Definitions

# Buffer solution

[buhf-er]
For an individual weak acid or weak base component, see Buffering agent. For uses not related to acid-base chemistry, see Buffer (disambiguation).

A buffer solution is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. It has the property that the pH of the solution changes very little when a small amount of acid or base is added to it. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of chemical applications.

## Theory

In a simple buffer solution there is an equilibrium between a weak acid, HA, and its conjugate base, A-.

HA + H2O $rightleftharpoons$ H3O+ + A
When hydrogen ions are added to the solution the equilibrium moves to the left, in accordance with Le Chatelier's principle, as there are hydrogen ions on the right-hand side of the equilibrium expression. When hydroxide ions are added the equilibrium moves to the right as hydrogen ions are removed in the reaction H+ + OH- → H2O. Thus, some of the added reagent is consumed in shifting the equilibrium and the pH changes by less than it would do if the solution were not buffered.

The acid dissociation constant for a weak acid, HA, is defined as

$Kmathrm\left\{_a = frac\left\{\left[H^+\right]\left[A^-\right]\right\}\left\{\left[HA\right]\right\}\right\}$
Simple manipulation with logarithms gives the Henderson-Hasselbalch equation, which describes pH in terms of pKa
$mbox\left\{pH=p\right\}Kmathrm\left\{_a+log_\left\{10\right\}frac\left\{\left[A^-\right]\right\}\left\{\left[HA\right]\right\}\right\}.$
In this equation [A] is the concentration of the conjugate base and [HA] is the concentration of the acid. It follows that when the concentrations of acid and conjugate base are equal, often described as half-neutralization, pH=pKa. In general, the pH of a buffer solution may be easily calculated, knowing the composition of the mixture, by means of an ICE table.

The same considerations apply to a mixture of a weak base, B and its conjugate acid BH+.

B + H2O $rightleftharpoons$ BH+ + OH-.
The pKa value to be used is that of the acid conjugate to the base.

In general a buffer solution may be made up of more than one weak acid and its conjugate base; if the individual buffer regions overlap a wider buffer region is created by mixing the two buffering agents.

## Buffer capacity

Buffer capacity is a quantitative measure of the resistance of a buffer solution to pH change on addition of hydroxide ions. It can be defined as follows.

buffer capacity = $mathrm\left\{frac\left\{dn\right\}\left\{d\left(pH\right)\right\}\right\}$
where dn is an infinitesimal amount of added base and d(pH) is the resulting infinitesimal change in pH. With this definition the buffer capacity can be expressed as
$mathrm\left\{frac\left\{dn\right\}\left\{d\left(pH\right)\right\}=2.303 left\left(frac\left\{mathit\left\{K\right\}_w\right\}\left\{\left[H^+\right]\right\}+\left[H^+\right]+frac\left\{C_A mathit\left\{K\right\}_a\left[H^+\right]\right\}\left\{left\left(mathit\left\{K\right\}_a+\left[H^+\right]right\right)^2\right\} right\right)\right\},$
where Kw is the self-ionization constant of water and CA is the analytical concentration of the acid, equal to [HA]+[A-]. The term Kw/[H+] becomes significant at pH greater than about 11.5 and the second term becomes significant at pH less than about 2. Both these terms are properities of water and are independent of the weak acid. Considering the third term, it follows that

1. Buffer capacity of a weak acid reaches its maximum value when pH = pKa
2. At pH = pKa ± 1 the buffer capacity falls to 33% of the maximum value. This is the approximate range within which buffering by a weak acid is effective. Note: at pH = pKa - 1, The Henderson-Hasselbalch equation shows that the ratio [HA]:[A-] is 10:1.
3. Buffer capacity is directly proportional to the analytical concentration of the acid.

## Applications

Their resistance to changes in pH makes buffer solutions very useful for chemical manufacturing and essential for many biochemical processes. The ideal buffer for a particular pH has a pKa equal to that pH, since such a solution has maximum buffer capacity.

Buffer solutions are necessary to keep the correct pH for enzymes in many organisms to work. Many enzymes work only under very precise conditions; if the pH strays too far out of the margin, the enzymes slow or stop working and can denature, thus permanently disabling its catalytic activity. A buffer of carbonic acid (H2CO3) and bicarbonate (HCO3) is present in blood plasma, to maintain a pH between 7.35 and 7.45.

Industrially, buffer solutions are used in fermentation processes and in setting the correct conditions for dyes used in colouring fabrics. They are also used in chemical analysis and calibration of pH meters.

### Useful buffer mixtures

Components pH range
HCl, sodium citrate 1 - 5
citric acid, sodium citrate 2.5 - 5.6
acetic acid, sodium acetate 3.7 - 5.6
Na2HPO4, NaH2PO4 6 - 9
Borax, sodium hydroxide 9.2 - 11

### "Universal" buffer mixtures

By combining substances with pKa values differing by only two or less and adjusting the pH a wide-range buffers can be obtained. Citric acid is a useful component of a buffer mixture because it has three pKa values, separated by less than two. The buffer range can be extended by adding other buffering agents. The following two-component mixtures have a buffer range of pH 3 to 8.
0.2M Na2HPO4 /mL 0.1M Citric Acid /mL pH
20.55 79.45 3.0
38.55 61.45 4.0
51.50 48.50 5.0
63.15 36.85 6.0
82.35 17.65 7.0
97.25 2.75 8.0

A mixture containing citric acid, potassium dihydrogen phosphate, boric acid, and diethyl barbituric acid can be made to cover the pH range 2.6 to 12.

### Common buffer compounds used in biology

Common Name pKa
at 25°C
Buffer Range Temp Effect
(pH / °C)**
Mol.
Weight
Full Compound Name
TAPS 8.43 7.7–9.1 −0.018 243.3 3-{[tris(hydroxymethyl)methyl]amino}propanesulfonic acid
Bicine 8.35 7.6–9.0 −0.018 163.2 N,N-bis(2-hydroxyethyl)glycine
Tris 8.06 7.5–9.0 −0.028 121.14 tris(hydroxymethyl)methylamine
Tricine 8.05 7.4–8.8 −0.021 179.2 N-tris(hydroxymethyl)methylglycine
HEPES 7.48 6.8–8.2 −0.014 238.3 4-2-hydroxyethyl-1-piperazineethanesulfonic acid
TES 7.40 6.8–8.2 −0.020 229.20 2-{[tris(hydroxymethyl)methyl]amino}ethanesulfonic acid
MOPS 7.20 6.5–7.9 −0.015 209.3 3-(N-morpholino)propanesulfonic acid
PIPES 6.76 6.1–7.5 −0.008 302.4 piperazine-N,N′-bis(2-ethanesulfonic acid)
Cacodylate 6.27 5.0–7.4 138.0 dimethylarsinic acid
MES 6.15 5.5–6.7 −0.011 195.2 2-(N-morpholino)ethanesulfonic acid

** Values are approximate