Concise Physical Chemistry

c07 JWBS043-Rogers September 13, 2010 11:25 Printer Name: Yet to Come

96 EQUILIBRIUM

“difficulty” of the experiment and how “good” previous measurements of the same

kind have been. Clearly, these are subjective value judgments.

7.3 THE EXTENT OF REACTION

In a chemical reaction, the participant concentrations change, but they do not change

independently, rather they are related by the stoichiometric coefficients of the reaction.

For example, if I know that reactant A decreases by 0.1 mol in the reaction system

A+B=2C

I know that reactant B also decreases by 0.1 mol and product C increases by 0.2 mol.

The infinitesimal changes in mole numbersdnA,dnB,anddnCare linearly depen-

dent. One frequently expresses the change in a reaction using the single variableξ

which, given the linear dependence of the reaction components, suffices to express

all three in the specific case cited. In general, infinitesimal variations in the amount

of any number of componentsdnican be expressed in terms of theextent of reaction

ξiwhere

ξi=

dni

νi

andνiis thestoichiometric coefficient:−1,−1, and 2 in the specific example cited.

Note that the stoichiometric coefficients of the two reactants are negative because

their concentrations decrease as the reaction proceeds. This is a convention of course,

because the reaction could equally well have been written

2C=A+B

whereupon the signs ofξiwould change.

Up to this point, we have stressed thermodynamic state functions for 1 mol of a

pure substance, for example, the molar energyU=f(V,T). When we express the

energy of any mixture, specifically a mixture of reactants and products in a reacting

system, the composition of the system in terms of mole numbersni= 1 .0 influences

the energy and other state functions. We can express this dependence in terms of the

extent of reaction:

U=f(V,T,ξi)

This dependence means that along withVandT,ξiis a full-fledged degree of freedom

and we can write the exact differential

dU=

(

∂U

∂V

)

T,ξi

dV+

(

∂U

∂T

)

V,ξi

dT+

(

∂U

∂ξi

)

T,V

dξi+...

whereiextends over all degrees of freedom.