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{{Acids and Bases}}
:''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 [[strong acid]] or [[Base_(chemistry)#Strong_bases|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. Many life forms thrive only in a relatively small pH range; an example of a buffer solution is blood.

== Acid dissociation constant ==
The [[acid dissociation constant]] for a weak acid, HA, is defined as
:<math> K\mathrm{_a = \frac{[H^+][A^-]}{[HA]}}</math>
Simple manipulation with [[logarithms]] gives the [[Henderson-Hasselbalch equation]], which describes [[pH]] in terms of [[acid dissociation constant|p''K''<sub>a</sub>]]
:<math>\mbox{pH=p}K\mathrm{_a+\log_{10}\frac{[A^-]}{[HA]}}.</math>
In this equation [A<sup>−</sup>] 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=p''K''<sub>a</sub>. 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 ''calculated'' pH may be different from ''measured'' pH. [[Glass electrode]]s found in common pH meters respond not to the concentration of hydrogen ions ([H<sup>+</sup>]), but to their [[Activity (chemistry)|activity]], which depends on several factors, primarily on the [[ionic strength]] of the media. For example, calculation of pH of [[Phosphate buffer|phosphate-buffered saline]] would give the value of 7.96, whereas the actual pH is 7.4.

The same considerations apply to a mixture of a weak base, B and its conjugate acid BH<sup>+</sup>.
:B + H<sub>2</sub>O {{eqm}} BH<sup>+</sup> + OH<sup>-</sup>.
The p''K''<sub>a</sub> 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 ==
[[Image:buffer capacity.png|thumb|Buffer capacity for p''K''<sub>a</sub>=7 as percentage of maximum]]
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 = <math>\mathrm{\frac{dn}{d(pH)}}</math>
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<ref name=hul>{{cite book |last= Hulanicki |first= A. |title= Reactions of acids and bases in analytical chemistry |publisher= Horwood |year= 1987 |isbn=0853123306}} (translation editor: Mary R. Masson)</ref>
:<math>\mathrm{\frac{dn}{d(pH)}=2.303 \left(\frac{\mathit{K}_w}{[H^+]}+[H^+]+\frac{C_A \mathit{K}_a[H^+]}{\left(\mathit{K}_a+[H^+]\right)^2} \right)},</math>
where ''K''<sub>w</sub> is the [[Self-ionization of water|self-ionization constant]] of water and C<sub>A</sub> is the analytical concentration of the acid, equal to [HA]+[A<sup>-</sup>]. The term ''K''<sub>w</sub>/[H<sup>+</sup>] 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
#Buffer capacity of a weak acid reaches its maximum value when pH = p''K''<sub>a</sub>  
#At pH = p''K''<sub>a</sub> ± 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 = p''K''<sub>a</sub> - 1, The Henderson-Hasselbach equation shows that the ratio [HA]:[A<sup>-</sup>] is 10:1.
#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 p''K''<sub>a</sub> equal to that [[pH]], since such a solution has [[maximum buffer capacity]].

Buffer solutions are necessary to keep the correct pH for [[enzyme]]s 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 [[denaturation (biochemistry)|denature]], thus permanently disabling their catalytic activity.<ref name="Scorpio 2000">{{cite book |title=Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems  |last=Scorpio |first=R. |year=2000 |publisher=|isbn=0787273740}}</ref>
A buffer of [[carbonic acid]] (H<sub>2</sub>CO<sub>3</sub>) and [[bicarbonate]] (HCO<sub>3</sub><sup>−</sup>) is present in [[blood plasma]], to maintain a pH between 7.35 and 7.45. 

Industrially, buffer solutions are used in [[fermentation (biochemistry)|fermentation]] processes and in setting the correct conditions for dyes used in colouring fabrics. They are also used in chemical analysis<ref name=hul/> and calibration of pH meters.

The majority of biological samples that are used in research are made in buffers, especially [[phosphate buffered saline]] (PBS) at pH 7.4. 

