Buffers and pH: pKa, the Henderson–Hasselbalch equation and choosing a buffer

A buffer is a solution that holds its pH steady when small amounts of acid or base are added. Most laboratory work with peptides and proteins happens in a buffer, because charge, solubility and stability all change with pH. This guide explains what pH and pKa mean, how the Henderson–Hasselbalch equation links them, and how to choose a buffer for a given job.

Terms are defined in the glossary.

pH in brief

pH measures how acidic a water-based solution is. It is the negative logarithm of the hydrogen ion concentration. Pure water at 25 °C has a pH of 7. Lower numbers are acidic and higher numbers are basic (alkaline).

The scale is logarithmic. A drop of one pH unit means ten times more hydrogen ions. A solution at pH 4 is ten times more acidic than one at pH 5, and a hundred times more acidic than one at pH 6.

What pKa means

A weak acid only partly gives up its proton in water. Some molecules stay as the acid (HA) and some become the conjugate base (A⁻). The balance between them depends on pH.

The pKa is the pH at which exactly half the acid is in each form. Below the pKa, the acid form dominates. Above it, the base form dominates. Each pH unit away from the pKa shifts the ratio tenfold.

Acetic acid, for example, has a pKa of 4.76. At pH 4.76, half is acetic acid and half is acetate. At pH 5.76, there is ten times more acetate than acetic acid.

The same idea decides the charge on each ionisable group in a peptide. The isoelectric point guide uses it to estimate a peptide's net charge at any pH.

The Henderson–Hasselbalch equation

The equation links pH, pKa and the ratio of the two forms:

pH = pKa + log([A⁻] / [HA])

Here [A⁻] is the concentration of the base form and [HA] is the concentration of the acid form. Three results follow:

• Equal amounts give pH = pKa. When [A⁻] = [HA], the ratio is 1 and log(1) = 0.
• A 10:1 ratio moves the pH by one unit. Ten times more base than acid gives pH = pKa + 1. Ten times more acid gives pH = pKa − 1.
• Only the ratio sets the pH, not the total amount. Diluting a buffer changes its pH very little, at least within the range where the equation holds.

Worked example: an acetate buffer

Mix acetic acid and sodium acetate so the solution is 0.10 M in each.

• The ratio is 0.10 / 0.10 = 1, so pH = 4.76 + 0 = 4.76.

To make a buffer at pH 5.00 instead:

• 5.00 = 4.76 + log(ratio), so log(ratio) = 0.24.
• The ratio is 10^0.24, which is about 1.74.
• So you need about 1.74 times as much acetate as acetic acid.

For the arithmetic of making up the solutions, see molarity, mg/mL and dilutions.

Where the equation falls short

The equation uses concentrations. Real solutions behave according to activities, which differ from concentrations as ionic strength rises. The equation also assumes the acid and base don't react significantly with water. It gets less reliable in very dilute or very concentrated solutions, and when the pH is far from the pKa (Po & Senozan, 2001). In practice, labs calculate a starting point and then adjust the pH with a calibrated meter.

How a buffer resists pH change

Add a little strong acid to a buffer and the base form (A⁻) takes up the extra protons, becoming HA. Add a little strong base and the acid form (HA) gives up protons to neutralise it. Either way, the ratio of A⁻ to HA shifts only slightly, so the pH barely moves.

Two numbers describe how well a buffer does this:

• Buffer range. A buffer works well within about one pH unit either side of its pKa. Outside that range, one form runs low and the buffer has little left to react with.
• Buffer capacity. This is how much acid or base the buffer can absorb before the pH moves by a set amount. It rises with concentration. A 100 mM buffer holds its pH far better than a 10 mM one at the same pH. Capacity is highest at the pKa.

Choosing a buffer

Start with the pH you need, then pick a buffer whose pKa is within about one unit of it. Common laboratory buffers, with approximate pKa values at 25 °C:

Other points to weigh:

• Temperature. pKa values shift with temperature. Tris is the best-known case: its pH falls by about 0.03 units for every 1 °C rise. A Tris buffer set to pH 8.0 at room temperature will read higher in a cold room. Set the pH at the temperature you'll use it.
• Interactions. Phosphate forms insoluble salts with calcium and some other metals. Citrate binds metal ions. Tris has a primary amine that can react with some reagents.
• Detection methods. Some buffers absorb UV light or interfere with assays. Non-volatile salts such as phosphate suppress the signal in mass spectrometry.
• Purity of the buffer itself. Use a grade suited to the method, and record the lot.

Good and colleagues listed the properties of an ideal biological buffer: a pKa between 6 and 8, high water solubility, low binding of metals, little UV absorbance and low reactivity (Good et al., 1966). MES and HEPES came from that work.

Phosphate-buffered saline (PBS)

PBS is a phosphate buffer with added sodium chloride and potassium chloride. A common recipe is 137 mM NaCl, 2.7 mM KCl, 10 mM Na₂HPO₄ and 1.8 mM KH₂PO₄, adjusted to pH 7.4 (Cold Spring Harbor Protocols). It is widely used for washing, diluting and storing samples in cell and protein work. Recipes vary between labs, so state which one you used.

Buffers and peptides

pH affects a peptide in solution in several ways:

• Solubility. A peptide is least soluble near its isoelectric point (pI), where its net charge is zero. Choosing a buffer pH well away from the pI usually helps. See peptide solubility: choosing a solvent and acetic acid as a peptide solvent.
• Stability. Some breakdown reactions speed up at certain pH values. Free cysteine thiols oxidise faster above pH 7, and deamidation of asparagine is faster at neutral to basic pH. See reading impurity peaks.
• Analysis. Volatile buffers such as ammonium acetate and ammonium bicarbonate leave little residue after freeze-drying and suit mass spectrometry. Phosphate does not.

Trifluoroacetic acid (TFA), present as a counter-ion in many synthetic peptides, is a strong acid rather than a buffer. Dissolving a TFA salt in unbuffered water can give a mildly acidic solution. See TFA counter-ions and salt exchange.

Making up a buffer

1. Calculate the masses from the molarity you need.
2. Dissolve the buffer components in about 80% of the final volume of purified water.
3. Calibrate the pH meter with at least two standard solutions that bracket your target pH.
4. Adjust the pH with a strong acid or base, adding it slowly while stirring. Measure at the temperature you'll use the buffer.
5. Make up to the final volume in a volumetric flask and mix.
6. Label it with the contents, pH, date and your initials.

Adjusting the pH changes the ionic strength, so for exact work weigh out both the acid and base forms in the ratio the Henderson–Hasselbalch equation gives, then make small final adjustments.

Related guides

For how pKa values decide a peptide's charge, see isoelectric point and net charge. For the side chains that carry those charges, see the 20 amino acids. Every lot has its own COA, published on the product page and on that lot's own page. See Quality.