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Buffer solution

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</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title" style="background:#d3d3d3;">Acids and bases</th></tr><tr><td class="sidebar-image" style="background:light-dark(transparent,#999);"></td></tr><tr><td class="sidebar-content hlist" style="padding:0.2em 0 0.75em;">

<ul><li><a href="Acceptor_number" class="mw-redirect" title="Acceptor number">Acceptor number</a></li>

<li><a href="Acid%E2%80%93base_reaction" title="Acid–base reaction">Acid–base reaction</a></li>

<li><a href="Acid%E2%80%93base_homeostasis" title="Acid–base homeostasis">Acid–base homeostasis</a></li>

<li><a href="Acid_strength" title="Acid strength">Acid strength</a></li>

<li><a href="Acidity_function" title="Acidity function">Acidity function</a></li>

<li><a href="Amphoterism" title="Amphoterism">Amphoterism</a></li>

<li><a href="Dissociation_constant" title="Dissociation constant">Dissociation constant</a></li>

<li><a href="Donor_number" title="Donor number">Donor number</a></li>

<li><a href="Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li>

<li><a href="Acid%E2%80%93base_extraction" title="Acid–base extraction">Extraction</a></li>

<li><a href="Hammett_acidity_function" title="Hammett acidity function">Hammett acidity function</a></li>

<li><a href="Proton_affinity" title="Proton affinity">Proton affinity</a></li>

<li><a href="Self-ionization_of_water" title="Self-ionization of water">Self-ionization of water</a></li>

<li><a href="Acid%E2%80%93base_titration" title="Acid–base titration">Titration</a></li>

<li><a href="Lewis_acid_catalysis" title="Lewis acid catalysis">Lewis acid catalysis</a></li>

<li><a href="Frustrated_Lewis_pair" title="Frustrated Lewis pair">Frustrated Lewis pair</a></li>

<li><a href="Chiral_Lewis_acid" title="Chiral Lewis acid">Chiral Lewis acid</a></li>

<li><a href="ECW_model" title="ECW model">ECW model</a></li></ul></td>

</tr><tr><th class="sidebar-heading" style="background:#e5e5e5;">

<a href="Acid" title="Acid">Acid</a> types</th></tr><tr><td class="sidebar-content hlist" style="padding:0.2em 0 0.75em;">

<ul><li><a href="Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory" title="Brønsted–Lowry acid–base theory">Brønsted–Lowry</a></li>

<li><a href="Lewis_acids_and_bases" title="Lewis acids and bases">Lewis</a></li>

<li><a href="Mineral_acid" title="Mineral acid">Mineral</a></li>

<li><a href="Organic_acid" title="Organic acid">Organic</a></li>

<li><a href="Acidic_oxide" title="Acidic oxide">Oxide</a></li>

<li><a href="Strong_acid" class="mw-redirect" title="Strong acid">Strong</a></li>

<li><a href="Superacid" title="Superacid">Superacids</a></li>

<li><a href="Solid_acid" title="Solid acid">Solid</a></li></ul></td>

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<a href="Base_(chemistry)" title="Base (chemistry)">Base</a> types</th></tr><tr><td class="sidebar-content hlist" style="padding:0.2em 0 0.75em;">

<ul><li><a href="Br%C3%B8nsted%E2%80%93Lowry_acid%E2%80%93base_theory" title="Brønsted–Lowry acid–base theory">Brønsted–Lowry</a></li>

<li><a href="Lewis_acids_and_bases" title="Lewis acids and bases">Lewis</a></li>

<li><a href="Organic_base" title="Organic base">Organic</a></li>

<li><a href="Basic_oxide" title="Basic oxide">Oxide</a></li>

<li><a href="Base_(chemistry)#Strong_bases" title="Base (chemistry)">Strong</a></li>

<li><a href="Superbase" title="Superbase">Superbases</a></li>

<li><a href="Non-nucleophilic_base" title="Non-nucleophilic base">Non-nucleophilic</a></li>

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A buffer solution is a solution where the <a href="PH" title="PH">pH</a> does not change significantly on dilution or if an acid or base is added at constant temperature.<a href="#cite_note-openstax-1">[1]</a> Its pH changes very little when a small amount of <a href="Strong_acid" class="mw-redirect" title="Strong acid">strong acid</a> or <a href="Base_(chemistry)#Strong_bases" title="Base (chemistry)">base</a> 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 <a href="Living_systems" title="Living systems">living systems</a> that use buffering for pH regulation. For example, the <a href="Bicarbonate_buffering_system" class="mw-redirect" title="Bicarbonate buffering system">bicarbonate buffering system</a> is used to regulate the <a href="PH" title="PH">pH</a> of <a href="Blood" title="Blood">blood</a>, and bicarbonate also acts as a <a href="Ocean_acidification" title="Ocean acidification">buffer in the ocean</a>.

