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.
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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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