The Henderson-Hasselbalch equation is a formula that relates the pH of a solution to the strength of the acid in it and the ratio of that acid to its conjugate base. It looks like this:
pH = pKa + log([Base] / [Acid])
If you’re studying chemistry or biochemistry, this equation will follow you everywhere: buffer preparation, titration problems, drug absorption, blood chemistry. It’s one of the most practical tools in acid-base chemistry because it lets you estimate pH without solving a full equilibrium expression.
What Each Term Means
pH is the measure of how acidic or basic a solution is. Lower numbers mean more acidic, higher numbers mean more basic, and 7 is neutral.
pKa is a number that describes how strong a particular weak acid is. Specifically, it’s the pH at which the acid is exactly half dissociated, meaning the concentrations of the acid and its conjugate base are equal. A lower pKa means a stronger acid.
[Base] is the concentration of the conjugate base (the form of the molecule that has given up a proton). [Acid] is the concentration of the undissociated weak acid (the form still holding onto its proton). The ratio between these two determines whether the solution sits above or below the pKa on the pH scale.
When the base and acid concentrations are equal, the log term becomes zero (because log of 1 is 0), and the pH simply equals the pKa. This is the midpoint of a titration and the point of maximum buffering capacity.
Where the Equation Comes From
The derivation starts with the acid dissociation constant expression. When a weak acid dissolves in water, it partially splits into a hydrogen ion and its conjugate base. That equilibrium is described by Ka:
Ka = [H⁺][Base] / [Acid]
Rearrange this to isolate the hydrogen ion concentration:
[H⁺] = Ka × [Acid] / [Base]
Now take the negative logarithm of both sides. The negative log of [H⁺] is pH, and the negative log of Ka is pKa. A logarithm rule converts the division inside the log, flipping acid and base, which gives the final form:
pH = pKa + log([Base] / [Acid])
That’s all it is: a rearranged version of the equilibrium expression, converted into logarithmic form so you can work directly with pH values instead of tiny hydrogen ion concentrations.
How Buffers Work With This Equation
A buffer is a solution that resists changes in pH when you add small amounts of acid or base. Buffers are made from a weak acid paired with its conjugate base (or a weak base paired with its conjugate acid). The Henderson-Hasselbalch equation is the standard tool for designing them.
If you need a buffer at pH 5.0, you’d choose a weak acid with a pKa near 5.0, then adjust the ratio of base to acid to fine-tune. Need the pH slightly higher than the pKa? Use a bit more conjugate base. Need it lower? Use more acid. Buffers work best when the pH is within about one unit of the pKa, which corresponds to the acid and base concentrations being within a factor of 10 of each other. Outside that range, the solution runs low on one component and loses its ability to absorb added acid or base.
The Bicarbonate Buffer in Blood
Your blood maintains a remarkably stable pH of about 7.4, and the main system responsible is the bicarbonate buffer. Dissolved carbon dioxide reacts with water to form carbonic acid, which can release a proton to become bicarbonate. The pKa of this system is 6.1.
Plugging in the numbers: normal blood contains about 24 mmol/L of bicarbonate and 1.2 mmol/L of dissolved CO₂. The ratio of base to acid is 20:1, and log(20) is about 1.3. So pH = 6.1 + 1.3 = 7.4. That’s how the equation predicts normal blood pH from just two measurable values. When doctors evaluate acid-base disorders, they’re essentially checking whether changes in bicarbonate or CO₂ have shifted that ratio.
Drug Absorption Across Membranes
Most drugs are weak acids or weak bases, and whether they can cross a cell membrane depends on whether they’re in their ionized or un-ionized form. The un-ionized form is fat-soluble and passes through membranes easily. The ionized form is water-soluble and essentially gets trapped.
The Henderson-Hasselbalch equation predicts what fraction of a drug is ionized at any given pH. Consider a weakly acidic drug like aspirin, which has a pKa of about 3.5. In the stomach, where the pH is roughly 1.4, the equation tells you the vast majority of the drug is un-ionized. That means it readily crosses the stomach lining into the blood. In the small intestine, where the pH is closer to 6 or 7, far more of that same drug becomes ionized and less able to cross membranes directly.
For a weak base, the situation reverses. A weakly basic drug with a pKa of 4.4 would be mostly ionized in stomach acid, making absorption there poor. This is why the route of drug delivery and the pH of different body compartments matter so much in pharmacology. The equation provides the quantitative framework for predicting all of it.
Amino Acids and Protein Chemistry
Amino acids have multiple groups that can gain or lose protons, each with its own pKa. The Henderson-Hasselbalch equation is used to calculate the charge state of each group at a given pH, which in turn determines the overall charge of the amino acid. The pH at which an amino acid carries no net charge is called its isoelectric point, and estimating it requires applying the equation to each ionizable group. The same principle scales up to whole proteins: by accounting for every charged amino acid side chain plus the two ends of the protein backbone, researchers use the equation to estimate the isoelectric point of native proteins.
When the Equation Breaks Down
The Henderson-Hasselbalch equation is an approximation, not an exact solution. It assumes that the concentrations you plug in (the “initial” amounts of acid and base you mixed) are close to the actual equilibrium concentrations. That assumption holds well under certain conditions and fails badly under others.
The equation works best for acids with pKa values in the range of about 5 to 9, at moderate concentrations, when the acid and base amounts aren’t wildly unequal. Under those conditions, the difference between the approximate and exact pH is negligibly small.
It becomes unreliable when the pKa drifts more than two units away from 7 in either direction. For relatively strong weak acids like hydrofluoric acid, formic acid, and lactic acid (with Ka values around 10⁻⁴ or higher), the equation can’t accurately trace a titration curve. At the other extreme, very weak acids with Ka below 10⁻¹⁰ also cause problems because the breakdown of the conjugate base in water becomes significant.
Dilute solutions amplify the errors dramatically. With a Ka of 10⁻³ and concentrations of 0.01 M, even the midpoint of a titration (where the equation should perform best) gives a hydrogen ion concentration that’s off by as much as 365%. Push the concentration down to 0.001 M, and errors near the start of the titration can exceed 3,000%. A published analysis in the Journal of Chemical Education concluded that many textbook buffer problems solved with the Henderson-Hasselbalch equation don’t really warrant more than a single significant digit in the answer.
The equation also struggles near the very beginning and very end of a titration, where the ratio of acid to base is extremely lopsided. In those regions, small amounts of dissociation or hydrolysis that the equation ignores become large relative to the smaller component.
None of this means the equation is useless. For the vast majority of buffer calculations in biology and chemistry, where you’re working with moderate concentrations of acids in the pKa 5 to 9 range, it gives answers that are accurate and practical. You just need to recognize the boundaries.