<div class="mw-heading mw-heading2"><h2 id="Principles_of_buffering">Principles of buffering</h2></div>

Buffer solutions resist pH change because of a <a href="Chemical_equilibrium" title="Chemical equilibrium">chemical equilibrium</a> between the weak acid HA and its conjugate base A−:

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</style><div class="block-indent" style="padding-left: 1.5em;">HA ⇌ H+ + A−</div>

When some strong acid is added to an equilibrium mixture of the weak acid and its conjugate base, hydrogen ions (H+) are added, and the equilibrium is shifted to the left, in accordance with <a href="Le_Chatelier's_principle" title="Le Chatelier's principle">Le Chatelier's principle</a>. 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. In Figure 1, the effect is illustrated by the simulated titration of a weak acid with <a href="Acid_dissociation_constant" title="Acid dissociation constant">pKa</a> = 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

and only a little is consumed in the neutralization reaction (which is the reaction that results in an increase in pH)

Once the acid is more than 95% <a href="Deprotonation" title="Deprotonation">deprotonated</a>, the pH rises rapidly because most of the added alkali is consumed in the neutralization reaction.

<div class="mw-heading mw-heading3"><h3 id="Buffer_capacity">Buffer capacity</h3></div>

Buffer capacity is a quantitative measure of the resistance to change of pH of a solution containing a buffering agent with respect to a change of acid or alkali concentration. It can be defined as follows:<a href="#cite_note-Skoog-2">[2]</a><a href="#cite_note-Urbansky-3">[3]</a>

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<annotation encoding="application/x-tex">{\displaystyle \beta ={\frac {dC_{b}}{d(\mathrm {pH} )}},}</annotation>

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where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dC_{b}}">

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<annotation encoding="application/x-tex">{\displaystyle dC_{b}}</annotation>

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</math><img src="./0fe778872cf38ee5ddc3898fbe5948ed6e5c884a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.815ex; height:2.509ex;" alt="{\displaystyle dC_{b}}" loading="lazy"> is an infinitesimal amount of added base, or

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<annotation encoding="application/x-tex">{\displaystyle \beta =-{\frac {dC_{a}}{d(\mathrm {pH} )}},}</annotation>

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where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dC_{a}}">

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<annotation encoding="application/x-tex">{\displaystyle dC_{a}}</annotation>

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</math><img src="./6691d056534ae130bfdd79eebf9cdbb0c5c06211.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.98ex; height:2.509ex;" alt="{\displaystyle dC_{a}}" loading="lazy"> is an infinitesimal amount of added acid. pH is defined as −log10[H+], and d(pH) is an infinitesimal change in pH.

With either definition the buffer capacity for a weak acid HA with dissociation constant Ka can be expressed as<a href="#cite_note-4">[4]</a><a href="#cite_note-Hulanicki-5">[5]</a><a href="#cite_note-Urbansky-3">[3]</a>

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<annotation encoding="application/x-tex">{\displaystyle \beta =2.303\left([{\ce {H+}}]+{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}+{\frac {K_{\text{w}}}{[{\ce {H+}}]}}\right),}</annotation>

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where [H+] is the concentration of hydrogen ions, and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\text{HA}}}">

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<annotation encoding="application/x-tex">{\displaystyle T_{\text{HA}}}</annotation>

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</math><img src="./0891867f30565d8f2477541ea0925867f3fdc8ce.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.055ex; height:2.509ex;" alt="{\displaystyle T_{\text{HA}}}" loading="lazy"> is the total concentration of added acid. Kw is the equilibrium constant for <a href="Self-ionization_of_water" title="Self-ionization of water">self-ionization of water</a>, equal to 1.0×10−14. Note that in solution H+ exists as the <a href="Hydronium" title="Hydronium">hydronium</a> ion H3O+, and further <a href="Aquation" title="Aquation">aquation</a> of the hydronium ion has negligible effect on the dissociation equilibrium, except at very high acid concentration.

