Buffer Equation

Buffer Equation, or Henderson-Hasselbalch equation, calculates the pH of a buffer solution based on the concentrations of its components.

For Acidic Buffers

• Equation:

  • $\mathrm{pH} = \mathrm{p}K_a + \log_{10} \left( \frac{[{A^-}]}{[{HA}]} \right)$

  • where:
  • ​ is the negative logarithm of the acid dissociation constant.
  • is the concentration of the conjugate base.
  • is the concentration of the weak acid.

• Derivation:

  • Starting from the acid dissociation expression:

  • $K_a = \frac{[{H^+}][{A^-}]}{[{HA}]}$

  • Rearranged to solve for [H+][\text{H}^+][H+]:

  • $[{H^+}] = \frac{K_a [{HA}]}{[{A^-}]}$

  • Taking negative logarithms:

  • $-\log_{10} [{H^+}] = -\log_{10} K_a – \log_{10} \left( \frac{[{HA}]}{[{A^-}]} \right)$

  • Simplifies to the Henderson-Hasselbalch equation.

For Basic Buffers

• Equation:

  • $\mathrm{pOH} = \mathrm{p}K_b + \log_{10} \left( \frac{[{BH^+}]}{[{B}]} \right)$
  • where:
  • $​\mathrm{p}K_b$
    is the negative logarithm of the base dissociation constant.
  • $[{BH^+}]$
    is the concentration of the conjugate acid.
  • $[{B}]$
    is the concentration of the weak base.

  • Applications

    • Designing Buffers: Calculate the required proportions of acid and conjugate base to achieve a desired pH.
    • Predicting pH Changes: Assess how changes in component concentrations affect pH.

  • Limitations

    • Assumptions: The equation assumes that activities equal concentrations, which is valid at low ionic strengths.
    • Temperature Dependence: pKa\text{p}K_apKa​ values change with temperature; calculations should account for this.

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