How Buffers Resist pH Change: The Henderson-Hasselbalch Equation

Add a few drops of acid to pure water and the pH drops sharply. Add the same drops to a buffer and the pH barely moves. Buffers are mixtures that resist pH change, and they are everywhere, from the lab bench to the fluid in your veins. Their behaviour follows from a simple balance between a weak acid and its conjugate base.

What a buffer is

A buffer contains a weak acid and its conjugate base in comparable amounts. The weak acid can absorb added hydroxide ions by donating a proton, and the conjugate base can absorb added hydrogen ions by accepting a proton. Both components are present at the same time, so each one neutralizes the stress that the other cannot handle alone.

The buffer does not stop pH from changing. It limits the change. Once one component is used up, the buffer loses its power, and the pH begins to move quickly. Understanding how much the pH moves, and when, requires the equation that links pH to the ratio of the two components.

The acetic acid example

Acetic acid, CH3COOH, is a weak acid with a dissociation constant Ka of about 1.8 × 10^-5. It establishes an equilibrium with its conjugate base, acetate, CH3COO-. Mixing acetic acid with sodium acetate supplies both components at once. When the acid and base concentrations are equal, the solution has a pH equal to the pKa, which is about 4.76.

The pKa is simply the negative logarithm of Ka. A smaller pKa means a stronger acid. Buffers work best near their pKa, because that is where both components are present in large amounts.

The Henderson-Hasselbalch equation

The relationship between pH and the component ratio is the Henderson-Hasselbalch equation: pH = pKa + log10([A-] / [HA]). Here [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. The equation comes from rearranging the Ka expression and taking logarithms. It is an approximation that ignores the small hydrogen ion contribution from the acid's own dissociation, so it works well when both concentrations are large compared with the hydrogen ion concentration.

The equation shows the key feature of buffers. The pH depends on the ratio of base to acid, not on their absolute amounts. Doubling both concentrations leaves the pH unchanged, but doubling the buffer's capacity to absorb acid or base.

Worked example: adding acid

Consider one litre of a solution containing 0.10 mol of acetic acid and 0.10 mol of acetate. Its pH equals the pKa, which is 4.76. Now add 0.010 mol of hydrochloric acid. The added hydrogen ions react with acetate and convert it to acetic acid. Acetate falls to 0.090 mol, and acetic acid rises to 0.110 mol.

Applying the equation gives pH = 4.76 + log10(0.090 / 0.110) = 4.76 + log10(0.818) = 4.76 - 0.087 ≈ 4.67. The pH dropped by only about 0.09 units. The same 0.010 mol of hydrochloric acid added to one litre of pure water would have produced a pH of 2.00, a drop of more than five units.

Worked example: adding base

Now add 0.010 mol of sodium hydroxide to the same buffer. The hydroxide ions react with acetic acid and convert it to acetate. Acetic acid falls to 0.090 mol, and acetate rises to 0.110 mol. The pH becomes 4.76 + log10(0.110 / 0.090) = 4.76 + 0.087 ≈ 4.85.

The following table compares the buffer and pure water under the same additions.

Condition	Starting pH	After 0.010 mol HCl	After 0.010 mol NaOH
Acetate buffer (0.10 M each)	4.76	about 4.67	about 4.85
Pure water (1 L)	7.00	2.00	12.00

The buffer shifts by about 0.09 units in either direction, while pure water shifts by five units with acid and five with base. That contrast is the whole point of a buffer.

Buffer range and capacity

A buffer works effectively over a range of about one pH unit on either side of its pKa, which corresponds to base-to-acid ratios between 10:1 and 1:10. Outside that range, one component is so dominant that the other cannot supply enough neutralizing capacity, and the pH changes quickly. This is why chemists choose a buffer whose pKa lies close to the target pH.

Buffer capacity measures how much acid or base the solution can absorb before the pH shifts a set amount. It depends on the total concentration of the buffer components. A 1.0 M acetate buffer can absorb ten times more acid than a 0.10 M buffer with the same ratio, while keeping the same pH.

Blood as a buffer

Human blood maintains pH close to 7.4, and the main buffer is the carbonic acid and bicarbonate system. Dissolved carbon dioxide forms carbonic acid, which releases a proton and bicarbonate. The effective pKa of this system in blood is about 6.1, which is well below 7.4. A bicarbonate-to-carbonic acid ratio of about 20 to 1 gives pH = 6.1 + log10(20) ≈ 6.1 + 1.3 = 7.4, which matches the measured value.

The lungs help regulate this buffer by controlling how much carbon dioxide leaves the blood. Breathing faster removes more carbon dioxide, which lowers carbonic acid and raises pH. Slower breathing does the opposite. The kidneys adjust bicarbonate levels over longer periods. Together these mechanisms keep the buffer working near its target ratio.

Choosing a buffer in the lab

Laboratory buffers are selected by matching pKa to the desired pH. Phosphate buffers have a pKa near 7.2, which makes them a common choice for biological work near neutral pH. Tris buffers have a pKa near 8.1 and suit slightly basic conditions. Acetate buffers near pH 4.8 are common for slightly acidic work.

Other factors also matter. Some buffers bind metal ions, and some change pKa noticeably with temperature. Temperature sensitivity is important when a procedure requires a pH that must hold across different working conditions. Always check the temperature dependence of the buffer before relying on it.

Limits of buffers

Buffers have limits. Adding a large amount of strong acid or base uses up one component entirely, and then the pH changes sharply. Diluting a buffer keeps the ratio the same, so the pH stays nearly unchanged, but the total capacity drops. Temperature shifts pKa, so a buffer prepared at one temperature may read a different pH at another.

Buffers also do not change the underlying chemistry. They control the pH of a solution, but they do not remove the cause of an acid or base addition. Understanding the limits prevents overconfidence in situations where the buffer will be overwhelmed.

Key takeaways

A buffer holds pH steady because a weak acid and its conjugate base can each neutralize added hydroxide or hydrogen ions. The Henderson-Hasselbalch equation links pH to the ratio of base to acid, which is why the pH depends on the ratio and not on the absolute amounts.

Buffers work best within about one pH unit of their pKa. Worked examples show a drop of about 0.09 units for acetate, compared with five units for pure water. Blood uses the same principle with a carbonate system and a 20 to 1 ratio that gives pH 7.4.

Choosing a buffer means matching its pKa to the target pH and checking its capacity and temperature behaviour. With those three points in mind, buffer design becomes a straightforward calculation rather than guesswork.