Editing Acid dissociation constant (section)

=== Thermodynamics ===
An equilibrium constant is related to the standard [[Gibbs free energy|Gibbs energy]] change for the reaction, so for an acid dissociation constant
: <math>\Delta G^\ominus = -RT \ln K_\text{a} \approx 2.303 RT\ \mathrm{p}K_\text{a}</math>.

''R'' is the [[gas constant]] and ''T'' is the [[kelvin|absolute temperature]]. Note that {{nowrap|p''K''<sub>a</sub> {{=}} −log(''K''<sub>a</sub>)}} and {{nowrap|2.303 ≈ [[natural logarithm|ln]](10)}}. At 25&nbsp;°C, Δ''G''{{sup|⊖}} in kJ·mol<sup>−1</sup> ≈ 5.708 p''K''<sub>a</sub> (1 kJ·mol<sup>−1</sup> = 1000 [[joule]]s per [[mole (unit)|mole]]). Free energy is made up of an [[enthalpy]] term and an [[entropy]] term.<ref name=Goldmine />
:<math>\Delta G^\ominus = \Delta H^\ominus - T \Delta S^\ominus</math>

The standard enthalpy change can be determined by [[calorimetry]] or by using the [[van 't Hoff equation]], though the calorimetric method is preferable. When both the standard enthalpy change and acid dissociation constant have been determined, the standard entropy change is easily calculated from the equation above. In the following table, the entropy terms are calculated from the experimental values of p''K''<sub>a</sub> and Δ''H''{{sup|⊖}}. The data were critically selected and refer to 25&nbsp;°C and zero ionic strength, in water.<ref name="Goldmine">{{cite journal
| title = Thermodynamic Quantities for the Ionization Reactions of Buffers
| last = Goldberg
| first = R.
| author2 = Kishore, N.
| author3 = Lennen, R.
| journal = J. Phys. Chem. Ref. Data
| volume = 31
| issue = 2
| pages = 231–370
| year = 2002
| url = https://www.nist.gov/data/PDFfiles/jpcrd615.pdf
| doi = 10.1063/1.1416902
| bibcode = 2002JPCRD..31..231G
| url-status = dead
| archive-url = https://web.archive.org/web/20081006062140/https://www.nist.gov/data/PDFfiles/jpcrd615.pdf
| archive-date = 2008-10-06
}}</ref>

{| class="wikitable" style="text-align:center;"
|+ Acids
! Compound
! Equilibrium
! p''K''<sub>a</sub>
! Δ''G''{{sup|⊖}} (kJ·mol{{sup|−1}}){{efn|{{nowrap|Δ''G''{{sup|⊖}} ≈ 2.303''RT''p''K''{{sub|a}}}}}}
! Δ''H''{{sup|⊖}} (kJ·mol{{sup|−1}})
! −''T''Δ''S''{{sup|⊖}} (kJ·mol{{sup|−1}}){{efn|Computed here, from Δ''H'' and Δ''G'' values supplied in the citation, using {{nowrap|−''T''Δ''S''{{sup|⊖}} {{=}} Δ''G''{{sup|⊖}} − Δ''H''{{sup|⊖}}}}}}
|-
| style="text-align:left;" | HA = [[Acetic acid]]
| style="text-align:left;" | HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
|  4.756
| 27.147
| −0.41
| 27.56
|-
| style="text-align:left;" | H<sub>2</sub>A<sup>+</sup> = [[Glycine]]H<sup>+</sup>
| style="text-align:left;" | H<sub>2</sub>A<sup>+</sup> {{eqm}} HA + H<sup>+</sup>
|  2.351
| 13.420
|  4.00
|  9.419
|-
| style="text-align:left;" |
| style="text-align:left;" | HA {{eqm}} H<sup>+</sup> + A<sup>−</sup>
| 9.78
| 55.825
| 44.20
| 11.6
|-
| style="text-align:left;" | H<sub>2</sub>A = [[Maleic acid]]
| style="text-align:left;" | H<sub>2</sub>A {{eqm}} HA<sup>−</sup> + H<sup>+</sup>
|  1.92
| 10.76
|  1.10
|  9.85
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>−</sup> {{eqm}} H<sup>+</sup> + A<sup>2−</sup>
|  6.27
| 35.79
| −3.60
| 39.4
|-
| style="text-align:left;" | H<sub>3</sub>A = [[Citric acid]]
| style="text-align:left;" | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
|  3.128
| 17.855
|  4.07
| 13.78
|-
|
| style="text-align:left;" | H<sub>2</sub>A<sup>−</sup> {{eqm}} HA<sup>2−</sup> + H<sup>+</sup>
|  4.76
| 27.176
|  2.23
|  24.9
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>2−</sup> {{eqm}} A<sup>3−</sup> + H<sup>+</sup>
|  6.40
| 36.509
| −3.38
| 39.9
|-
| style="text-align:left;" | H<sub>3</sub>A = [[Boric acid]]
| style="text-align:left;" | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
| 9.237
| 52.725
| 13.80
| 38.92
|-
| style="text-align:left;" | H<sub>3</sub>A = [[Phosphoric acid]]
| style="text-align:left;" | H<sub>3</sub>A {{eqm}} H<sub>2</sub>A<sup>−</sup> + H<sup>+</sup>
|  2.148
| 12.261
| −8.00
| 20.26
|-
| style="text-align:left;" |
| style="text-align:left;" | H<sub>2</sub>A<sup>−</sup> {{eqm}} HA<sup>2−</sup> + H<sup>+</sup>
|  7.20
| 41.087
|  3.60
|  37.5
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>2−</sup> {{eqm}} A<sup>3−</sup> + H<sup>+</sup>
| 12.35
| 80.49
| 16.00
| 54.49
|-
| style="text-align:left;" | HA<sup>−</sup> = [[Bisulfate|Hydrogen sulfate]]
| style="text-align:left;" | HA<sup>−</sup> {{eqm}} A<sup>2−</sup> + H<sup>+</sup>
|   1.99
|  11.36
| −22.40
|  33.74
|-
| style="text-align:left;" | H<sub>2</sub>A = [[Oxalic acid]]
| style="text-align:left;" | H<sub>2</sub>A {{eqm}} HA<sup>−</sup> + H<sup>+</sup>
|   1.27
|   7.27
|  −3.90
| 11.15
|-
| style="text-align:left;" |
| style="text-align:left;" | HA<sup>−</sup> {{eqm}} A<sup>2−</sup> + H<sup>+</sup>
|  4.266
| 24.351
| −7.00
| 31.35
|}