This equation shows that there are three regions of raised buffer capacity (see figure 2).

<ul><li>In the central region of the curve (colored green on the plot), the second term is dominant, and <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx 2.303{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}.}">

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<annotation encoding="application/x-tex">{\displaystyle \beta \approx 2.303{\frac {T_{{\ce {HA}}}K_{a}[{\ce {H+}}]}{(K_{a}+[{\ce {H+}}])^{2}}}.}</annotation>

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</math> Buffer capacity rises to a local maximum at pH = pKa. The height of this peak depends on the value of pKa. Buffer capacity is negligible when the concentration [HA] of buffering agent is very small and increases with increasing concentration of the buffering agent.<a href="#cite_note-Urbansky-3">[3]</a> Some authors show only this region in graphs of buffer capacity.<a href="#cite_note-Skoog-2">[2]</a><div class="paragraphbreak" style="margin-top:0.5em"></div> Buffer capacity falls to 33% of the maximum value at pH = pKa ± 1, to 10% at pH = pKa ± 1.5 and to 1% at pH = pKa ± 2. For this reason the most useful range is approximately pKa ± 1. When choosing a buffer for use at a specific pH, it should have a pKa value as close as possible to that pH.<a href="#cite_note-Skoog-2">[2]</a></li>

<li>With strongly acidic solutions, pH less than about 2 (coloured red on the plot), the first term in the equation dominates, and buffer capacity rises exponentially with decreasing pH: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx 10^{-\mathrm {pH} }.}">

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<annotation encoding="application/x-tex">{\displaystyle \beta \approx 10^{-\mathrm {pH} }.}</annotation>

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</math> This results from the fact that the second and third terms become negligible at very low pH. This term is independent of the presence or absence of a buffering agent.</li>

<li>With strongly alkaline solutions, pH more than about 12 (coloured blue on the plot), the third term in the equation dominates, and buffer capacity rises exponentially with increasing pH: <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta \approx 10^{\mathrm {pH} -\mathrm {p} K_{\text{w}}}.}">

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<annotation encoding="application/x-tex">{\displaystyle \beta \approx 10^{\mathrm {pH} -\mathrm {p} K_{\text{w}}}.}</annotation>

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</math> This results from the fact that the first and second terms become negligible at very high pH. This term is also independent of the presence or absence of a buffering agent.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Applications_of_buffers">Applications of buffers</h2></div>

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 <a href="Enzyme" title="Enzyme">enzymes</a> to function correctly. For example, in <a href="Blood" title="Blood">human blood</a> a mixture of <a href="Carbonic_acid" title="Carbonic acid">carbonic acid</a> (H 2CO 3) and <a href="Bicarbonate" title="Bicarbonate">bicarbonate</a> (HCO− 3) is present in the <a href="Blood_plasma" title="Blood plasma">plasma</a> fraction; this constitutes the major mechanism for maintaining the pH of blood between 7.35 and 7.45. Outside this narrow range (7.40 ± 0.05 pH unit), <a href="Acidosis" title="Acidosis">acidosis</a> and <a href="Alkalosis" title="Alkalosis">alkalosis</a> metabolic conditions rapidly develop, ultimately leading to death if the correct buffering capacity is not rapidly restored.

If the pH value of a solution rises or falls too much, the effectiveness of an enzyme decreases in a process, known as <a href="Denaturation_(biochemistry)" title="Denaturation (biochemistry)">denaturation</a>, which is usually irreversible.<a href="#cite_note-Scorpio_2000-6">[6]</a> The majority of biological samples that are used in research are kept in a buffer solution, often <a href="Phosphate_buffered_saline" class="mw-redirect" title="Phosphate buffered saline">phosphate buffered saline</a> (PBS) at pH 7.4.

In industry, buffering agents are used in <a href="Fermentation_(biochemistry)" class="mw-redirect" title="Fermentation (biochemistry)">fermentation</a> processes and in setting the correct conditions for dyes used in colouring fabrics. They are also used in chemical analysis<a href="#cite_note-Hulanicki-5">[5]</a> and calibration of <a href="PH_meter" title="PH meter">pH meters</a>.

