Buffers

1. Basic Principles

The term buffer solution usually refers to a solution that minimizes changes in pH when hydrogen ions (hydrons, H+) are added to the solution or removed from it. (As discussed in reference1, IUPAC has approved hydron to designate a hydrogen cation when a term independent of hydrogen isotope is desired.) Such a solution is therefore said to buffer the pH. Solutions can also be designed to buffer other species, particularly metal ions, as will be described below.

Because the concentration of hydrogen ions in biological media is low, usually about 0.1 µM, it could be greatly changed by the production or consumption of very small quantities of hydrogen ions in chemical reactions. This is what makes buffering commonly necessary in experiments in molecular biology. The principle of a buffer is simple. Relative to the low concentration of free hydrogen ions, the buffer consists of much higher concentrations of both a base, A–(ie, a substance that can combine reversibly with the hydrons), and its conjugate acid, HA, which is formed when the base combines with a hydron. Hence the equilibrium

is established. Subsequently, any addition of H+ causes a much smaller increase in its free concentration, [H+], because some of the hydrons are used up in making more HA to displace this equilibrium to the left. Likewise, any fall in [H+] is diminished because it leads to the dissociation of HA.

2. Simple Theory

Users of buffers need to be aware of many features of their action if they are not to make mistakes that can easily ruin their experiments. For this, a little theory of buffer solutions is required.

2.1. Dissociation of Water 

Water spontaneously dissociates into one hydrogen ion and one hydroxide ion:

Because of the equilibrium, the product [H+][OH–] is constant; its value, about 10–14 M2, changes only slightly with temperature. Both the hydrons and the hydroxide ions will be largely hydrated, reversibly combined with one or more water molecules. In this article, the term acid is used in the sense of a Brønsted acid, a substance that can donate a hydron, and base is used to mean a Brønsted base, a substance that can combine with one. If no such acid or base is added to pure water, the values of [H+] and [OH–] are equal, namely, 10–7M, ie, 0.1 µM. Given that the pH is defined as 

the pH is 7. The pH scale is useful in water over about the range 0 to 14, over which [H+] varies from 1 M to 10^–14 M, and [OH–] from 10^–14 M to 1 M.

2.2. The pKa and the pH

The acid HA will have a dissociation constant, K_a, the equilibrium constant for reaction (1), which is defined as 

Rearranging this to find [H+] gives 

and taking the negative logarithm of each side to find the pH [eq. (3)] gives 

 if we define pK_a as –logK_a. This is known as the Henderson–Hasselbalch equation, and it is fundamental for understanding buffer action and how single groups titrate.

Figure 1 shows the fractional concentration of the base, ie, [A–]/([HA] + [A–]), as a function of pH. The first point to note is that, when the pH = pK_a,log([A–]/[HA] = 0, and so [A–]/[HA] = 1, and [A–]is 0.5 of its maximal value. Hence, the pKa is the pH at which the acid is half-dissociated. When the pH is one unit above the pKa, log([A–]/[HA]) = 1, and so [A–]/[HA] = 0, and hence [A–] is 10/11, ie, 0.91, of its maximal value as shown; when the pH is two units above the pKa, log([A–]/[HA]) = 2, and so [A–]/[HA] = 100 and, hence, [A–] is 100/101, ie, 0.99 of its maximal value. Similarly, when the pH is one unit below the pKa, log([A–]/[HA]) = –1, and so [A–]/[HA] = 0.1, and [A–] is 0.091 of its maximal value; when the pH is two units below the pKa, [A–] is 0.01 of its maximal value. These figures illustrate that comparing the pH with the pK of a substance instantly indicates how much of the substance or group is in its hydronated and unhydronated forms. All simple acids follow the curve of Figure 1; they differ only in their pK_a values.

Figure 1. The dependence of the fractional concentration of the basic form of a monobasic acid on the pH. The vertical axis shows the concentration of A– expressed as a fraction of the sum of the concentrations of A– and HA. Vertical lines mark: (1) pH = pK_a – 1, when [A–] = 0.1[HA], so the fractional concentration of A– is 1/11; (2) pH = pKa, when [A–] = [HA], so the fractional concentration of A– is 1/2; (3) pH = pK_a + 1, when [A–] = 10[HA], so the fractional concentration of A– is 10/11.