{| class="wikitable"
|+ Conjugate acids of bases
! Compound
! Equilibrium
! p''K''<sub>a</sub>
! ΔH{{sup|⊖}} (kJ·mol{{sup|−1}})
! −''T''Δ''S''{{sup|⊖}} (kJ·mol{{sup|−1}})
|-
| style="text-align:left;" | B = [[Ammonia]]
| style="text-align:left;" | HB<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 9.245
| 51.95
| 0.8205
|-
| style="text-align:left;" | B = [[Methylamine]]
| style="text-align:left;" | HB<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 10.645
| 55.34
| 5.422
|-
| style="text-align:left;" | B = [[Triethylamine]]
| style="text-align:left;" | HB<sup>+</sup> {{eqm}} B + H<sup>+</sup>
| 10.72
| 43.13
| 18.06
|}

The first point to note is that, when p''K''<sub>a</sub> is positive, the standard free energy change for the dissociation reaction is also positive. Second, some reactions are [[exothermic]] and some are [[endothermic]], but, when Δ''H''{{sup|⊖}} is negative ''T''ΔS{{sup|⊖}} is the dominant factor, which determines that Δ''G''{{sup|⊖}} is positive. Last, the entropy contribution is always unfavourable ({{nowrap|Δ''S''{{sup|⊖}} < 0}}) in these reactions. Ions in aqueous solution tend to orient the surrounding water molecules, which orders the solution and decreases the entropy. The contribution of an ion to the entropy is the [[partial molar quantity|partial molar]] entropy which is often negative, especially for small or highly charged ions.<ref>{{cite book
| last1 = Atkins
| first1 = Peter William
| last2 = De Paula
| first2 = Julio
| title = Atkins' physical chemistry.
| url = https://archive.org/details/atkinsphysicalch00pwat
| url-access = registration
| date = 2006
| publisher = W H Freeman
| location = New York
| isbn = 978-0-7167-7433-4
| page = [https://archive.org/details/atkinsphysicalch00pwat/page/94 94]
}}</ref> The ionization of a neutral acid involves formation of two ions so that the entropy decreases ({{nowrap|Δ''S''{{sup|⊖}} < 0}}). On the second ionization of the same acid, there are now three ions and the anion has a charge, so the entropy again decreases.

Note that the ''standard'' free energy change for the reaction is for the changes ''from'' the reactants in their standard states ''to'' the products in their standard states. The free energy change ''at'' equilibrium is zero since the [[chemical potential]]s of reactants and products are equal at equilibrium.