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| {{Acids and bases}}
| | Hi there, I am Alyson Pomerleau and I believe it sounds quite great when you say it. Distributing production is exactly where her primary earnings arrives from. To climb is something I truly appreciate performing. My spouse and I reside in Mississippi and I adore every working day living right here.<br><br>Feel free to surf to my weblog; psychic phone ([http://xantin.spb.ru/video/uprofile.php?UID=189415 spb.ru]) |
| :''For an individual weak acid or weak base component, see [[Buffering agent]]. For uses not related to acid-base chemistry, see [[Buffer (disambiguation)]].''
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| A '''buffer''' is an [[aqueous solution]] consisting of a mixture of a [[weak acid]] and its [[conjugate base]] or a [[weak base]] and its [[conjugate acid]]. Its [[pH]] changes very little when a small amount of [[strong acid]] or [[Base (chemistry)#Strong bases|base]] is added to it and thus it is used to prevent changes in the pH of a solution. 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 so they utilize a buffer solution to maintain a constant pH. One example of a buffer solution found in nature is [[blood]].
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| ==Principles of buffering==
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| [[File:Buffer titration.png|thumb|250px|left|Simulated titration of an acidified solution of a weak acid (pK<sub>a</sub> = 4.7) with alkali.]]
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| [[File:Buffer Wiki Edit.png|thumb|File:Buffer Wiki Edit.png|thunb|300px|Addition of [[hydroxide]] to a mixture of a weak acid and its conjugate base ]]
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| Buffer solutions achieve their resistance to pH change because of the presence of an equilibrium between the acid HA and its conjugate base A<sup>-</sup>.
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| :HA {{eqm}} H<sup>+</sup> + A<sup>-</sup>
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| 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 Chatelier's principle]]. Because of this, the hydrogen ion concentration increases by less than the amount expected for the quantity of strong acid added.
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| 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 pK<sub>a</sub> = 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 = pK<sub>a</sub> ± 1, centered at pH = 4.7 where [HA] = [A<sup>-</sup>]. The hydrogen ion concentration decreases by less than the amount expected because most of the added hydroxide ion is consumed in the reaction
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| :OH<sup>-</sup> + HA → H<sub>2</sub>O + A<sup>-</sup>
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| and only a little is consumed in the neutralization reaction which results in an increase in pH. | |
| :OH<sup>-</sup> + H<sup>+</sup> → H<sub>2</sub>O
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| Once the acid is more than 95% deprotonated the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.
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| ==Applications==
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| 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 moves outside of a narrow range, the enzymes slow or stop working and can [[denaturation (biochemistry)|denature]]. In many cases denaturation can permanently disable 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=0-7872-7374-0}}</ref>
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| 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.
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| 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=Hulanicki>{{cite book |last= Hulanicki |first= A. |title= Reactions of acids and bases in analytical chemistry |publisher= Horwood |year= 1987 |isbn=0-85312-330-6}} (translation editor: Mary R. Masson)</ref> and calibration of pH meters.
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| The majority of biological samples that are used in research are made in buffers, especially [[phosphate buffered saline]] (PBS) at pH 7.4.
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| ===Simple buffering agents===
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| :{| class="wikitable" style="text-align:center"
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| !Buffering agent!!pK<sub>a</sub>!!useful pH range
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| |-
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| |[[Citric acid]]||3.13, 4.76, 6.40||2.1 - 7.4
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| |-
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| |[[Acetic acid]]||4.8||3.8 - 5.8
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| |-
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| |[[potassium dihydrogenphosphate|KH<sub>2</sub>PO<sub>4</sub>]],||7.2|| 6.2 - 8.2
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| |-
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| |[[N-Cyclohexyl-2-aminoethanesulfonic acid|CHES]]||9.3|| 8.3–10.3
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| |-
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| |[[Borate]]||9.24||8.25 - 10.25
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| |}
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| 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 buffering agent. For alkaline buffers, a strong base such as [[sodium hydroxide]] may be added. Alternatively, a buffer mixture can be made from a mixure 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.
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| ==="Universal" buffer mixtures===
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| 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.