2.3. Theory of Buffering 

With properly buffered solutions, both [A–] and [HA] will be much greater than [H+] and [OH–]. In this case, any H+ produced in a reaction converts A– into HA, and any H+ taken up dissociates from HA to convert it into A–. To see the consequences of this, it is convenient to modify the Henderson–Hasselbalch equation as follows:

For good buffering, it is necessary for both [A–] and [HA–] to be large enough so the logarithm of neither is changed enough to produce an unacceptable change in pH when some of one is converted into the other.

 This means that there are two basic requirements for a buffer: (1) It must be sufficiently concentrated (in terms of the total of [A–] + [HA–]), and (2) the pH must not be too far from the pKa of the buffer so that the concentrations of both A– and HA will be large. It is the second of these that is most often forgotten. If the pH and pKa differ by one unit, only 1/11 of the total buffer concentration will be in the minor form.

This point may be illustrated by the example of a worker who wondered why mercaptoethanol and iodoacetate inhibited his enzyme when neither one by itself did so. He was using more than 10 mM of each reagent in a 10-mM Tris buffer of pH 7. Hence, the 10-mM H+ released when the mercaptoethanol and iodoacetate reacted exceeded by tenfold the concentration of free Tris, which was less than 1 mM in a solution far below its pKa of 8.1.

To a first approximation, dilution does not affect the pH of a buffer solution because it does not affect the ratio [A–]/[HA–]. There are, however, two qualifications to this conclusion. First, it is assumed that the dissociation constant of the buffering acid is unaltered whereas, in fact, it is likely to change with ionic strength. It is also assumed that dilution is not so extreme that either [A–] or [HA–] become comparable to [H+] or [OH–]. In any case, dilution decreases the concentrations of both A– and HA; hence dilution makes the solution a worse buffer in that a given amount of conversion of one form into the other will produce a larger change in the ratio.

3. Practical Points

3.1. pH Measurement 

Methods of measuring pH are outside the scope of this article but the process is important because reproducibility of buffer preparation often depends on it (see below). The most common method uses a glass electrode. This method depends on dipping the electrode into the solution to be tested in such a way that an electrical cell is created and that the potential given by this cell depends on the pH of the solution. Normally, a layer of thin glass separates the solution under test from one containing one of the electrodes of the cell. This glass is selectively permeable to hydrons, so that the potential across it depends on the pH of the solution. Provided that the other junction potential between this solution and the other electrode is negligible—a condition approached by a bridge containing concentrated KCl—the potential should reliably indicate the pH.

Such pH meters require calibration, and standard buffers are used for this. The makers normally give reliable instructions for calibrating the electrode, but some of these are easily overlooked. The first concerns the temperature. The pH standards have pH values that may themselves vary with temperature. Standardization is valid at only one particular temperature, and it cannot be assumed that an electrode standardized at one temperature gives a meaningful reading at a different one. The pH range specified by the makers of the apparatus should also be noted. Glass membranes may be slightly permeable to Na+, so that when [H+] is low, as in alkaline solution, even a slight sensitivity to Na+ may cause overestimation of [H+] and hence too low an estimate of a high pH.

3.2. Specifying a Buffer Solution 

Buffer solutions are often specified in a conventional way, such as 0.2-M sodium acetate buffer, pH 4.8 .The concentration given should refer to the sum of the two forms of the buffering species, designated here as [AcO^–] and [HOAc] in the case of acetate buffer, but such a specification does not make fully clear how this solution has been obtained. It might have been prepared by (1) mixing the appropriate amounts of sodium acetate and acetic acid, as calculated from the pK and the Henderson–Hasselbalch equation, (2) adding 0.2-M sodium acetate to 0.2-M acetic acid until a pH of 4.9 was reached, or (3) adding strong NaOH to 0.2-M acetic acid to reach pH 4.9, on the assumption that the volume added diluted the acetic acid negligibly. It would not have been appropriate, however, to have added strong HCl to 0.2-M sodium acetate, as this would have produced NaCl in addition to the buffering species.

Measuring pH is not straightforward, especially in view of the effects of temperature on the measurements; for reproducibility, especially between different laboratories, it is much safer to specify the concentration of each form of the buffering substance, given that weighing material out with an accuracy of 1% to 2% is easy. Even an error of 2% in each would change the pH by only log(1.04), ie, by 0.017 of a pH unit. Hence, it would be better to describe the buffer just mentioned as 0.12-M sodium acetate, 0.08-M acetic acid (pH 4.8), thus adding the pH for information rather than as part of the definition.

