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In [[physical chemistry]], '''the extent of reaction''' is a quantity that measures the extent in which the reaction proceeds. It is usually denoted by the Greek letter [[Xi (letter)|ξ]]. The extent of a reaction has units of amount ([[Mole (unit)|moles]]).

==Definition==
Consider the reaction
:A ⇌ B
Suppose an infinitesimal amount dξ of the reactant A that changes into B. The change of the amount of A can be represented by the equation dn<sub>A</sub>=-dξ and the change of B is dn<sub>B</sub>=dξ.<ref name=atkins>{{cite book
|first1=Peter
|last1 =Atkins
|first2 = Julio
|last2 = de Paula
|edition = 8
|page = 201
|title = Physical chemistry
|isbn = 0-7167-8759-8
|year= 2006
}}</ref>
The extent of reaction is then defined as<ref>{{cite book
|first1 = Ján Mikuláš
|last1 = Lisý
|first2 = Ladislav
|last2 = Valko
|title = Príklady a úlohy z fyzikálnej chémie
|year = 1979
|page = 593
}}</ref><ref>{{cite book
|first1 = Ladislav
|last1 = Ulický
|title = Chemický náučný slovník
|year = 1983
|page = 313
}}</ref>

:<math> d\xi= \frac{dn_i}{\nu_i}</math>

where <math>n_i</math> denotes the amount of the i-th reactant and <math>\nu_i</math> is the [[Stoichiometry|stoichiometric]] number of the i-th reactant.
In other words, it is the amount of substance that is being changed in an [[equilibrium reaction]].
Considering finite changes instead of infinitesimal changes, one can write the equation for the extent of a reaction as
:<math>\Delta \xi=\frac{\Delta n_i}{\nu_i}</math>
The extent of a reaction is defined as zero at the beginning of the reaction. Thus the change of ξ is the extent itself.
:<math>\xi=\frac{\Delta n_i}{\nu_i}=\frac{n_{equilibrium}-n_{initial}}{\nu_i}</math>

==Relations==
The relation between the change in Gibbs reaction energy and [[Gibbs free energy|Gibbs energy]] can be defined as the slope of the [[Gibbs free energy|Gibbs energy]] plotted against the extent of reaction at constant [[pressure]] and [[temperature]].<ref name=atkins />
:<math>\Delta _r G=\left (\frac{\partial G}{\partial \xi}\right )_{p,T}</math>
Analogously, the relation between the change in reaction [[enthalpy]] and enthalpy can be defined.<ref>{{cite book
|first1 = Ján
|middle1 = Mikuláš
|last1 = Lisý
|first2 = Ladislav
|last2 = Valko
|title = Príklady a úlohy z fyzikálnej chémie
|year = 1979
|page = 593
}}</ref>
:<math>\Delta _r H=\left (\frac{\partial H}{\partial \xi}\right )_{p,T}</math>

==Use==
The extent of reaction is a useful quantity in computations with equilibrium reactions. Let us consider the reaction
:2A ⇌ B + 3 C
where the initial amounts are <math>n_A = 2 mol , n_B=1mol , n_C=0 mol</math>, and the equilibrium amount of A is 0.5 . We can calculate the extent of reaction from its definition
:<math>\xi=\frac{\Delta n_A}{\nu_A}=\frac{0.5-2}{-2}=0.75</math>
Do not forget that the stoichiometric number of reactants is negative. Now when we know the extent, we can rearrange the equation and calculate the equilibrium amounts of B and C.
:<math>n_{equilibrium}=\xi \nu_i+n_{initial}</math>
:<math>n_{B}=0.75*1+1=1.75 mol</math>
:<math>n_{C}=0.75*3+0=2.25 mol</math>

==References==
{{reflist}}

[[Category:Physical chemistry]]
[[Category:Analytical chemistry]]

Set-theoretic topology - Revision history

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