Buffer Solutions and Buffer Capacity

A buffer solution resists changes in pH when small amounts of acid or base are added, because it contains a weak acid and its conjugate base (or a weak base and its conjugate acid) in comparable amounts; buffer capacity is the amount of acid or base the buffer can absorb before its pH changes significantly. In brief: adding 0.010 mol of HCl to 1.00 L of pure water changes the pH from 7 to 2, but adding it to 1.00 L of an acetic acid/acetate buffer (0.100 mol/L each) changes the pH only from 4.76 to 4.67.

Living organisms, many industrial processes and analytical methods need a stable pH. Buffers make that possible. This article explains how buffers work, how to choose and prepare them, how to calculate pH changes after additions, what determines the capacity and range, lists common buffers in a table, works through examples and gives some history.

How does a buffer work?

In an acetic acid/acetate buffer, CH3COOH ⇌ H+ + CH3COO−. If acid (H+) is added, it reacts with the conjugate base: CH3COO− + H+ → CH3COOH. If base (OH−) is added, it reacts with the weak acid: CH3COOH + OH− → CH3COO− + H2O. Either way the ratio [A−] ÷ [HA] changes only a little, and so does the pH.

CH3COO− + H+ → CH3COOH CH3COOH + OH− → CH3COO− + H2O

How do you make a buffer?

  1. Choose a weak acid with pKa close to the pH wanted (within ±1).
  2. Calculate the ratio [A−] ÷ [HA] = 10(pH − pKa).
  3. Choose the total concentration for the capacity required (typically 0.05 to 0.5 mol/L).
  4. Prepare by mixing the acid and its salt, or by adding strong base to a measured amount of weak acid (partial neutralization), or strong acid to a weak base.
  5. Check and adjust the pH with a calibrated meter.

What is buffer capacity?

Capacity depends on two things. It is greater when the total concentration is greater, and it is largest when [HA] = [A−], that is when pH = pKa. The effective range is pKa ± 1, where the ratio lies between 1 : 10 and 10 : 1. Beyond this range one component is nearly used up. A buffer can neutralize at most about as many moles of strong acid as it contains conjugate base, and as many moles of strong base as it contains weak acid.

Relative buffer capacity against pH minus pKa −3 −2 −1 0 1 2 3 0 0.5 1 pH − pKa Relative buffer capacity pKa ± 1 33%
Buffer capacity relative to its maximum, for a fixed total concentration. It peaks where pH equals pKa (equal amounts of acid and base) and falls off on both sides. At pKa ± 1, the edges of the useful range (shaded), the capacity is about one third of the maximum.

Common buffer systems

Common buffers and their useful pH ranges
Buffer pairpKaUseful rangeUse
Acetic acid / acetate4.763.8 to 5.8Food, laboratory
Carbonic acid / hydrogencarbonate6.35 (6.1 in blood)5.4 to 7.4Blood, natural waters
Dihydrogen / hydrogen phosphate7.206.2 to 8.2Cells, biochemistry
Tris / tris-H+8.077.1 to 9.1Molecular biology
Ammonium / ammonia9.258.3 to 10.3Analytical chemistry
Hydrogencarbonate / carbonate10.339.3 to 11.3Water treatment

Worked examples

  1. pH of a buffer. 0.100 mol/L acetic acid and 0.100 mol/L sodium acetate: pH = pKa + log(1) = 4.76.
  2. Adding acid. 0.0100 mol of HCl is added to 1.00 L of this buffer. Acetate falls to 0.090, acetic acid rises to 0.110: pH = 4.76 + log(0.090 ÷ 0.110) = 4.67 (change −0.09).
  3. Adding base. 0.0100 mol of NaOH instead: acetate 0.110, acid 0.090: pH = 4.76 + log(0.110 ÷ 0.090) = 4.85 (change +0.09).
    A− HA 0.100 : 0.100 pH = 4.76 0.090 : 0.110 pH = 4.67 0.110 : 0.090 pH = 4.85
  4. Pure water for comparison. 0.0100 mol of HCl in 1.00 L of water gives pH 2.00, a change of 5 units.
  5. Prepare pH 5.00. The ratio [A−] ÷ [HA] = 10(5.00 − 4.76) = 1.74. For 1.00 L with total 0.274 mol/L: 0.100 mol of acetic acid and 0.174 mol of acetate.
  6. Partial neutralization. 0.200 mol of acetic acid with 0.050 mol of NaOH gives 0.150 mol HA and 0.050 mol A−: pH = 4.76 + log(0.050 ÷ 0.150) = 4.28.
  7. Capacity limit. The buffer with 0.100 mol of each in 1.00 L can absorb about 0.100 mol of added acid before the acetate is gone, but the pH is stable only for much less. After 0.090 mol of HCl, the ratio is 0.010 ÷ 0.190 and pH = 4.76 + log(0.0526) = 3.48.

Where are buffers found?

Who developed buffers?

Lawrence Henderson described the buffering of blood by carbonic acid and bicarbonate in 1908. Søren Sørensen introduced pH in 1909 and designed standard buffer mixtures. Norman Good and colleagues developed a set of organic buffers for biology in 1966.

Which mistakes are common?

Mistake 1: Mixing a strong acid with its salt

HCl and NaCl is not a buffer. You need a weak acid and its conjugate base.

Mistake 2: Choosing a buffer with the wrong pKa

Outside pKa ± 1, capacity is poor.

Mistake 3: Believing that a buffer fixes the pH forever

It resists change only until one component is used up.

Mistake 4: Forgetting that dilution barely changes the pH but lowers capacity

The ratio stays the same, but there is less buffer to react.