Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.2 THEADVANCEMENT ANDMOLARREACTIONQUANTITIES 314

The notationfnigstands for the set of amounts of all substances in the mixture, and the
quantitiesHN 2 ,HH 2 , andHNH 3 are partial molar enthalpies. For example,HN 2 is defined
by

HN 2 D

@H

@nN 2

!

T;p;nH 2 ;nNH 3

(11.2.2)

If the system isclosed, the amounts of the three substances can still change because of
the reaction N 2 + 3 H 2 !2 NH 3 , and the number of independent variables is reduced from
five to three. We can choose them to beT,p, and a variable called advancement.
Theadvancement(or extent of reaction),, is the amount by which the reaction de-
fined by the reaction equation has advanced in the forward direction from specified initial
conditions. The quantityhas dimensions of amount of substance, the usual unit being the
mole.
Let the initial amounts benN 2 ;0,nH 2 ;0, andnNH 3 ;0. Then at any stage of the reaction
process in the closed system, the amounts are given by

nN 2 DnN 2 ;0 nH 2 DnH 2 ;03 nNH 3 DnNH 3 ;0C2 (11.2.3)

These relations come from the stoichiometry of the reaction as expressed by the stoichio-
metric coefficients in the reaction equation. The second relation, for example, expresses
the fact that when one mole of reaction has occurred (D 1 mol), the amount of H 2 in the
closed system has decreased by three moles.
Taking the differentials of Eqs.11.2.3, we find that infinitesimal changes in the amounts
are related to the change ofas follows:

dnN 2 Dd dnH 2 D 3 d dnNH 3 D 2 d (11.2.4)

These relations show that in a closed system, the changes in the various amounts are not
independent. Substitution in Eq.11.2.1of the expressions for dnN 2 , dnH 2 , and dnNH 3 gives

dHD



@H

@T



p;

dTC



@H

@p



T;

dp

C

HN 2 3HH 2 C2HNH 3

d (11.2.5)

(closed system)

(The subscriptfnigon the partial derivatives has been replaced byto indicate the same
thing: that the derivative is taken with the amount of each species held constant.)
Equation11.2.5gives an expression for the total differential of the enthalpy withT,p,
andas the independent variables. The coefficient of din this equation is called themolar
reaction enthalpy, or molar enthalpy of reaction,ÅrH:

ÅrHDHN 2 3HH 2 C2HNH 3 (11.2.6)

We identify this coefficient as the partial derivative

ÅrHD



@H

@



T;p

(11.2.7)

That is, the molar reaction enthalpy is the rate at which the enthalpy changes with the
advancement as the reaction proceeds in the forward direction at constantTandp.