|Acids and bases|
A buffer solution (more precisely, pH buffer or hydrogen ion buffer) is an aqueous solution consisting of a mixture of a weak acid and its conjugate base, or vice versa. Its pH changes very little when a small amount of strong 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. In nature, there are many systems that use buffering for pH regulation. For example, the bicarbonate buffering system is used to regulate the pH of blood.
Principles of buffering
Buffer solutions achieve their resistance to pH change because of the presence of an equilibrium between the acid HA and its conjugate base A−.
- HA ⇌ H+ + A−
When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, the equilibrium is shifted to the left, in accordance with Le Châtelier's principle. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added. Similarly, if strong alkali is added to the mixture the hydrogen ion concentration decreases by less than the amount expected for the quantity of alkali added. The effect is illustrated by the simulated titration of a weak acid with pKa = 4.7. The relative concentration of undissociated acid is shown in blue and of its conjugate base in red. The pH changes relatively slowly in the buffer region, pH = pKa ± 1, centered at pH = 4.7 where [HA] = [A−]. The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction
- OH− + HA → H2O + A−
and only a little is consumed in the neutralization reaction which results in an increase in pH.
- OH− + H+ → H2O
Once the acid is more than 95% deprotonated the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.
Buffer capacity, β, 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.
where is an infinitesimal amount of added base and is the resulting infinitesimal change in the cologarithm of the hydrogen ion concentration. With this definition the buffer capacity of a weak acid, with a dissociation constant Ka, can be expressed as the
- At very low pH the first term in the equation dominates and buffer capacity rises exponentially with decreasing pH.
- At very high pH the second term in the equation dominates and buffer capacity rises exponentially with increasing pH.
- The buffer capacity of a buffering agent is at a local maximum when pH = pKa. It falls to 33% of the maximum value at pH = pKa ± 1 and to 10% at pH = pKa ± 1.5. For this reason the useful range is approximately pKa ± 1. Buffer capacity is proportional to the concentration of the buffering agent, CA, so dilute solutions have little buffer capacity.
Properties 1 and 2 are independent of the presence or absence of added buffering agents. They are concentration effects and reflect the fact that pH is related to the logarithm of the hydrogen ion concentration.
The pH of a solution containing a buffering agent can only vary within a narrow range, regardless of what else may be present in the solution. In biological systems this is an essential condition for enzymes to function correctly. For example,in humans a mixture of carbonic acid (H
3) and bicarbonate (HCO−
3) is present in blood plasma; this constitutes the major mechanism for maintaining the pH of blood between 7.35 and 7.45.
If the pH value of a solution rises or falls too much the effectiveness of an enzyme decreases in a process, known as denaturation, which is usually irreversible. The majority of biological samples that are used in research are kept in a buffer solution, often phosphate buffered saline (PBS) at pH 7.4.
In industry, buffering agents 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.
Simple buffering agents
Buffering agent pKa Useful pH range Citric acid 3.13, 4.76, 6.40 2.1–7.4 Acetic acid 4.8 3.8–5.8 KH2PO4 7.2 6.2–8.2 CHES 9.3 8.3–10.3 Borate 9.24 8.25–10.25
For buffers in acid regions, the pH may be adjusted to a desired value by adding a strong acid such as hydrochloric acid to the particular buffering agent. For alkaline buffers, a strong base such as sodium hydroxide may be added. Alternatively, a buffer mixture can be made from a mixture of an acid and its conjugate base. For example, an acetate buffer can be made from a mixture of acetic acid and sodium acetate. Similarly an alkaline buffer can be made from a mixture of the base and its conjugate acid.
"Universal" buffer mixtures
By combining substances with pKa values differing by only two or less and adjusting the pH, a wide range of 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 mixtures (McIlvaine's buffer solutions) have a buffer range of pH 3 to 8.
