Henderson Hasselbalch Calculator
Calculate pH of buffer solutions using the Henderson-Hasselbalch equation from pKa and concentrations.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
pH = pKa + log([A-] / [HA])
Where pH is the acidity of the buffer solution, pKa is the negative log of the acid dissociation constant, [A-] is the molar concentration of the conjugate base, and [HA] is the molar concentration of the weak acid. When [A-] = [HA], the log term becomes zero and pH = pKa.
Worked Examples
Example 1: Acetate Buffer pH Calculation
Problem:Calculate the pH of a buffer containing 0.15 M acetic acid and 0.20 M sodium acetate (pKa = 4.76).
Solution:pH = pKa + log([A-]/[HA])\npH = 4.76 + log(0.20/0.15)\npH = 4.76 + log(1.333)\npH = 4.76 + 0.125\npH = 4.885\n[H+] = 10^(-4.885) = 1.303 x 10^(-5) M
Result:Buffer pH = 4.885 (slightly above pKa due to excess base)
Example 2: Phosphate Buffer for Cell Culture
Problem:A phosphate buffer (pKa = 7.20) uses 0.05 M NaH2PO4 and 0.08 M Na2HPO4. Find the pH.
Solution:pH = pKa + log([HPO4 2-]/[H2PO4-])\npH = 7.20 + log(0.08/0.05)\npH = 7.20 + log(1.60)\npH = 7.20 + 0.204\npH = 7.404\nThis is very close to physiological pH (7.4)
Result:Buffer pH = 7.404 (ideal for cell culture and biological experiments)
Frequently Asked Questions
What is the Henderson-Hasselbalch equation?
The Henderson-Hasselbalch equation is a mathematical relationship that relates the pH of a buffer solution to the pKa of the acid and the ratio of conjugate base to acid concentrations. The equation is pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. It was derived independently by Lawrence Joseph Henderson in 1908 and Karl Albert Hasselbalch in 1917. The equation is a rearrangement of the acid dissociation constant expression and provides a convenient way to calculate the pH of buffer solutions without solving quadratic equations. It is one of the most frequently used equations in biochemistry, pharmacology, and analytical chemistry.
What are the limitations of the Henderson-Hasselbalch equation?
The Henderson-Hasselbalch equation has several important limitations that users should understand. It assumes that the equilibrium concentrations of the acid and conjugate base are approximately equal to the analytical (prepared) concentrations, which is only valid when the acid is weak and concentrations are not too dilute. For very dilute solutions (below 0.001 M) or very strong acids, the approximation breaks down significantly. The equation also ignores activity coefficients, which become important at high ionic strengths above 0.1 M. It does not account for the autoionization of water, which matters when pH is very high or very low. Polyprotic acids require separate Henderson-Hasselbalch calculations for each ionizable group, adding complexity that the simple equation does not address.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy