Editing Acid dissociation constant (section)

== Polyprotic acids ==
[[File:H3PO4 speciation.png|thumb|200px|alt=Acids with more than one ionizable hydrogen atoms are called polyprotic acids, and have multiple deprotonation states, also called species. This image plots the relative percentages of the different protonation species of phosphoric acid H 3 P O 4 as a function of solution p H. Phosphoric acid has three ionizable hydrogen atoms whose p K A's are roughly 2, 7 and 12. Below p H 2, the triply protonated species H 3 P O 4 predominates; the double protonated species H 2 P O 4 minus predominates near p H 5; the singly protonated species H P O 4 2 minus predominates near p H 9 and the unprotonated species P O 4 3 minus predominates above p H 12|Phosphoric acid speciation]]

A polyprotic acid is a compound which may lose more than 1 proton. Stepwise dissociation constants are each defined for the loss of a single 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. [[Phosphoric acid]], {{chem2|H3PO4}}, is an example of a polyprotic acid as it can lose three protons.
:{| class="wikitable"
! Equilibrium
! p''K'' definition and value<ref>The values are for 25{{nbsp}}°C and 0 ionic strength – {{cite journal| last1=Powell| first1=Kipton J.| last2=Brown| first2=Paul L.| last3=Byrne| first3=Robert H.| last4=Gajda| first4=Tamás| last5=Hefter| first5=Glenn| last6=Sjöberg| first6=Staffan| last7=Wanner| first7=Hans| title=Chemical speciation of environmentally significant heavy metals with inorganic ligands. Part 1: The Hg<sup>2+</sup> – Cl<sup>−</sup>, OH<sup>−</sup>, CO<sub>3</sub><sup>2-</sup>, SO<sub>4</sub><sup>2-</sup>, and PO<sub>4</sub><sup>3-</sup> aqueous systems|journal=Pure Appl. Chem. |date=2005 |volume=77 |issue=4 |pages=739–800 |doi=10.1351/pac200577040739| doi-access=free}}</ref>
|-
| <chem>H3PO4 <=> H2PO4- + H+</chem>
| <math chem="">\mathrm{p}K_\ce{a1} = \log_{10} \frac{[\ce{H_3PO_4}]}{[\ce{H_2PO_4^{-}}][\ce{H^+}]} = 2.14</math>
|-
| <chem>H2PO4- <=> HPO4^2- + H+</chem>
| <math chem="">\mathrm{p}K_\ce{a2} = \log_{10} \frac{[\ce{H_2PO_4^{-}}]}{[\ce{HPO_4^{2-}}][\ce{H^+}]} = 7.2 </math>
|-
| <chem>HPO4^2- <=> PO4^3- + H+</chem>
| <math chem="">\mathrm{p}K_\ce{a3} = \log_{10} \frac{[\ce{HPO4^2-}]}{[\ce{PO4^3-}][\ce{H+}]} = 12.37 </math>
|}

When the difference between successive p''K'' values is about four or more, as in this example, each species may be considered as an acid in its own right;<ref>{{cite book| last= Brown| first= T.E.| author2= Lemay, H.E.| author3= Bursten, B.E.| author4= Murphy, C.| author5= Woodward, P.| year= 2008| title= Chemistry: The Central Science| edition= 11th| location = New York| publisher = Prentice-Hall| isbn= 978-0-13-600617-6| page= 689}}</ref> In fact salts of {{chem|H|2|PO|4|−}} may be crystallised from solution by adjustment of pH to about 5.5 and salts of {{chem2|HPO4(2-)}} may be crystallised from solution by adjustment of pH to about 10. The species distribution diagram shows that the concentrations of the two ions are maximum at pH&nbsp;5.5 and 10.

[[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 with the program HySS for a 10 millimolar solution of citric acid. p''K''<sub>a1</sub>&nbsp;=&nbsp;3.13, p''K''<sub>a2</sub>&nbsp;=&nbsp;4.76, p''K''<sub>a3</sub>&nbsp;=&nbsp;6.40.]]

When the difference between successive p''K'' values is less than about four there is overlap between the pH range of existence of the species in equilibrium. The smaller the difference, the more the overlap. The case of citric acid is shown at the right; solutions of citric acid are buffered over the whole range of pH&nbsp;2.5 to 7.5.

According to Pauling's first rule, successive p''K'' values of a given acid increase {{nowrap|(p''K''<sub>a2</sub> > p''K''<sub>a1</sub>)}}.<ref name="pauling">{{cite book| last= Greenwood| first= N.N.| author2= Earnshaw, A.| year = 1997| title= Chemistry of the Elements| edition= 2nd| location = Oxford| publisher = Butterworth-Heinemann| isbn= 0-7506-3365-4| page= 50}}</ref> For oxyacids with more than one ionizable hydrogen on the same atom, the p''K''<sub>a</sub> values often increase by about 5 units for each proton removed,<ref name=Miessler2ed>{{cite book| title= Inorganic Chemistry| last= Miessler| first= Gary L.| author2= Tarr Donald A.| year= 1999| publisher = Prentice Hall| isbn= 0-13-465659-8| edition = 2nd| page= 164}}</ref><ref name="Huheey">{{cite book| last= Huheey| first= James E.| year= 1983| title= Inorganic Chemistry| edition= 3rd| publisher = Harper & Row| isbn= 0-06-042987-9| page= 297}}</ref> as in the example of phosphoric acid above.

It can be seen in the table above that the second proton is removed from a negatively charged species. Since the proton carries a positive charge extra work is needed to remove it, which is why p''K''<sub>a2</sub> is greater than p''K''<sub>a1</sub>. p''K''<sub>a3</sub> is greater than p''K''<sub>a2</sub> because there is further charge separation. When an exception to Pauling's rule is found, it indicates that a major change in structure is also occurring. In the case of {{chem2|VO2+}}(aq), the vanadium is [[octahedral molecular geometry|octahedral]], 6-coordinate, whereas vanadic acid is [[tetrahedral molecular geometry|tetrahedral]], 4-coordinate. This means that four "particles" are released with the first dissociation, but only two "particles" are released with the other dissociations, resulting in a much greater entropy contribution to the standard [[Gibbs free energy]] change for the first reaction than for the others.
:{| class="wikitable"
! Equilibrium
! p''K''<sub>a</sub>
|-
| <chem>[VO2(H2O)4]+ <=> H3VO4 + H+ + 2H2O</chem>
|<math chem>\mathrm{p}K_{a_1} = 4.2</math>
|-
| <chem>H3VO4 <=> H2VO4- + H+</chem>
|<math chem>\mathrm{p}K_{a_2} = 2.60</math>
|-
| <chem>H2VO4- <=> HVO4^2- + H+</chem>
| <math chem>\mathrm{p}K_{a_3} = 7.92</math>
|-
| <chem>HVO4^2- <=> VO4^3- + H+</chem>
| <math chem>\mathrm{p}K_{a_4} = 13.27</math>
|}

=== Isoelectric point ===
{{Main|isoelectric point}}
For substances in solution, the isoelectric point (p''I'') is defined as the pH at which the sum, weighted by charge value, of concentrations of positively charged species is equal to the weighted sum of concentrations of negatively charged species. In the case that there is one species of each type, the isoelectric point can be obtained directly from the p''K'' values. Take the example of [[glycine]], defined as AH. There are two dissociation equilibria to consider.
: <chem>AH2+ <=> AH~+ H+ \qquad [AH][H+] = \mathit{K}_1 [AH2+]</chem>
: <chem>AH <=> A^-~+H+ \qquad [A^- ][H+] = \mathit{K}_2 [AH]</chem>

Substitute the expression for [AH] from the second equation into the first equation
: <chem>[A^- ][H+]^2 = \mathit{K}_1 \mathit{K}_2 [AH2+]</chem>

At the isoelectric point the concentration of the positively charged species, {{chem2|AH2+}}, is equal to the concentration of the negatively charged species, {{chem2|A-}}, so
: <math chem>[\ce{H+}]^2 = K_1 K_2</math>

Therefore, taking [[cologarithm]]s, the pH is given by
: <math>\mathrm{p}I = \frac{\mathrm{p}K_1 + \mathrm{p}K_2}{2}</math>

p''I'' values for amino acids are listed at [[proteinogenic amino acid#Chemical properties|proteinogenic amino acid]]. When more than two charged species are in equilibrium with each other a full speciation calculation may be needed.