<div class="mw-heading mw-heading3"><h3 id="Simple_buffering_agents">Simple buffering agents</h3></div>

<th>Buffering agent</th>

<th>Useful pH range

</th></tr>

<tr>

<td><a href="Citric_acid" title="Citric acid">Citric acid</a></td>

<td>2.1–7.4

</td></tr>

<tr>

<td><a href="Acetic_acid" title="Acetic acid">Acetic acid</a></td>

<td>3.8–5.8

</td></tr>

<tr>

<td>6.2–8.2

</td></tr>

<tr>

<td>8.3–10.3

</td></tr>

<tr>

<td><a href="Borate" title="Borate">Borate</a></td>

<td>8.25–10.25

</td></tr></tbody></table></dd></dl>

For buffers in acid regions, the pH may be adjusted to a desired value by adding a strong acid such as <a href="Hydrochloric_acid" title="Hydrochloric acid">hydrochloric acid</a> to the particular buffering agent. For alkaline buffers, a strong base such as <a href="Sodium_hydroxide" title="Sodium hydroxide">sodium hydroxide</a> 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 <a href="Sodium_acetate" title="Sodium acetate">sodium acetate</a>. Similarly, an alkaline buffer can be made from a mixture of the base and its conjugate acid.

<div class="mw-heading mw-heading3"><h3 id=""Universal"_buffer_mixtures">"Universal" buffer mixtures</h3></div>

By combining substances with pKa values differing by only two or less and adjusting the pH, a wide range of buffers can be obtained. <a href="Citric_acid" title="Citric acid">Citric acid</a> 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 (<a href="McIlvaine's_buffer" class="mw-redirect" title="McIlvaine's buffer">McIlvaine's buffer</a> solutions) have a buffer range of pH 3 to 8.<a href="#cite_note-7">[7]</a>

<th>0.2 M <a href="Disodium_phosphate" title="Disodium phosphate">Na2HPO4</a> (mL)

</th>

<th>0.1 M <a href="Citric_acid" title="Citric acid">citric acid</a> (mL)

</th>

<th>pH

</th></tr>

<tr>

<td>20.55

</td>

<td>79.45

</td>

<td style="background:#ff0000; color:white">3.0

</td></tr>

<tr>

<td>38.55

</td>

<td>61.45

</td>

<td style="background:#ff7777; color:white">4.0

</td></tr>

<tr>

<td>51.50

</td>

<td>48.50

</td>

<td style="background:#ff7700;">5.0

</td></tr>

<tr>

<td>63.15

</td>

<td>36.85

</td>

<td style="background:#ffff00;">6.0

</td></tr>

<tr>

<td>82.35

</td>

<td>17.65

</td>

<td style="background:#007777; color:white">7.0

</td></tr>

<tr>

<td>97.25

</td>

<td>2.75

</td>

<td style="background:#0077ff; color:white">8.0

</td></tr></tbody></table></dd></dl>

A mixture containing <a href="Citric_acid" title="Citric acid">citric acid</a>, <a href="Monopotassium_phosphate" title="Monopotassium phosphate">monopotassium phosphate</a>, <a href="Boric_acid" title="Boric acid">boric acid</a>, and <a href="Barbital" title="Barbital">diethyl barbituric acid</a> can be made to cover the pH range 2.6 to 12.<a href="#cite_note-8">[8]</a>

Other universal buffers are the Carmody buffer<a href="#cite_note-carmody-9">[9]</a> and the <a href="Britton%E2%80%93Robinson_buffer" title="Britton–Robinson buffer">Britton–Robinson buffer</a>, developed in 1931.

<div class="mw-heading mw-heading3"><h3 id="Common_buffer_compounds_used_in_biology">Common buffer compounds used in biology</h3></div>

For effective range see <a href="#buffer_capacity">Buffer capacity</a>, above. Also see <a href="Good's_buffers" title="Good's buffers">Good's buffers</a> for the historic design principles and favourable properties of these buffer substances in biochemical applications.

