buffer solution with a pH of approximately 4.25.
Explanation:
The Henderson-Hasselbalch equation is fundamental for calculating the pH of buffer solutions. By determining the required ratio of the conjugate base to the acid, we can calculate the necessary amounts of each component to achieve the desired pH. In this case, the ratio of 1.12 indicates that for every mole of benzoic acid, approximately 1.12 moles of sodium benzoate are needed. By adding the calculated amount of benzoic acid to the sodium benzoate solution, we establish the desired buffer capacity and pH.
For a visual explanation of calculating the pH of a buffered solution containing benzoic acid and sodium benzoate, you may find the following video helpful: