Buffer Solution Calculations Using the Henderson-Hasselbalch Equation

Introduction

• The Henderson-Hasselbalch equation is used to calculate the pH of buffer solutions.
• pH = pKa + log([A⁻]/[HA])
  • HA and A⁻ represent the conjugate acid-base pair.
  • Example given: HA = NH₄⁺ (acid), A⁻ = NH₃ (base).

Calculating pKa

• Given: Ka for NH₄⁺ = 5.6 x 10⁻¹⁰.
• pKa = -log(Ka).
• Calculation:
  • pKa = -log(5.6 x 10⁻¹⁰) = 9.25 (rounded).

Calculating Initial pH

• Buffer solution concentrations:
  • [NH₃] = 0.24 M
  • [NH₄⁺] = 0.20 M
• Using the Henderson-Hasselbalch equation:
  • pH = 9.25 + log(0.24/0.20)
  • pH = 9.25 + 0.08 = 9.33

Effect of Adding a Base

• Adding 0.005 moles of NaOH to 0.50 L solution:
  • [OH⁻] = 0.01 M
• Reaction:
  • NH₄⁺ + OH⁻ → NH₃ + H₂O
• New concentrations:
  • [NH₄⁺] = 0.19 M
  • [NH₃] = 0.25 M
• New pH:
  • pH = 9.25 + log(0.25/0.19)
  • pH = 9.25 + 0.12 = 9.37
• Comparison:
  • Initial pH = 9.33
  • After base addition: slight increase to 9.37

Effect of Adding an Acid

• Adding 0.03 moles of HCl to 0.50 L solution:
  • [H₃O⁺] = 0.06 M
• Reaction:
  • NH₃ + H₃O⁺ → NH₄⁺ + H₂O
• New concentrations:
  • [NH₃] = 0.18 M
  • [NH₄⁺] = 0.26 M
• New pH:
  • pH = 9.25 + log(0.18/0.26)
  • pH = 9.25 - 0.16 = 9.09
• Comparison:
  • Initial pH = 9.33
  • After acid addition: slight decrease to 9.09

Conclusion

• Buffer solutions resist drastic pH changes upon addition of acids or bases.
• Demonstrated through changes in pH when adding base or acid to the buffer solution.