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| The following two-component mixtures (McIlvaine's buffer solutions) have a buffer range of pH 3 to 8.<ref>{{cite journal|last=McIlvaine|first=T.C.|year=1921|title=A buffer solution for colorimetric comparaison|journal=J. Biol. Chem.|volume=49|pages=183–186|url=http://www.jbc.org/content/49/1/183.full.pdf|issue=1}}</ref>
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| :{| class="wikitable" style="text-align:center"
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| ! 0.2M Na<sub>2</sub>HPO<sub>4</sub> /mL
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| ! 0.1M Citric Acid /mL
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| ! pH...
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| |-
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| | 20.55
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| | 79.45
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| | style="background:#ff0000;" | 3.0
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| |-
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| | 38.55
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| | 61.45
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| | style="background:#ff7777;" |4.0
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| |-
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| | 51.50
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| | 48.50
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| | style="background:#ff7700;" | 5.0
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| |-
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| | 63.15
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| | 36.85
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| | style="background:#ffff00;" |6.0
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| |-
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| | 82.35
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| | 17.65
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| | style="background:#007777;" | 7.0
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| |-
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| | 97.25
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| | 2.75
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| |style="background:#0077ff;" | 8.0
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| |}
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| 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>
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| Other universal buffers are Carmody buffer<ref name=carmody>{{cite journal|last=Carmody|first=Walter R.|title=Easily prepared wide range buffer series|journal=J. Chem. Educ.|year=1961|volume=38|issue=11|pages=559–560|doi=10.1021/ed038p559|url=http://dx.doi.org/10.1021/ed038p559|bibcode = 1961JChEd..38..559C }}</ref> and [[Britton-Robinson buffer]], developed in 1931.
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| ===Common buffer compounds used in biology===
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| {| class="wikitable" style="text-align:center"
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| |- bgcolor="#DDDD22"
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| ! 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)<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> !! Mol.<br>Weight !! Full Compound Name
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| | [[TAPS (buffer)|TAPS]] || 8.43 || 7.7–9.1 || −0.018 || 243.3 || 3-{[tris(hydroxymethyl)methyl]amino}propanesulfonic acid
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| | [[Bicine]] || 8.35 || 7.6–9.0 || −0.018 || 163.2 || N,N-bis(2-hydroxyethyl)glycine
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| |-
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| | [[Tris]] || 8.06 || 7.5–9.0 || −0.028 || 121.14 || tris(hydroxymethyl)methylamine
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| |-
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| | [[Tricine]] || 8.05 || 7.4–8.8 || −0.021 || 179.2 || N-tris(hydroxymethyl)methylglycine
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| | [[TAPSO (buffer)|TAPSO]] ||7.635|| 7.0-8.2 || ||259.3 || 3-[N-Tris(hydroxymethyl)methylamino]-2-hydroxypropanesulfonic Acid
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| | [[HEPES]] || 7.48 || 6.8–8.2 || −0.014 || 238.3 || 4-2-hydroxyethyl-1-piperazineethanesulfonic acid
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| | [[TES (buffer)|TES]] || 7.40 || 6.8–8.2 || −0.020 || 229.20 || 2-{[tris(hydroxymethyl)methyl]amino}ethanesulfonic acid
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| |-
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| | [[MOPS]] || 7.20 || 6.5–7.9 || −0.015 || 209.3 || 3-(N-morpholino)propanesulfonic acid
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| | [[PIPES]] || 6.76 || 6.1–7.5 || −0.008 || 302.4 || piperazine-N,N′-bis(2-ethanesulfonic acid)
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| | [[Cacodylate]] || 6.27 || 5.0–7.4 || || 138.0 || dimethylarsinic acid
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| | [[SSC buffer|SSC]] || 7.0 || 6.5-7.5 || || 189.1 || saline sodium citrate
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| | [[MES (buffer)|MES]] || 6.15 || 5.5–6.7 || −0.011 || 195.2 || 2-(N-morpholino)ethanesulfonic acid
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| | [[Succinic acid]] || 7.4(?) || 7.4-7.5 || ? || 118.1 || 2(R)-2-(methylamino)succinic acid
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| |}
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| Biological buffers cover 1.9 to 11 pH range.
