Buffer Design: Target pH
Buffer planning context
Buffer design sets the conjugate base/acid ratio to hit a target pH. Henderson-Hasselbalch directly maps target pH and pKa to required mole ratios, then to absolute preparation amounts.
\[ \mathrm{pH}=\mathrm{p}K_a+\log\frac{n_{A^-}}{n_{HA}} \]
Practical workflow: determine ratio first, then compute absolute moles and optional masses for the intended batch size.
- Set target pH within buffer range
- Plan conjugate pair moles before preparation
- Convert moles to masses for weighing
Crosslink: For equation fundamentals and transformations, use the Henderson-Hasselbalch Calculator.
Formulas (MathJax)
\[ R = \frac{n_{A^-}}{n_{HA}} = 10^{(\mathrm{pH}-\mathrm{p}K_a)} \]
\[ n_{HA}=\frac{n_T}{1+R},\qquad n_{A^-}=\frac{R\,n_T}{1+R} \]
\[ n_{A^-}=R\cdot n_{HA}\quad(\text{for given }n_{HA}) \]
\[ n_{HA}=\frac{n_{A^-}}{R}\quad(\text{for given }n_{A^-}) \]
\[ m=n\cdot M \]
Symbol legend
- \(\mathrm{pH}\): desired target pH
- \(\mathrm{p}K_a\): acid constant of buffer system
- \(R\): required mole ratio \(n_{A^-}/n_{HA}\)
- \(n_{HA}\): moles of acid form [mol]
- \(n_{A^-}\): moles of base form [mol]
- \(n_T\): total moles \(n_{HA}+n_{A^-}\) [mol]
- \(M\): molar mass [g/mol]
- \(m\): mass to weigh [g]
Detailed examples
Example 1 (fixed total moles):
Target \(\mathrm{pH}=7.40\), \(\mathrm{p}K_a=7.21\), \(n_T=0.100\,\mathrm{mol}\).
Then \(R=10^{0.19}\approx1.55\).
\(n_{HA}\approx0.039\,\mathrm{mol}\), \(n_{A^-}\approx0.061\,\mathrm{mol}\).
Target \(\mathrm{pH}=7.40\), \(\mathrm{p}K_a=7.21\), \(n_T=0.100\,\mathrm{mol}\).
Then \(R=10^{0.19}\approx1.55\).
\(n_{HA}\approx0.039\,\mathrm{mol}\), \(n_{A^-}\approx0.061\,\mathrm{mol}\).
Example 2 (acid moles given):
\(n_{HA}=0.050\,\mathrm{mol}\), same target pH.
Required base form: \(n_{A^-}=R\cdot n_{HA}\approx0.0775\,\mathrm{mol}\).
\(n_{HA}=0.050\,\mathrm{mol}\), same target pH.
Required base form: \(n_{A^-}=R\cdot n_{HA}\approx0.0775\,\mathrm{mol}\).
Example 3 (base moles given):
\(n_{A^-}=0.040\,\mathrm{mol}\), same target pH.
Required acid form: \(n_{HA}=n_{A^-}/R\approx0.0258\,\mathrm{mol}\).
\(n_{A^-}=0.040\,\mathrm{mol}\), same target pH.
Required acid form: \(n_{HA}=n_{A^-}/R\approx0.0258\,\mathrm{mol}\).
Example 4 (mass planning):
With known molar masses (e.g., phosphate pair), required masses follow directly from \(m=n\cdot M\) for each component.
With known molar masses (e.g., phosphate pair), required masses follow directly from \(m=n\cdot M\) for each component.
Deeper insight
Best operating range
Henderson-Hasselbalch is most reliable around \(\mathrm{pH}\approx\mathrm{p}K_a\pm1\). Outside this range, sensitivity to uncertainty and activity effects increases.
Practical correction step
Temperature, ionic strength, and non-ideal behavior can shift final pH. After preparing by calculation, perform fine pH adjustment with small acid/base additions.
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