Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.2 THEADVANCEMENT ANDMOLARREACTIONQUANTITIES 316

The infinitesimal change in the amount due to an infinitesimal change in the advancement
is

dniDid (11.2.12)

(closed system)

In an open system, the total differential of extensive propertyXis

dXD



@X

@T



p;fnig

dTC



@X

@p



T;fnig

dpC

X

i

Xidni (11.2.13)

whereXiis a partial molar quantity. We restrict the system to a closed one withT,p, and
as the independent variables. Then, with the substitution dniDidfrom Eq.11.2.12,
the total differential ofXbecomes

dXD



@X

@T



p;

dTC



@X

@p



T;

dpCÅrXd (11.2.14)

(closed system)

where the coefficientÅrXis themolar reaction quantitydefined by

ÅrX

def

D

X

i

iXi (11.2.15)

Equation11.2.14allows us to identify the molar reaction quantity as a partial derivative:

ÅrXD



@X

@



T;p

(11.2.16)

(closed system)

It is important to observe the distinction between the notationsÅX, the finite change
ofXduring a process, andÅrX, a differential quantity that is a property of the system in
a given state. The fact that both notations use the symbolÅcan be confusing. Equation
11.2.16shows that we can think ofÅras anoperator.
In dealing with the change of an extensive propertyXaschanges, we must distinguish
between molar integral and molar differential reaction quantities.

 ÅX=Åis a molarintegralreaction quantity, the ratio of two finite differences be-

tween the final and initial states of a process. These states are assumed to have

the same temperature and the same pressure. This book will use a notation such

asÅHm(rxn) for a molar integral reaction enthalpy:

ÅHm(rxn)D

ÅH(rxn)

Å

D

H. 2 /H. 1 /

 2  1

(11.2.17)

(T 2 DT 1 ; p 2 Dp 1 )

 ÅrXis a molardifferentialreaction quantity. Equation11.2.16shows thatÅrXis the

rate at which the extensive propertyXchanges with the advancement in a closed sys-

tem at constantTandp. The value ofÅrXis in general a function of the independent

variablesT,p, and.