Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.3 MOLARREACTIONENTHALPY 323

H. 2 ;T^0 /

H. 2 ;T^00 /

H. 1 ;T^0 /

H. 1 ;T^00 /

H(rxn,T^0 )

H(rxn,T^00 )

T

H

Figure 11.7 Dependence of reaction enthalpy on temperature at constant pressure.

11.3.4 Effect of temperature on reaction enthalpy

Consider a reaction occurring with a certain finite change of the advancement in a closed
system at temperatureT^0 and at constant pressure. The reaction is characterized by a change
of the advancement from 1 to 2 , and the integral reaction enthalpy at this temperature is
denotedÅH(rxn,T^0 ). We wish to find an expression for the reaction enthalpyÅH(rxn,T^00 )
for the same values of 1 and 2 at the same pressure but at a different temperature,T^00.
The heat capacity of the system at constant pressure is related to the enthalpy by Eq.
5.6.3on page 143 : Cp D.@H=@T /p;. We integrate dH D CpdT fromT^0 toT^00 at
constantpand, for both the final and initial values of the advancement:

H. 2 ; T^00 /DH. 2 ; T^0 /C

ZT 00

T^0

Cp. 2 /dT (11.3.7)

H. 1 ; T^00 /DH. 1 ; T^0 /C

ZT 00

T^0

Cp. 1 /dT (11.3.8)

Subtracting Eq.11.3.8from Eq.11.3.7, we obtain

ÅH(rxn,T^00 )DÅH(rxn,T^0 )C

ZT 00

T^0

ÅCpdT (11.3.9)

whereÅCpis the difference between the heat capacities of the system at the final and initial
values of, a function ofT:ÅCpDCp. 2 /Cp. 1 /. Equation11.3.9is theKirchhoff
equation.
WhenÅCpis essentially constant in the temperature range fromT^0 toT^00 , the Kirchhoff
equation becomes

ÅH(rxn,T^00 )DÅH(rxn,T^0 )CÅCp.T^00 T^0 / (11.3.10)

Figure11.7illustrates the principle of the Kirchhoff equation as expressed by Eq.
11.3.10.ÅCpequals the difference in the slopes of the two dashed lines in the figure, and
the product ofÅCpand the temperature differenceT^00 T^0 equals the change in the value
ofÅH(rxn). The figure illustrates an exothermic reaction with negativeÅCp, resulting in
a more negative value ofÅH(rxn) at the higher temperature.