<th>Common name (chemical name)

</th>

<th>Structure

</th>

<th><a href="Acid_dissociation_constant" title="Acid dissociation constant">pKa</a>, 25 °C

</th>

<th><abbr title="Temperature">Temp.</abbr> effect, <style data-mw-deduplicate="TemplateStyles:r1214402035">

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</style>⁠dpH/dT⁠ (K−1)<a href="#cite_note-10">[10]</a>

</th>

<th><a href="Molecular_weight" class="mw-redirect" title="Molecular weight">Mol. weight</a>

</th></tr>

<tr>

<td><a href="TAPS_(buffer)" title="TAPS (buffer)">TAPS</a>, ([tris(hydroxymethyl)methylamino]propanesulfonic acid)

</td>

<td>243.3

</td></tr>

<tr>

<td><a href="Bicine" title="Bicine">Bicine</a>, (2-(bis(2-hydroxyethyl)amino)acetic acid)

</td>

<td>163.2

</td></tr>

<tr>

<td><a href="Tris" title="Tris">Tris</a>, (tris(hydroxymethyl)aminomethane, or 2-amino-2-(hydroxymethyl)propane-1,3-diol)

</td>

<td>121.14

</td></tr>

<tr>

<td><a href="Tricine" title="Tricine">Tricine</a>, (N-[tris(hydroxymethyl)methyl]glycine)

</td>

<td>179.2

</td></tr>

<tr>

<td><a href="TAPSO_(buffer)" class="mw-redirect" title="TAPSO (buffer)">TAPSO</a>, (3-[N-tris(hydroxymethyl)methylamino]-2-hydroxypropanesulfonic acid)

</td>

<td>259.3

</td></tr>

<tr>

<td><a href="HEPES" title="HEPES">HEPES</a>, (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid)

</td>

<td>238.3

</td></tr>

<tr>

<td><a href="TES_(buffer)" title="TES (buffer)">TES</a>, (2-[[1,3-dihydroxy-2-(hydroxymethyl)propan-2-yl]amino]ethanesulfonic acid)

</td>

<td>229.20

</td></tr>

<tr>

<td><a href="MOPS" title="MOPS">MOPS</a>, (3-(N-morpholino)propanesulfonic acid)

</td>

<td>209.3

</td></tr>

<tr>

<td><a href="PIPES" title="PIPES">PIPES</a>, (piperazine-N,N′-bis(2-ethanesulfonic acid))

</td>

<td>302.4

</td></tr>

<tr>

<td><a href="Cacodylate" class="mw-redirect" title="Cacodylate">Cacodylate</a>, (dimethylarsenic acid)

</td>

<td>138.0

</td></tr>

<tr>

<td><a href="MES_(buffer)" title="MES (buffer)">MES</a>, (2-(N-morpholino)ethanesulfonic acid)

</td>

<td>195.2

</td></tr></tbody></table>

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</style><div class="reflist reflist-lower-alpha">

<li id="cite_note-11"><a href="#cite_ref-11">^</a> Tris is a base, the pKa = 8.07 refers to its conjugate acid.

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Calculating_buffer_pH">Calculating buffer pH</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Monoprotic_acids">Monoprotic acids</h3></div>

First write down the equilibrium expression

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 <a href="ICE_table" class="mw-redirect" title="ICE table">ICE table</a> (ICE standing for "initial, change, equilibrium").

<caption>ICE table for a monoprotic acid

</caption>

<th>

</th>

<th>[H+]

</th></tr>

<tr>

<th>I

</th>

<td>y

</td></tr>

<tr>

<th>C

</th>

<td>x

</td></tr>

<tr>

<th>E

</th>

<td>x + y

</td></tr></tbody></table></dd></dl>

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, then 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", 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:

<msub>

</mrow>

</msub>

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<annotation encoding="application/x-tex">{\displaystyle K_{\text{a}}={\frac {[{\ce {H+}}][{\ce {A-}}]}{[{\ce {HA}}]}}.}</annotation>

</semantics>

</math>

Substitute the concentrations with the values found in the last row of the ICE table:

<msub>

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<annotation encoding="application/x-tex">{\displaystyle K_{\text{a}}={\frac {x(x+y)}{C_{0}-x}}.}</annotation>

</semantics>

</math>

Simplify to <math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+(K_{\text{a}}+y)x-K_{\text{a}}C_{0}=0.}">

<msup>

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<msub>

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<annotation encoding="application/x-tex">{\displaystyle x^{2}+(K_{\text{a}}+y)x-K_{\text{a}}C_{0}=0.}</annotation>

</semantics>

</math>

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).

<div class="mw-heading mw-heading3"><h3 id="Polyprotic_acids">Polyprotic acids</h3></div>

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. <a href="Citric_acid" title="Citric acid">Citric acid</a> is an example of a polyprotic acid H3A, as it can lose three protons.

