Buffer Solution Calculations Overview

Aug 22, 2024

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Buffer Solution Calculations using Henderson-Hasselbalch Equation

Introduction to Buffer Solutions

  • A buffer solution consists of a conjugate acid-base pair.
  • Example:
    • Acid: NH₄⁺ (ammonium)
    • Base: NH₃ (ammonia)

Henderson-Hasselbalch Equation

  • Formula:
    pH = pKa + log([A⁻]/[HA])
    Where:
    • [A⁻] = concentration of the base
    • [HA] = concentration of the acid

Step 1: Calculating pKa

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

Step 2: Calculate Initial pH of Buffer Solution

  • Concentrations:
    • [A⁻] (NH₃) = 0.24 M
    • [HA] (NH₄⁺) = 0.20 M
  • Plug values into the equation:
    • pH = 9.25 + log(0.24/0.20)
    • log(0.24/0.20) = 0.08
    • Final pH = 9.25 + 0.08 = 9.33

Step 3: Adding Base to the Buffer Solution

  • Added:
    • 0.005 moles of NaOH in 0.50 L
  • Calculate concentration of NaOH:
    • Concentration = moles/volume = 0.005/0.50 = 0.01 M
    • This is also the concentration of OH⁻ ions.

Reaction of NaOH with NH₄⁺

  • Reaction:
    • NH₄⁺ + OH⁻ → NH₃ + H₂O
  • Changes in concentrations:
    • NH₄⁺: 0.20 - 0.01 = 0.19 M
    • NH₃: 0.24 + 0.01 = 0.25 M

Step 4: New pH Calculation after Base Addition

  • Plug into Henderson-Hasselbalch Equation:
    • pH = 9.25 + log(0.25/0.19)
    • log(0.25/0.19) = 0.12
    • Final pH = 9.25 + 0.12 = 9.37
  • Conclusion:
    • Added base, pH increased from 9.33 to 9.37. Buffer resists drastic changes in pH.

Step 5: Adding Acid to the Buffer Solution

  • Added:
    • 0.03 moles of HCl in 0.50 L
  • Calculate concentration of HCl:
    • Concentration = 0.03/0.50 = 0.06 M
  • This is also the concentration of H₃O⁺ ions.

Reaction of HCl with NH₃

  • Reaction:
    • NH₃ + H₃O⁺ → NH₄⁺ + H₂O
  • Changes in concentrations:
    • NH₃: 0.24 - 0.06 = 0.18 M
    • NH₄⁺: 0.20 + 0.06 = 0.26 M

Step 6: New pH Calculation after Acid Addition

  • Plug into Henderson-Hasselbalch Equation:
    • pH = 9.25 + log(0.18/0.26)
    • log(0.18/0.26) = -0.16
    • Final pH = 9.25 - 0.16 = 9.09
  • Conclusion:
    • Added acid, pH decreased from 9.33 to 9.09. Buffer again resists drastic pH changes.