0.2 M Na2HPO4 (mL) 0.1 M 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
Common buffer compounds used in biology
For effective range see Buffer capacity, above.
|Common name (Chemical Name)||Structure||pKa
at 25 °C
|TAPS ([Tris(hydroxymethyl)methylamino]propanesulfonic acid)||8.43||−0.018||243.3|
|Bicine (2-(Bis(2-hydroxyethyl)amino)acetic acid)||8.35||−0.018||163.2|
|Tris (Tris(hydroxymethyl)aminomethane) or, (2-Amino-2-(hydroxymethyl)propane-1,3-diol)||8.07*||−0.028||121.14|
|Tricine (3-[N-Tris(hydroxymethyl)methylamino]-2-hydroxypropanesulfonic acid)||8.05||−0.021||179.2|
|TAPSO (3-[N-Tris(hydroxymethyl)methylamino]-2-hydroxypropanesulfonic acid)||7.635||259.3|
|HEPES (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid)||7.48||−0.014||238.3|
|TES (2-[[1,3-dihydroxy-2-(hydroxymethyl)propan-2-yl]amino]ethanesulfonic acid)||7.40||−0.020||229.20|
|MOPS (3-(N-morpholino)propanesulfonic acid)||7.20||−0.015||209.3|
|PIPES (Piperazine-N,N′-bis(2-ethanesulfonic acid))||6.76||−0.008||302.4|
|Cacodylate (Dimethylarsenic acid)||6.27||138.0|
|MES (2-(N-morpholino)ethanesulfonic acid)||6.15||−0.011||195.2|
(*) Tris is a base, the pKa of 8.07 refers to its conjugate acid.
Calculating buffer pH
First write down the equilibrium expression.
- HA ⇌ A− + H+
This shows that when the acid dissociates equal amounts of hydrogen ion and anion are produced. The equilibrium concentrations of these three components can be calculated in an ICE table.
ICE table for a monoprotic acid [HA] [A−] [H+] I C0 0 y C −x x x E C0 − x x x + y
The first row, labelled I, lists the initial conditions: the concentration of acid is C0, initially undissociated, so the concentrations of A− and H+ would be zero; y is the initial concentration of added strong acid, such as hydrochloric acid. If strong alkali, such as sodium hydroxide, is added y will have a negative sign because alkali removes hydrogen ions from the solution. The second row, labelled C for change, specifies the changes that occur when the acid dissociates. The acid concentration decreases by an amount −x and the concentrations of A− and H+ both increase by an amount +x. This follows from the equilibrium expression. The third row, labelled E for equilibrium concentrations, adds together the first two rows and shows the concentrations at equilibrium.
To find x, use the formula for the equilibrium constant in terms of concentrations:
Substitute the concentrations with the values found in the last row of the ICE table:
With specific values for C0, Ka and y this equation can be solved for x. Assuming that pH = −log10[H+] the pH can be calculated as pH = −log10(x + y).
Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as Ka1 and the constants for dissociation of successive protons as Ka2, etc. Citric acid, H3A, is an example of a polyprotic acid as it can lose three protons.
Equilibrium pKa value H3A ⇌ H2A− + H+ pKa1 = 3.13 H2A− ⇌ HA2− + H+ pKa2 = 4.76 HA2− ⇌ A3− + H+ pKa3 = 6.40
When the difference between successive pKa values is less than about three there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. In the case of citric acid, the overlap is extensive and solutions of citric acid are buffered over the whole range of pH 2.5 to 7.5.
Calculation of the pH with a polyprotic acid requires a speciation calculation to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance
CA is the analytical concentration of the acid, CH is the analytical concentration of added hydrogen ions, βq are the cumulative association constants
Kw is the constant for self-ionization of water. There are two non-linear simultaneous equations in two unknown quantities [A3−] and [H+]. Many computer programs are available to do this calculation. The speciation diagram for citric acid was produced with the program HySS.
- Henderson–Hasselbalch equation
- Buffering agent
- Good's buffers
- Common-ion effect
- Metal ion buffer
- Mineral redox buffer
- Butler, J. N. (1964). Ionic Equilibrium: A Mathematical Approach. Addison-Wesley. p. 151.
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- Understanding, Deriving, and Computing Buffer Capacity, Edward T. Urbansky and Michael R. Schock, Journal of Chemical Education 2000 77 (12), 1640, DOI: 10.1021/ed077p1640
- Scorpio, R. (2000). Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems. ISBN 978-0-7872-7374-3.
- McIlvaine, T. C. (1921). "A buffer solution for colorimetric comparaison" (PDF). J. Biol. Chem. 49 (1): 183–186. Archived (PDF) from the original on 2015-02-26.
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- Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. (1999). "Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species". Coordination Chemistry Reviews. 184 (1): 311–318. doi:10.1016/S0010-8545(98)00260-4. Archived from the original on 2007-07-04.
- "Biological buffers". REACH Devices.