Selecting a Buffer Pair

Introduction

Designing a buffer starts with a choice: which weak acid and conjugate base should be used? The obvious rule is to match pKa to the target pH, but that is only the first filter. A buffer that complexes a metal ion, precipitates with calcium, shifts with temperature or interferes with a measurement can ruin an experiment even if its pH is perfect. This page sets out a systematic way to choose a buffer pair.

Core explanation

Match pKa to the target pH. A buffer works best when the conjugate ratio is near 1 : 1, because there are then large reserves of both acid and base. Since pH = pKa + log([A⁻]/[HA]), the ratio stays between 1 : 10 and 10 : 1 only when the target pH lies within about one unit of pKa. Outside this range one reserve is small, and capacity against acid or base collapses. Ideally choose a pair with pKa within about 0.5 of the target.

Common pairs and their pKa values at 25 °C:

Conjugate pair pKa Useful range --- --- --- CH₃COOH / CH₃COO⁻ 4.76 3.8–5.8 H₂PO₄⁻ / HPO₄²⁻ 7.20 6.2–8.2 Tris-H⁺ / Tris 8.07 7.1–9.1 NH₄⁺ / NH₃ 9.25 8.3–10.3 HCO₃⁻ / CO₃²⁻ 10.33 9.3–11.3

Polyprotic choices. A polyprotic acid supplies several pairs. Phosphate gives buffers near pH 2.1, 7.2 and 12.3; citrate, with overlapping constants, covers a broad acid range. Always identify which step is being used, because the "acid" of one pair may be the "base" of another.

Chemical compatibility. The buffer must not interfere with the system:

- Phosphate precipitates Ca²⁺ and many transition-metal ions, and inhibits some enzymes. - Citrate and other carboxylates complex metal ions, lowering their free concentration. - Borate binds to compounds with neighbouring –OH groups, such as sugars. - Amine buffers such as Tris react with aldehydes and interfere with some protein assays. - Carbonate buffers exchange CO₂ with air, so they drift unless kept closed. - Ammonia is volatile, so open ammonia buffers slowly lose base and fall in pH.

Physical factors. The pKa of an amine buffer changes noticeably with temperature: Tris falls by about 0.03 per kelvin, so a Tris buffer made at 25 °C is about 0.3 units more acidic at 37 °C. Carboxylic acid and phosphate buffers change much less. Buffers with highly charged ions (phosphate, citrate) are also more sensitive to ionic strength through activity effects.

Optical and analytical demands. In spectroscopy the buffer must not absorb at the working wavelength; in electrochemistry it must not be oxidised or reduced; and in biology it should not pass through membranes. These needs led to the zwitterionic "Good's buffers" such as HEPES (pKa ≈ 7.5) and MES (pKa ≈ 6.1).

Step-by-step reasoning

To select a buffer pair:

1. State the target pH and working temperature. 2. List pairs with pKa within about ±1 of the target, preferring ±0.5. 3. Remove any pair that reacts with, binds or precipitates species in the system. 4. Check temperature sensitivity and volatility. 5. Choose the survivor and then design the ratio and concentration.

Visual explanation

Draw a pH scale from 2 to 12 and mark each pair's pKa with a bar extending one unit either side. For any target pH, draw a vertical line: the bars it crosses are the candidates. The bar whose centre is nearest the line gives the highest capacity.

Real-world analogy

Choosing a buffer is like choosing a tyre. The size (pKa) must fit the wheel (target pH), but you must also consider the road surface: a perfect-sized tyre made of the wrong material (an incompatible buffer) can still fail badly in use.

Real-world example

Cell-culture media are usually buffered with bicarbonate in a carbon dioxide incubator, sometimes supplemented with HEPES. Phosphate alone is avoided at high concentrations with calcium-rich media because calcium phosphate can precipitate, removing both calcium and buffer.

Why?

Why must pKa be close to the target pH? If pH is two units above pKa, the ratio [A⁻]/[HA] is 100 : 1. There is almost no HA left, so even a small amount of added base exhausts the acid reserve and the pH rises sharply.

Common misconception

"Any buffer can be made to give any pH by adjusting the ratio." Mathematically, a ratio of 1000 : 1 gives pH = pKa + 3, but such a mixture has almost no capacity in one direction. It is a poor buffer, even if its initial pH is correct.

Worked example

Question: A reaction must be run at pH 9.0 and 25 °C in the presence of Ca²⁺ ions. Choose a suitable buffer pair and find the required ratio.

Reasoning: Candidates within one unit: Tris (8.07) and NH₄⁺/NH₃ (9.25). Phosphate and carbonate are excluded because they precipitate calcium. NH₄⁺/NH₃ is closer to the target. Ratio: log([NH₃]/[NH₄⁺]) = 9.0 − 9.25 = −0.25, so [NH₃]/[NH₄⁺] = 10^(−0.25) = 0.56.

Answer: Ammonium/ammonia with NH₃ : NH₄⁺ ≈ 0.56 : 1, kept in a closed vessel because ammonia is volatile.

Quick check

1. Which of ethanoate, phosphate or ammonia buffers is best for a target pH of 7.0, and why? Answer: Phosphate, because pKa₂ = 7.20 is within 0.2 units of the target.

Exam focus

State the rule "pKa within one unit of the target pH" and justify it using the ratio range 1 : 10 to 10 : 1. For higher marks, mention at least one compatibility problem, such as phosphate precipitating calcium or Tris changing with temperature.

Advanced insight

For very precise work, the relevant constant is the apparent pKa at the actual ionic strength and temperature, not the thermodynamic value at infinite dilution. For H₂PO₄⁻/HPO₄²⁻ the apparent pKa at physiological ionic strength is about 6.8, noticeably lower than 7.20, because the doubly charged HPO₄²⁻ has a small activity coefficient.

Summary

Select a buffer pair whose pKa lies within about one unit, and ideally half a unit, of the target pH, so both reserves are substantial. Then reject pairs that precipitate, complex or react with components of the system, and consider temperature, volatility, ionic strength and analytical interference. Only then design the ratio and concentration.

Practice questions

1. Suggest a buffer pair for pH 4.5 and justify your choice. Answer: Ethanoic acid/ethanoate, because its pKa of 4.76 is within 0.3 units of 4.5. 2. Why is a Tris buffer prepared at pH 8.0 at 20 °C not at pH 8.0 at 37 °C? Answer: Tris pKa falls by about 0.03 per kelvin, so over 17 K the pH drops by about 0.5 units. 3. Why should a phosphate buffer be avoided for an enzyme that needs free Zn²⁺ or Ca²⁺ ions? Answer: Phosphate can precipitate these metal ions as insoluble phosphates, lowering their free concentration. 4. A carbonate buffer at pH 10 is left open to the air. Predict and explain the pH change. Answer: Carbon dioxide dissolves and converts CO₃²⁻ into HCO₃⁻, lowering the ratio [CO₃²⁻]/[HCO₃⁻], so the pH falls.