3.3.  Effects of Temperature 

Users should remember that the pH of a buffer may change with temperature. This is because the dissociation constant of the buffering acid, like any other equilibrium constant, depends on temperature if the dissociation has an appreciable enthalpy change, DH. Dissociations of carboxylic acids and phosphoric acid have low values of DH, and so this effect is small with buffers based on them, but the dissociation of ammonium to ammonia and a hydron is accompanied by a large heat intake (ie, DH is positive), and increasing temperature promotes dissociation, ie, lowers the pK_a. Hence, the pH of a buffer that uses an amino group decreases on heating. The effect is quite large, a fall of 0.028 per degree Celsius.

The importance of this needs to be considered in each experiment. If a user wished the glutamate residues of an enzyme to be hydronated to the same extent in an experiment at 0 °C as they would be in a buffer of pH 7 at 20 °C, it would be wrong to use an amino buffer with a pH of 7 at 20 °C and simply cool it. Cooling would raise the pH of the buffer, but not the pKa of the residues, so these residues would dissociate more on cooling. But this would be a proper procedure if the experimenter was concerned with the state of the lysine residues because their pKa would rise with that of the buffering amine so that their degree of hydronation would remain the same.

3.4. Effects of Concentration 

The dissociation constants referred to above are those actually exhibited by the buffering species in the solution being used; ie, they are not idealized values extrapolated to standard conditions of ionic strength and temperature. They therefore change with ionic strength and the addition of other components to the solution, eg, organic solvents or deuterium oxide. Many experiments may require a solution with a particular ionic strength or particular concentrations of specified ions. Remember that these may affect the apparent value of the pK of the buffering species.

 An acid and its conjugate base differ by one H+ and therefore by one charge. Typically, they will have charges 0 and –1, or +1 and 0. If, however, one of the forms has more than unit charge, positive or negative, the pK will have a greater dependence on ionic strength. The most commonly used buffer to which this applies is phosphate buffer, where the acid is H₂PO₄ ^– and its conjugate base is the doubly charged HPO₄^2-This makes its pKa particularly sensitive to ionic strength. For example, a solution of 0.2-M phosphate may increase its pH by over 0.2 of a unit on tenfold dilution.

Many chemical reactions are catalyzed by acids or bases, so that an increased buffer concentration can accelerate them even at a fixed pH. This should be borne in mind when altering buffer concentrations. It is not very common for enzyme-catalyzed reactions because natural selection often ensures that if such catalysis accelerates the reaction, a corresponding acidic or basic group will be present in the enzyme to provide it.

3.5. Volatile Buffers 

Separation methods such as chromatography and electrophoresis often require a buffered solution. This solution needs appreciable ionic strength (in ion-exchange chromatography to give a constant competition for the sites of the exchanger, in electrophoresis to give a constant conductivity and therefore electric field) that is negligibly affected by the substances being separated. Because it is convenient to be able to remove the buffer at the end of the procedure, a volatile buffer that can be removed by evaporation is desirable. The two forms of the buffering substance must differ in charge, however, so that one at least will have a net charge and hence be nonvolatile. Nevertheless, volatile buffers can be prepared by mixing a volatile acid with a volatile base, provided that their pKa values are not greatly separated. An example is a mixture of pyridine (pKa 5.2) and acetic acid (pKa 4.8). On mixing, some of the acetic acid dissociates to acetate and hydronates some of the pyridine to pyridinium. Hence, the pH will be given by

The concentrations of pyridinium (C₅H₅N⁺-H) and acetate (AcO^–) ions will be equal, because each acetic acid molecule that dissociates to acetate forms one pyridinium ion. As the solution is evaporated off, water, pyridine (C₅H₅N) and acetic acid (AcOH) evaporate, and so the equilibrium 

is displaced to the right to replace the un-ionized forms as they are removed.

Ammonium bicarbonate forms a useful buffer of this type. Although it is highly volatile in solution, it is not volatile when dry, as it has a stable crystal lattice. Hence to allow ammonium and bicarbonate to react to form ammonia and carbon dioxide, it may be necessary after one drying to add a little water and then dry it again. Alternatively, triethylammonium bicarbonate, prepared from triethylamine and carbon dioxide, may be used, as it does not form nonvolatile crystals. Ammonium acetate and ammonium formate have been used in this way (2), but the procedures for drying them are complicated because their pKa values are so far apart that there is very little of the un-ionized forms at equilibrium.