<caption>Stepwise dissociation constants

</caption>

<th>Equilibrium</th>

<th>Citric acid

</th></tr>

<tr>

<td>pKa1 = 3.13

</td></tr>

<tr>

<td>pKa2 = 4.76

</td></tr>

<tr>

<td>pKa3 = 6.40

</td></tr></tbody></table></dd></dl>

When the difference between successive pKa values is less than about 3, 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 <a href="Determination_of_equilibrium_constants#Speciation_calculations" title="Determination of equilibrium constants">speciation calculation</a> to be performed. In the case of citric acid, this entails the solution of the two equations of mass balance:

<mtr>

<mtd>

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<mtd>

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<msub>

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<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}C_{{\ce {A}}}&=[{\ce {A^3-}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3},\\C_{{\ce {H}}}&=[{\ce {H+}}]+\beta _{1}[{\ce {A^3-}}][{\ce {H+}}]+2\beta _{2}[{\ce {A^3-}}][{\ce {H+}}]^{2}+3\beta _{3}[{\ce {A^3-}}][{\ce {H+}}]^{3}-K_{\text{w}}[{\ce {H+}}]^{-1}.\end{aligned}}}</annotation>

</semantics>

</math>

CA is the analytical concentration of the acid, CH is the analytical concentration of added hydrogen ions, βq are the <a href="Equilibrium_constant#Cumulative_and_stepwise_formation_constants" title="Equilibrium constant">cumulative association constants</a>. Kw is the constant for <a href="Self-ionization_of_water" title="Self-ionization of water">self-ionization of water</a>. There are two <a href="Non-linear" class="mw-redirect" title="Non-linear">non-linear</a> <a href="Simultaneous_equation" class="mw-redirect" title="Simultaneous equation">simultaneous equations</a> 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.<a href="#cite_note-12">[11]</a>

N.B. The numbering of cumulative, overall constants is the reverse of the numbering of the stepwise, dissociation constants.

<caption>Relationship between cumulative association constant (β) values and stepwise dissociation constant (K) values for a tribasic acid.

</caption>

<th>Equilibrium</th>

<th>Relationship

</th></tr>

<tr>

<td>Log β1= pka3

</td></tr>

<tr>

<td>Log β2 =pka2 + pka3

</td></tr>

<tr>

<td>Log β3 = pka1 + pka2 + pka3

</td></tr></tbody></table></dd></dl>

Cumulative association constants are used in general-purpose computer programs such as the one used to obtain the speciation diagram above.

<ul><li><a href="Henderson%E2%80%93Hasselbalch_equation" title="Henderson–Hasselbalch equation">Henderson–Hasselbalch equation</a></li>

<li><a href="Good's_buffers" title="Good's buffers">Good's buffers</a></li>

<li><a href="Common-ion_effect" title="Common-ion effect">Common-ion effect</a></li>

<li><a href="Metal_ion_buffer" title="Metal ion buffer">Metal ion buffer</a></li>

<li><a href="Mineral_redox_buffer" title="Mineral redox buffer">Mineral redox buffer</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFJ._Gordon_Betts2013" class="citation book cs1">J. Gordon Betts (25 April 2013). "Inorganic compounds essential to human functioning". <a rel="nofollow" class="external text" href="https://openstax.org/books/anatomy-and-physiology/pages/2-4-inorganic-compounds-essential-to-human-functioning">Anatomy and Physiology</a>. OpenStax. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-947172-04-3</bdi>. Retrieved 14 May 2023.</cite>

</li>

<li id="cite_note-Skoog-2">^ <a href="#cite_ref-Skoog_2-0">a</a> <a href="#cite_ref-Skoog_2-1">b</a> <a href="#cite_ref-Skoog_2-2">c</a> <cite id="CITEREFSkoogWestHollerCrouch2014" class="citation book cs1">Skoog, Douglas A.; West, Donald M.; Holler, F. James; Crouch, Stanley R. (2014). Fundamentals of Analytical Chemistry (9th ed.). Brooks/Cole. p. 226. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-495-55828-6</bdi>.</cite>