=== Useful buffer mixtures ===
:{| class="wikitable" style="text-align:center"
!Components!!pH range
|-
|[[Hydrochloric acid|HCl]], [[Sodium citrate]]||1 - 5
|-
|[[Citric acid]], [[Sodium citrate]]||2.5 - 5.6
|-
|[[Acetic acid]], [[Sodium acetate]]||3.7 - 5.6
|-
|[[Dipotassium phosphate|K<sub>2</sub>HPO<sub>4</sub>]], [[Monopotassium phosphate|KH<sub>2</sub>PO<sub>4</sub>]]|| 5.8 - 8 <ref>http://www.cnr.berkeley.edu/soilmicro/methods/phosphate%20buffer.pdf</ref>
|-
|[[Disodium phosphate|Na<sub>2</sub>HPO<sub>4</sub>]], [[Monosodium phosphate|NaH<sub>2</sub>PO<sub>4</sub>]]|| 6 - 7.5 <ref>http://wheat.pw.usda.gov/~lazo/methods/lazo/phosphat.html</ref>
|-
|[[Borax]], [[Sodium hydroxide]]||9.2 - 11
|}

=== "Universal" buffer mixtures ===
By combining substances with p''K''<sub>a</sub> 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 p''K''<sub>a</sub> values, separated by less than two. The buffer range can be extended by adding other buffering agents.
The following two-component mixtures (McIlvaine's buffer solutions<ref>McIlvaine, T. C. (1921). A buffer solution for colorimetric comparaison. J. Biol. Chem. 49: 183-186. http://www.jbc.org/content/49/1/183.full.pdf</ref>) have a buffer range of pH 3 to 8. 
:{| class="wikitable" style="text-align:center"
! 0.2M Na<sub>2</sub>HPO<sub>4</sub> /mL
! 0.1M Citric Acid /mL
! pH...
|-
|  20.55 
| 79.45
| style="background:#ff0000;" | 3.0
|-
| 38.55
| 61.45
| style="background:#ff7777;" |4.0 
|-
|  51.50
|  48.50
| style="background:#ff7700;" | 5.0
|-
| 63.15
| 36.85
| style="background:#ffff00;" |6.0
|-
| 82.35
|  17.65
| style="background:#007777;" | 7.0
|-
| 97.25
| 2.75
|style="background:#0077ff;" | 8.0
|}

A mixture containing [[citric acid]], [[potassium dihydrogen phosphate]], [[boric acid]], and [[Barbital|diethyl barbituric acid]] can be made to cover the pH range 2.6 to 12.<ref>{{cite book |title=Vogel's textbook of quantitative chemical analysis |last=Medham |first=J. |coauthors= Denny, R.C.; Barnes, J.D.; Thomas, M |edition=5th. Ed.|year=2000 |publisher=Pearson Education |location=Harlow |isbn=0 582 22628 7}} Appendix 5</ref>

Other universal buffers are [[Carmody buffer]] and [[Britton-Robinson buffer]], developed in 1931.

===Common buffer compounds used in biology===

{| class="wikitable" style="text-align:center"
|- bgcolor="#DDDD22"
! Common Name !! [[Acid dissociation constant|pK<sub>a</sub>]]<BR>at 25°C !! Buffer Range !! Temp Effect<BR>''d''pH/''d''T in (1/K) ** !! Mol.<BR>Weight !! Full Compound Name
|-
| [[TAPS (buffer)|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]] || 7.55 || 6.8–8.2 || −0.014 || 238.3 || 4-2-hydroxyethyl-1-piperazineethanesulfonic acid
|-
| [[TES (buffer) | 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
|-
| [[SSC buffer | SSC]] ||  7.0 || 6.5-7.5 || || 189.1 || saline sodium citrate
|-
| [[MES (buffer)|MES]] || 6.15 || 5.5–6.7 || −0.011 ||  195.2 || 2-(N-morpholino)ethanesulfonic acid
|}

<nowiki>**</nowiki> Values are approximate.
<ref>{{Cite web|title=Buffer Reference Center |url=http://www.sigmaaldrich.com/life-science/core-bioreagents/biological-buffers/learning-center/buffer-reference-center.html |publisher=Sigma-Aldrich | accessdate=2009-04-17}}</ref>

==See also==
*[[Buffering agent]]
*[[Good's buffers]]
*[[Common-ion effect]]

== References ==
<references/>

==External links==
*[http://www.chembuddy.com/?left=pH-calculation&right=pH-buffers-henderson-hasselbalch Derivation and discussion of Henderson-Hasselbalch equation]
*[http://www.popproperty.net/PopularTools/PHBuffer1.aspx Online pH buffer calculator]

[[Category:Acid-base chemistry]]
[[Category:Equilibrium chemistry]]
[[Category:Buffers]]

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