3.6.  Appropriate pKa Values

 Biological material usually has a pH near 7, and it is not always easy to find a buffering species with the desired pK_a. Carboxylic acids possess values that are too low, whereas amines have values that are too high. A large number of the commonly used buffers are amines with electron-attracting substituents, which make the lone pair of electrons on the nitrogen atom less available and so lower the atom's pKa. Examples include:

with pKa values of 8.1 and 6.2, respectively. Phosphate Buffers are commonly used because they have a convenient pKa of about 7 between H2PO₄^– and HPO₄^2-Their main disadvantages are their propensity to support fungal and algal growth and the sensitivity of their pKa to ionic strength.

3.7. The Need for Buffers 

It should be remembered that it is pointless to add a buffer if the components of the reaction mixture are already highly buffering. Glycolytic intermediates, for example, are phosphate esters, and adjusting them to a pH near 7 creates a buffered solution.

3.8. Chemical Reactivity 

It is often important to use buffering species that will not react chemically under the conditions of an experiment. Hence an experiment to acylate amino groups of proteins should use a buffer whose basic component has as low a nucleophilic reactivity as possible. Exclusion of primary amines, such as Tris, may be all that is needed. But extreme conditions may demand introduction of steric hindrance; eg, 2,6-dimethylpyridine has a pKa close to that of pyridine but vastly less nucleophilic reactivity because the methyl groups have little steric effect on protonation of the nitrogen atom but greatly slow its reaction with larger molecules.

 Another form of reactivity is the possibility of precipitating desired components in the solution, eg, cations such as Ca²⁺, by phosphate. Occasionally, reactivity may even be of advantage. Urea is often used as a protein denaturant but, if kept for long in concentrated solution, especially at raised temperatures, its equilibration 

can produce about 20-mM cyanate (CNO^–) from 8 M urea (3). The harm in this is the reverse reaction, because the cyanate can carbamoylate lysine residues in proteins, forming uncharged ureas and destabilizing the folded protein. This process is minimized if ammonium ions are present in the buffer as they compete with the protein for the cyanate. 3.9. “Good” Buffers  A number of buffers were recommended by Good and colleagues (4) for a variety of reasons. The most important was that both acidic and basic forms were charged and, therefore they could not rapidly permeate biological membranes. If organelles are suspended in a buffer without this feature, acetate, for example, molecules of acetic acid, but not acetate ions, may penetrate them and lower the internal pH below that of the external buffer. Many of the Good buffers have strongly acid groups, such as sulfonate,  -SO₃^– .An example is 2-morpholinoethanesulfonate (eq. 10); its sulfonate group renders it impermeant even when its nitrilo group is un-ionized. Other desirable characteristics of buffering species are also listed (4). For many purposes, transparency at UV wavelengths is necessary.

 Under other circumstances, the possession of a further charge can be a disadvantage. Ideally, buffers for ion-exchange chromatography possess only one species with a charge opposite in sign to that of the exchanger so that the equilibration of the exchanger can be followed by pH changes; for example, a buffer cation cannot adsorb to, or desorb from, the exchanger except by exchange with H+, which changes the pH.

4.  Metal-Ion Buffers

 The free concentration of many metal ions in biological media is very low, and it may be necessary to buffer it. The principles are exactly the same as those that apply to buffering [H+]. Some compound that binds the metal ion is introduced in roughly equal concentrations of the free and metal-bound forms. A substance that buffers in the correct concentration range can be chosen from a tabulation of binding constants (5).

A complication is that many of the compounds that ligate metal ions with suitable affinity also bind hydrons, resulting in competition between the cations for the ligand. This means that the affinity of the ligand for the metal ion varies with pH. The complex of the buffering species with the metal ion is often a chelate, so that two or more ligating groups are involved. Hence, the competition is not a simple 1:1 replacement, and the pH dependence of the net affinity may be complex.

References

1. J. F. Bunnett and R. A. Y. Jones (1988) Pure Appl. Chem. 60, 1115–1116. 

2. C. H. W. Hirs, S. Moore, and W. H. Stein (1952) J. Biol. Chem. 195, 669–683. 

3. G. R. Stark, W. H. Stein, and S. Moore (1960) J. Biol. Chem. 235, 3177–3181. 

4. N. E. Good and S. Izawa (1972) Methods Enzymol. 24, 53–68. 

5.  R. M. Smith and A. E. Martell (1974-89) Critical Stability Constants, vols. 1–6, Plenum Press, New York.