 In chemistry, the Henderson Hasselbalch equation describes the derivation of pH as a measure of acidity (using pKa, the negative log of the acid dissociation constant) in biological and chemical systems. The equation is also useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions (it is widely used to calculate the isoelectric point of proteins).

## The Henderson Hasselbalch Equation is given by: $Henderson Hasselbalch Equation$

Here, [HA] is the molar concentration of the undissociated weak acid, [A⁻] is the molar concentration (molarity, M) of this acid’s conjugate base & pKa is −log10Ka where Ka is the acid dissociation constant, that is: $\mathrm{p}K_\mathrm{a} = - \log_{10} (K_\mathrm{a}) = - \log_{10} \left ( \frac{[\mathrm{H}_{3}\mathrm{O}^+][\mathrm{A}^-]}{[\mathrm{HA}]} \right)$

For the non-specific Brønsted acid-base reaction: $\mathrm{HA} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{A}^- + \mathrm{H}_{3}\mathrm{O}^+$

In these equations, A⁻ denotes the ionic form of the relevant acid. Bracketed quantities such as [base] and [acid] denote the molar concentration of the quantity enclosed.

The Henderson-Hasselbalch equation is valid when it contains equilibrium concentrations of an acid and a conjugate base. In the case of solutions containing not-so-weak acids (or not-so-weak bases) equilibrium concentrations can be far from those predicted by the neutralization stoichiometry.

Here are several observations from Henderson Hasselbalch equation:

• If the pH = pKa, the log of the ratio of dissociate acid and associated acid will be zero, so the concentrations of the two species will be the same. In other words, when the pH equals the pKa, the acid will be half dissociated.
• As the pH increases or decreases by one unit relative to the pKa, the ratio of the dissociate form to the associated form of the acid changes by factors of 10. That is, if the pH of a solution is 6 and the pKa is 7, the ratio of [ A-]/[ HA] will be 0.1, will if the pH were 5, the ratio would be 0.01 and if the pH were 7, the ratio would be 1.
• If the pH is below the pKa, the ratio will be < 1, while if the pH is above the pKa, the ratio will be >1.
• The Henderson-Hasselbalch equation can be also used in the case of polyprotic acids, as long as the consecutive pKa values differ by at least 2 (better 3). Thus it can be safely used in the case of phosphoric buffers (pKa1=2.148, pKa2=7.199, pKa3=12.35), but not in the case of citric acid (pKa1=3.128, pKa2=4.761, pKa3=6.396).

## Limitations

• The assumption that the concentration of the acid and its conjugate base at equilibrium will remain the same as the formal concentration. This neglects the dissociation of the acid and the binding of H+ to the base.
• The dissociation of water and relative water concentration itself is neglected as well.

These approximations will fail when dealing with relatively strong acids or bases (pKa more than a couple units away from 7), dilute or very concentrated solutions (less than 1 mM or greater than 1M), or heavily skewed acid/base ratios (more than 100 to 1). In high buffer dilutions, where the concentration of protons arising from water become equally or more prevalent than the buffer species themselves (at pH 7, this means buffer component concentrations of <10−5 M formally, but practically much higher), the pKa of the ‘buffer’ system will tend towards neutrality.

That’s all there’s to know about the equation. Want to know how Chemistry plays a role in our everyday life click here.

All the best!

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