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<li id="cite_note-Urbansky-3">^ <a href="#cite_ref-Urbansky_3-0">a</a> <a href="#cite_ref-Urbansky_3-1">b</a> <a href="#cite_ref-Urbansky_3-2">c</a> <cite id="CITEREFUrbanskySchock2000" class="citation journal cs1">Urbansky, Edward T.; Schock, Michael R. (2000). "Understanding, Deriving and Computing Buffer Capacity". Journal of Chemical Education. 77 (12): 1640–1644. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000JChEd..77.1640U">2000JChEd..77.1640U</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed077p1640">10.1021/ed077p1640</a>.</cite>

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<li id="cite_note-4"><a href="#cite_ref-4">^</a> <cite id="CITEREFButler1998" class="citation book cs1">Butler, J. N. (1998). Ionic Equilibrium: Solubility and pH calculations. Wiley. pp. 133–136. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-471-58526-8</bdi>.</cite>

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<li id="cite_note-Hulanicki-5">^ <a href="#cite_ref-Hulanicki_5-0">a</a> <a href="#cite_ref-Hulanicki_5-1">b</a> <cite id="CITEREFHulanicki1987" class="citation book cs1">Hulanicki, A. (1987). Reactions of acids and bases in analytical chemistry. Translated by Masson, Mary R. Horwood. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-85312-330-9</bdi>.</cite>

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<li id="cite_note-Scorpio_2000-6"><a href="#cite_ref-Scorpio_2000_6-0">^</a> <cite id="CITEREFScorpio2000" class="citation book cs1">Scorpio, R. (2000). Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems. Kendall/Hunt Publishing Company. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7872-7374-3</bdi>.</cite>

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<li id="cite_note-7"><a href="#cite_ref-7">^</a> <cite id="CITEREFMcIlvaine1921" class="citation journal cs1">McIlvaine, T. C. (1921). <a rel="nofollow" class="external text" href="http://www.jbc.org/content/49/1/183.full.pdf">"A buffer solution for colorimetric comparaison"</a> (PDF). J. Biol. Chem. 49 (1): 183–186. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0021-9258%2818%2986000-8">10.1016/S0021-9258(18)86000-8</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150226111238/http://www.jbc.org/content/49/1/183.full.pdf">Archived</a> (PDF) from the original on 2015-02-26.</cite>

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<li id="cite_note-8"><a href="#cite_ref-8">^</a> <cite id="CITEREFMendhamDennyBarnesThomas2000" class="citation book cs1">Mendham, J.; Denny, R. C.; Barnes, J. D.; Thomas, M. (2000). "Appendix 5". Vogel's textbook of quantitative chemical analysis (5th ed.). Harlow: Pearson Education. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-582-22628-9</bdi>.</cite>

</li>

<li id="cite_note-carmody-9"><a href="#cite_ref-carmody_9-0">^</a> <cite id="CITEREFCarmody1961" class="citation journal cs1">Carmody, Walter R. (1961). "Easily prepared wide range buffer series". J. Chem. Educ. 38 (11): 559–560. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1961JChEd..38..559C">1961JChEd..38..559C</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1021%2Fed038p559">10.1021/ed038p559</a>.</cite>

</li>

<li id="cite_note-10"><a href="#cite_ref-10">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.sigmaaldrich.com/life-science/core-bioreagents/biological-buffers/learning-center/buffer-reference-center.html">"Buffer Reference Center"</a>. Sigma-Aldrich. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090417003507/http://www.sigmaaldrich.com/life-science/core-bioreagents/biological-buffers/learning-center/buffer-reference-center.html">Archived</a> from the original on 2009-04-17. Retrieved 2009-04-17.</cite>

</li>

<li id="cite_note-12"><a href="#cite_ref-12">^</a> <cite id="CITEREFAlderighiGansIencoPeters1999" class="citation journal cs1">Alderighi, L.; Gans, P.; Ienco, A.; Peters, D.; Sabatini, A.; Vacca, A. (1999). <a rel="nofollow" class="external text" href="http://www.hyperquad.co.uk/hyss.htm">"Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species"</a>. Coordination Chemistry Reviews. 184 (1): 311–318. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0010-8545%2898%2900260-4">10.1016/S0010-8545(98)00260-4</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070704083413/http://www.hyperquad.co.uk/hyss.htm">Archived</a> from the original on 2007-07-04.</cite>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.reachdevices.com/Protein/BiologicalBuffers.html">"Biological buffers"</a>. REACH Devices.</cite>

