Response to Stress of Aqueous Buffers

James Richard Fromm

Buffers are capable of absorbing H+ ions (and OH- ions) and in this way can resist changes of pH which would otherwise occur with the additions of acids (or bases). This phenomenon can be explained again by the law of mass action. If acid is added to the equilibrium mixture presented by [A-]/[HA] X [H+] = K, the H+ will rise. But in order to reach equilibrium again, [HA] must also rise; the latter can be achieved only by the recombination of H+ and A- to form HA. This reaction consumes nearly all of the added H+ ions, and the consequent change in pH is negligible. All of this presupposes, of course, that not too many H+ ions, or not too much acid, have been added. The capacity of the buffer is limited by the number of A- ions available to trap H+ ions.

Weak acids or weak bases in combination with their salts are, in general, adaptable for setting up buffers; their greatest capacity to buffer is around their pK value. Buffers are indispensable in most biochemical work. Commonly used are buffers of phosphate, citrate, glycine, and tris(hydroxymethyl)aminomethane (or simply "tris buffer"). The exact compositions of different buffer mixtures are listed in biochemical handbooks.

A chemical buffer or buffer solution is a solution which resists change in pH when hydrogen ions are added to or subtracted from the solution by chemical reactions or by other means. Buffer solutions are important because many chemical reactions will work best, or only, within a certain narrow range of pH values. This is particularly true of the chemical reactions which take place in living organisms. In biological systems a change in pH of one unit can change the rate of a particular reaction by a factor of between ten and over 100,000. To get an idea what this might mean, consider the reaction to be your food digestion and let it change in rate by four orders of magnitude. Since there are about 10,000 seconds in a day, this would mean eating three square meals every second (faster) or one square meal every nine years (slower).

Solutions which are very strongly acidic or very strongly basic are rarely deliberately buffered by addition of a chemical buffer because it already takes a relatively large amount of strong acid or strong base to change their pH significantly. For example, one liter of 0.01 molar HCl is at pH 2 and contains 10 mmol of hydrogen ion. Addition of 1.0 mmol of strong acid would increase this to 11 mmol, pH = 1.96, while addition of 1.0 mmol of strong base would reduce the amount of hydrogen ion to 9 mmol by reaction for a pH of 2.05. However, solutions which have an intermediate pH, between 2 and 12, can have their pH dramatically altered by addition of a small amount of strong acid or strong base unless a chemical buffer is present.

A chemical buffer is a solution which, by acid-base reactions, is capable of absorbing both added strong acid and added strong base. Since acids react with bases and not with other acids, while bases react with acids but not with other bases, only a solution which contains both an acid and a base can resist the effect of both kinds of addition by reaction. A chemical buffer consists of a solution of a conjugate acid-base pair with both species present in solution at reasonable concentrations.

The presence of both the acid and the base is necessary if the buffer is to be able to deal with both addition and subtraction of hydrogen ions. The equilibrium for the ionization of any arbitrary acid HA,

HA + H2O larrow.GIF (55 bytes)rarrow.gif (63 bytes) H3O+ + A-,

shifts one way or the other as required to absorb or give up protons.

The solution is at a maximum buffer capacity (the minimum dpH/dn) when pH = pKa, as can be seen algebraically:

Ka = [H3O+][A-]/[HA]; [H3O+] = Ka[HA]/[A-]

log [H3O+] = log Ka + log ([HA]/[A-])

pH = pKa - log([HA]/[A-])

This rearranged form of the ionization constant of an acid is sometimes called the Henderson-Hasselbalch equation.

Since pH = pKa if and only if [HA] = [A-], maximum buffer capacity of a conjugate acid-base pair is always found at pH = pKa. Reasonable buffer capacity is still obtained if the ratio of [HA] to [A-] is somewhere between 0.1 and 10, but outside this range it decreases rapidly. A chemical buffer can be effective about pH = pKa +/- 1. To make up a buffer solution one would first choose a reasonable acid-base conjugate pair on the basis of its pKa value and any other chemical constraints (one would not use the HCN/CN- pair, for example, in biological systems because cyanide is toxic). One would then adjust the concentrations such that both are reasonable (say 10-3 molar or above) while the desired pH is still obtained. The conjugate acid-base pairs glycinium ion/glycine, hydrogen citrate/citrate, dihydrogen phosphate/monohydrogen phosphate, and boric acid/hydrogen borate are often used for the preparation of aqueous buffers.

Example. Let us select an appropriate buffer for an aqueous solution of pH 8.00. Of the acid-base conjugate pairs commonly used for buffer preparation, boric acid/dihydrogen borate could be useful at pH 8.00 as could dihydrogen phosphate/monohydrogen phosphate. The monoprotic species hydrazine and hypochlorous acid have acid ionization constants of the right magnitude but tend to be otherwise reactive in aqueous solutions. Using the boric acid/dihydrogen borate pair,

[H3O+][H2BO3-]/[H3BO3] = 5.78 x 10-10

[H2BO3-]/[H3BO3] = 5.78 x 10-10/(1.0 x 10-8) = 0.0578

Borate buffers are most conveniently prepared from solid sodium borate with addition of sufficient hydrochloric acid to obtain the correct pH. In this example that would require for each mole of sodium borate almost three moles of hydrochloric acid.

Example. Let us select an appropriate buffer for an aqueous solution of pH 5.00 and calculate the equilibrium concentration ratio of acid and base forms at this pH. Then we will calculate the concentrations of acid and base forms if the total concentration of both is 0.01 molar.

For a buffer of pH 5.00 one would ideally have an acid-base conjugate pair for which pKa = 5.00. No convenient such conjugate acid-base pair exists, but for acetic acid pKa = 4.756 which is reasonably close.

Ka = [H3O+][CH3COO-]/[CH3COOH] = 1.75 x 10-5

[CH3COO-]/[CH3COOH] = 1.75 x 10-5/1.0 x 10-5 = 1.75

[CH3COO-] + [CH3COOH] = 0.01; 1.75[CH3COOH] + [CH3COOH] = 0.01; 2.75[CH3COOH] = 0.01; [CH3COOH] = 0.01/2.75 = 0.00364

[CH3COO-] = 0.01 - 0.00364 = 0.00636

Any procedure which yields these concentrations will produce an appropriate buffer.

Example. Let us calculate the concentrations of the buffer ions in a phenol/phenolate buffer whose pH is exactly 10.50. We can then give appropriate instructions for the preparation of this buffer from phenol and sodium phenolate, assuming the total phenol/phenolate concentration is to be 0.10 molar.

We begin with the acid ionization constant of the phenolate ion:

Ka = 1.08 x 10-10 = [H3O+][C6H5O-]/[C6H5OH]

1.08 x 10-10/3.16 x 10-11 = 3.42 = [C6H5O-]/[C6H5OH]

[C6H5O-] + [C6H5OH] = 0.10

3.42 = [C6H5O-]/(0.10 - [C6H5O-])

0.342 - 3.42[C6H5O-] = [C6H5O-]; 0.342 = 4.42[C6H5O-]

[C6H5O-] = 0.0773, [C6H5OH] = 0.0227

While any buffer solution having the correct mole ratio of 3.42 will have the correct pH, only the concentrations above would total 0.10 molar. Appropriate instructions would be to prepare a 0.100 molar solution of phenol and add to it sufficient strong base (NaOH) to amount to 0.0773 mol. This would produce the desired concentrations.

Copyright 1997 James R. Fromm