PHYSICAL CHEMISTRY IN BRIEF

CHAP. 8: CHEMICAL EQUILIBRIUM [CONTENTS] 232

8.2.3 Gibbs energy of a system.

The Gibbs energy of a k-component system is given by the relation

G=

∑k

i=1

niμi, (8.6)

whereμiis the chemical potential of thei-th component in the mixture, for which it holds [see

6.4.2]

μi=Gi=

(

∂G

∂ni

)

T,p,nj 6 =i

=μsti +RTlnai. (8.7)

S Symbols: We use superscriptstto denote a quantity in an unspecified standard state. According
to the new IUPAC recommendations, symbol◦is used instead.
If changes in the amount of substance occur in a closed system due to a chemical reaction,
we may substitute (8.4) into (8.6) to obtain

G=

∑k

i=1

(ni, 0 +νiξ)μi. (8.8)

The Gibbs energy of a closed system in which a chemical reaction proceeds thus depends

on the extent of reaction, i.e. on the extent of the initial substances (reactants) transformation

to the products.

Figure8.1shows two possible cases of this dependence at constant temperature and pres-

sure:

a) the Gibbs energy changes linearly with the extent of reaction. This case occurs when all

components involved in the reaction are mutually immiscible.

b) the Gibbs energy reaches its minimum in dependence on the extent of reaction. This

case always occurs in reactions proceeding in a closed system in a homogeneous mixture.

By differentiating (8.8) with respect to the extent of reaction while taking into account the

Gibbs-Duhem equation [see6.3.2], we obtain ∆rG, i.e. thechange in Gibbs energy at one

mole of reactionin an infinitely large reactor

∆rG≡

(

∂G

∂ξ

)

T, p

=

∑k

i=1

νiμi=

∑k

i=1

νi(μsti +RTlnai). (8.9)