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</style></div><div role="navigation" class="navbox" aria-labelledby="Chemical_equilibria112" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Chemical_equilibria112" style="font-size:114%;margin:0 4em"><a href="Chemical_equilibrium" title="Chemical equilibrium">Chemical equilibria</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Chemical_stability" title="Chemical stability">Chemical stability</a></li>

<li><a href="Chelation" title="Chelation">Chelation</a></li>

<li><a href="Dynamic_equilibrium" class="mw-redirect" title="Dynamic equilibrium">Dynamic equilibrium</a></li>

<li><a href="Equilibrium_chemistry" title="Equilibrium chemistry">Equilibrium chemistry</a></li>

<li><a href="Equilibrium_stage" class="mw-redirect" title="Equilibrium stage">Equilibrium stage</a></li>

<li><a href="Thermodynamic_free_energy" title="Thermodynamic free energy">Free energy</a>

<ul><li><a href="Gibbs_free_energy" title="Gibbs free energy">Gibbs</a></li>

<li><a href="Helmholtz_free_energy" title="Helmholtz free energy">Helmholtz</a></li></ul></li>

<li><a href="Le_Chatelier's_principle" title="Le Chatelier's principle">Le Chatelier's principle</a></li>

<li><a href="Phase_separation" title="Phase separation">Phase separation</a></li>

<li><a href="Reversible_reaction" title="Reversible reaction">Reversible reaction</a></li>

<li><a href="Thermodynamic_equilibrium" title="Thermodynamic equilibrium">Thermodynamic equilibrium</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="Mathematical_model" title="Mathematical model">Models</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Equilibrium_constant" title="Equilibrium constant">Equilibrium constant</a>

<ul><li><a href="Determination_of_equilibrium_constants" title="Determination of equilibrium constants">determination</a></li></ul></li>

<li><a href="Phase_diagram" title="Phase diagram">Phase diagram</a></li>

<li><a href="Predominance_diagram" title="Predominance diagram">Predominance diagram</a></li>

<li><a href="Phase_rule" title="Phase rule">Phase rule</a></li>

<li><a href="Reaction_quotient" title="Reaction quotient">Reaction quotient</a></li>

<li><a href="Thermodynamic_activity" title="Thermodynamic activity">Thermodynamic activity</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul>

<li><a href="Equilibrium_unfolding" title="Equilibrium unfolding">Equilibrium unfolding</a></li>

<li><a href="Liquid%E2%80%93liquid_extraction" title="Liquid–liquid extraction">Liquid–liquid extraction</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Specific equilibria</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Acid_dissociation_constant" title="Acid dissociation constant">Acid dissociation</a>

<ul><li><a href="Hammett_acidity_function" title="Hammett acidity function">Hammett acidity function</a></li></ul></li>

<li><a href="Binding_constant" title="Binding constant">Binding constant</a></li>

<li><a href="Binding_selectivity" title="Binding selectivity">Binding selectivity</a></li>

<li><a href="Stability_constants_of_complexes" title="Stability constants of complexes">Coordination complexes</a>

<ul><li><a href="Macrocyclic_effect" class="mw-redirect" title="Macrocyclic effect">Macrocyclic effect</a></li></ul></li>

<li><a href="Dissociation_constant" title="Dissociation constant">Dissociation constant</a></li>

<li><a href="Hydrolysis_constant" title="Hydrolysis constant">Hydrolysis</a></li>

<li><a href="Molecular_autoionization" title="Molecular autoionization">Self-ionization</a>

<ul><li><a href="Self-ionization_of_water" title="Self-ionization of water">of water</a></li></ul></li>

<li><a href="Partition_equilibrium" title="Partition equilibrium">Partition</a>

<ul><li><a href="Partition_coefficient" title="Partition coefficient">Distribution coefficient</a></li></ul></li>

<li><a href="Solubility_equilibrium" title="Solubility equilibrium">Solubility</a>

<ul><li><a href="Common-ion_effect" title="Common-ion effect">Common-ion effect</a></li></ul></li>

<li><a href="Vapor%E2%80%93liquid_equilibrium" title="Vapor–liquid equilibrium">Vapor–liquid</a>

<ul><li><a href="Henry's_law" title="Henry's law">Henry's law</a></li></ul></li></ul>

</div></td></tr></tbody></table></div></div><div><div class="zim-footer">

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