Editing Chelation (section)

== Chelate effect ==
[[file:Me-EN.svg|thumb|[[Ethylenediamine]] [[ligand]] chelating to a metal with two bonds]]
[[file:Cu chelate.svg|thumb|Cu<sup>2+</sup> [[Coordination complex|complexes]] with nonchelating [[methylamine]] (left) ''and'' chelating [[ethylenediamine]] (right) ligands]]

The chelate effect is the greater affinity of chelating ligands for a metal ion than that of similar nonchelating (monodentate) ligands for the same metal.

The thermodynamic principles underpinning the chelate effect are illustrated by the contrasting affinities of [[copper]](II) for [[ethylenediamine]] (en) vs. [[methylamine]].
{{NumBlk|:|Cu<sup>2+</sup> + en {{eqm}} [Cu(en)]<sup>2+</sup>|{{EquationRef|1}}}}
{{NumBlk|:|Cu<sup>2+</sup> + 2 MeNH<sub>2</sub> {{eqm}} [Cu(MeNH<sub>2</sub>)<sub>2</sub>]<sup>2+</sup>|{{EquationRef|2}}}}
In ({{EquationNote|1}}) the ethylenediamine forms a chelate complex with the copper ion. Chelation results in the formation of a five-membered CuC<sub>2</sub>N<sub>2</sub> ring. In ({{EquationNote|2}}) the bidentate ligand is replaced by two [[Denticity|monodentate]] methylamine ligands of approximately the same donor power, indicating that the Cu–N bonds are approximately the same in the two reactions.

The [[equilibrium thermodynamics|thermodynamic]] approach to describing the chelate effect considers the [[equilibrium constant]] for the reaction: the larger the equilibrium constant, the higher the concentration of the complex.
{{NumBlk|:|[Cu(en)] {{=}} ''β''<sub>11</sub>[Cu][en]|{{EquationRef|3}}}}
{{NumBlk|:|[Cu(MeNH<sub>2</sub>)<sub>2</sub>] {{=}} ''β''<sub>12</sub>[Cu][MeNH<sub>2</sub>]<sup>2</sup>|{{EquationRef|4}}}}
Electrical charges have been omitted for simplicity of notation. The square brackets indicate concentration, and the subscripts to the [[Stability constants of complexes|stability constant]]s, ''β'', indicate the [[stoichiometry]] of the complex. When the [[analytical concentration]] of methylamine is twice that of ethylenediamine and the concentration of copper is the same in both reactions, the concentration [Cu(en)] is much higher than the concentration [Cu(MeNH<sub>2</sub>)<sub>2</sub>] because {{nowrap|''β''<sub>11</sub> ≫ ''β''<sub>12</sub>}}.

An equilibrium constant, ''K'', is related to the standard [[Gibbs energy|Gibbs free energy]], {{tmath|\Delta G^\ominus}} by
: <math>\Delta G^\ominus = - RT \ln K = \Delta H^\ominus - T \Delta S^\ominus</math>
where ''R'' is the [[gas constant]] and ''T'' is the temperature in [[kelvin]]s. {{tmath|\Delta H^\ominus}} is the standard [[enthalpy]] change of the reaction and {{tmath|\Delta S^\ominus}} is the standard [[Entropy (statistical thermodynamics)|entropy]] change.

Since the enthalpy should be approximately the same for the two reactions, the difference between the two stability constants is due to the effects of entropy. In equation ({{EquationNote|1}}) there are two particles on the left and one on the right, whereas in equation ({{EquationNote|2}}) there are three particles on the left and one on the right. This difference means that less [[Entropy (order and disorder)|entropy of disorder]] is lost when the chelate complex is formed with bidentate ligand than when the complex with monodentate ligands is formed. This is one of the factors contributing to the entropy difference. Other factors include solvation changes and ring formation. Some experimental data to illustrate the effect are shown in the following table.<ref name="GE">{{Greenwood&Earnshaw2nd|page=910| name-list-style=vanc}}</ref>

{| class="wikitable"
! Equilibrium !! log ''β'' !! {{tmath|\Delta G^\ominus}} !! <math>\Delta H^\ominus \mathrm{/kJ\ mol^{-1}}</math> !! <math>-T\Delta S^\ominus \mathrm{/kJ\ mol^{-1}}</math>
|-
| Cu<sup>2+</sup> + 2 MeNH<sub>2</sub> {{eqm}} Cu(MeNH<sub>2</sub>)<sub>2</sub><sup>2+</sup>
||6.55|| −37.4 || −57.3||19.9
|-
| Cu<sup>2+</sup> + en {{eqm}} Cu(en)<sup>2+</sup>
||10.62|| −60.67 || −56.48||−4.19
|}

These data confirm that the enthalpy changes are approximately equal for the two reactions and that the main reason for the greater stability of the chelate complex is the entropy term, which is much less unfavorable. In general it is difficult to account precisely for thermodynamic values in terms of changes in solution at the molecular level, but it is clear that the chelate effect is predominantly an effect of entropy.

Other explanations, including that of [[Gerold Schwarzenbach|Schwarzenbach]],<ref>{{cite journal |vauthors=Schwarzenbach G |title=Der Chelateffekt |trans-title=The Chelation Effect |language=de |journal=Helvetica Chimica Acta |volume=35 |issue=7 |year=1952 |pages=2344–59 |doi=10.1002/hlca.19520350721}}</ref> are discussed in Greenwood and Earnshaw (''loc.cit'').