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| <ref>{{Cite web|title=Biological buffers |url=http://www.reachdevices.com/Protein/BiologicalBuffers.html |publisher=REACH Devices}}</ref>
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| ==Buffer capacity==
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| [[File:Buffer1 12.png|thumb|200px|Buffer capacity for a 0.1 M solution of an acid with pK<sub>a</sub> of 7]]
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| 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.
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| :<math>\beta = \frac{dn}{d(p[H^+])}</math>
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| where dn is an infinitesimal amount of added base and d(p[H<sup>+</sup>]) 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 K<sub>a</sub>, can be expressed as
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| :<math>\frac{dn}{d(pH)}=2.303\left([H^+]+\frac{C_AK_a[H^+]}{\left(K_a+[H^+]\right)^2}+[OH^-] \right)</math>
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| where C<sub>A</sub> is the analytical concentration of the acid.<ref name=Hulanicki/> pH is defined as -log<sub>10</sub>[H<sup>+</sup>].
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| There are three regions of high buffer capacity.
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| * At very low p[H<sup>+</sup>] the first term predominates and β increases in proportion to the hydrogen ion concentration. This is independent of the presence or absence of buffering agents and applies to all solvents.
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| * In the region p[H<sup>+</sup>] = pK<sub>a</sub> ± 2 the second term becomes important. Buffer capacity is proportional to the concentration of the buffering agent, C<sub>A</sub>, so dilute solutions have little buffer capacity.
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| * At very high p[H<sup>+</sup>] the third term predominates and β increases in proportion to the hydroxide ion concentration. This is due to the [[self-ionization of water]] and is independent of the presence or absence of buffering agents.
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| The buffer capacity of a buffering agent is at a maximum p[H<sup>+</sup>] = pK<sub>a</sub>. It falls to 33% of the maximum value at p[H<sup>+</sup>] = pK<sub>a</sub> ± 1 and to 10% at p[H<sup>+</sup>] = pK<sub>a</sub> ± 1.5. For this reason the useful range is approximately pK<sub>a</sub> ± 1.
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| == Calculating buffer pH ==
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| === Monoprotic acids ===
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| First write down the equilibrium expression.
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| :HA {{eqm}} A<sup>-</sup> + H<sup>+</sup>
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| 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]].
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| :{| class="wikitable" style="text-align:center"
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| |+ICE table for a monoprotic acid
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| |-
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| !width=50| ||width=50|[HA]||width=50|[A<sup>-</sup>]||width=50|[H<sup>+</sup>]
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| |-
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| |I||C<sub>0</sub>||0||y
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| |-
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| |C||-x||x||x
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| |E||C<sub>0</sub>-x||x||x+y
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| |}
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| The first row, labelled I, lists the initial conditions: the concentration of acid is C<sub>0</sub>, initially undissociated, so the concentrations of A<sup>-</sup> and H<sup>+</sup> 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<sup>-</sup> and H<sup>+</sup> 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.
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| To find ''x'', use the formula for the equilibrium constant in terms of concentrations:
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| :<math>K_a = \frac{[H^+] [A^-]}{[HA]}</math>
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| Substitute the concentrations with the values found in the last row of the ICE table:
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| :<math>K_a = \frac{x(x+y)}{C_0 - x}</math>
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| Simplify to:
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| :<math>x^2 + (K_a +y) x - K_a C_0 = 0</math>
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| With specific values for C<sub>0</sub>, K<sub>a</sub> and y this equation can be solved for x. Assuming that pH = -log<sub>10</sub>[H<sup>+</sup>] the pH can be calculated as pH = -log<sub>10</sub>x.
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| ===Polyprotic acids===
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| [[File:Citric acid speciation.png|thumb|200 px|alt=This image plots the relative percentages of the protonation species of citric acid as a function of p H. Citric acid has three ionizable hydrogen atoms and thus three p K A values. Below the lowest p K A, the triply protonated species prevails; between the lowest and middle p K A, the doubly protonated form prevails; between the middle and highest p K A, the singly protonated form prevails; and above the highest p K A, the unprotonated form of citric acid is predominant.|% species formation calculated for a 10 millimolar solution of citric acid.]]
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| Polyprotic acids are acids that can lose more than one proton. The constant for dissociation of the first proton may be denoted as ''K''<sub>a1</sub> and the constants for dissociation of successive protons as ''K''<sub>a2</sub>, etc. [[Citric acid]], H<sub>3</sub>A, is an example of a polyprotic acid as it can lose three protons.
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| :{| class="wikitable"
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| !equilibrium!!p''K''<sub>a</sub> value
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| | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
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| | p''K''<sub>a1</sub> = 3.13
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| |-
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| | H<sub>2</sub>A<sup>−</sup> {{eqm}} HA<sup>2−</sup> + H<sup>+</sup>
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| | p''K''<sub>a2</sub> = 4.76
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| |-
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| | HA<sup>2−</sup> {{eqm}} A<sup>3−</sup> + H<sup>+</sup>
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| | p''K''<sub>a3</sup> = 6.40
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| |}
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| When the difference between successive p''K'' 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.
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| Calculation of the pH with a polyprotic acid requires a [[Determination of equilibrium constants#Speciation calculations|speciation calculation]] to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance
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| :<math> C_A = [A^{3-}]+\beta_1 [A^{3-}][H^+] +\beta_2 [A^{3-}][H^+]^2 +\beta_3 [A^{3-}][H^+]^3</math>
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| :<math> C_H = [H^+]+ \beta_1 [A^{3-}][H^+]+ 2\beta_2 [A^{3-}][H^+]^2+ 3\beta_3 [A^{3-}][H^+]^3 -K_w[H]^{-1}</math>
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| C<sub>A</sub> is the analytical concentration of the acid, C<sub>H</sub> is the analytical concentration of added hydrogen ions, β<sub>q</sub> are the [[equilibrium constant#Cumulative and stepwise formation constants|cumulative association constants]]
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| :<math>\log \beta_1=pK_{a3}, \ \log \beta_2=pK_{a2}+ pK_{a3},\ \log \beta_3=pK_{a1}+ pK_{a2}+ pK_{a3} </math>
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| K<sub>w</sub> is the constant for [[Self-ionization of water]]. There are two [[non-linear]] [[simultaneous equation]]s in two unknown quantities [A<sup>3-</sup>] and [H<sup>+</sup>]. Many computer programs are available to do this calculation. The speciation diagram for citric acid was produced with the program HySS.<ref>{{cite journal | last1 = Alderighi | first1 = L. | last2 =Gans | first2 = P. | last3 = Ienco | last4 = Peters | first3 = D. | last4 = Sabatini | first4 = A. | last5 = Vacca | first3 = A. | year = 1999 | title = Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species | journal = Coordination Chemistry Reviews | volume = 184 | issue = 1 | pages = 311–318 | doi = 10.1016/S0010-8545(98)00260-4 | url = http://www.hyperquad.co.uk/hyss.htm}}</ref>
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| In general the two mass-balance equations can be written as
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| :<math>
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| \begin{align}
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| C_A & = [A]+\sum p\beta_q [A]^p[H^+]^q \\
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| C_H & = [H^+]+\sum q\beta_q [A]^p[H^+]^q -K_w[H]^{-1}
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| \end{align}
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| </math>
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| In this general expression [A] stands for the concentration of the fully deprotonated acid and the electrical charge on this species is not specified.
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| ==See also==
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| * [[Henderson–Hasselbalch equation]]
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| * [[Buffering agent]]
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| * [[Good's buffers]]
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| * [[Common-ion effect]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| * [http://www.popproperty.net/PopularTools/PHBuffer1.aspx Online pH buffer calculator]
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| * [http://www.cnr.berkeley.edu/soilmicro/methods/phosphate%20buffer.pdf phosphate buffer]
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| {{Bases and Acids}}
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| {{Chemical equilibria}}
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| [[Category:Acid-base chemistry]]
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| [[Category:Equilibrium chemistry]]
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| [[Category:Buffers]]
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