Page 109 - Modeling of Chemical Kinetics and Reactor Design

Thermodynamics of Chemical Reactions 79

If no phase change occurs, the difference ∆H products – ∆H reactants can
be written as

T
∆H − ∆H = ∫ ∆C dT
products reactants p (2-102)
298

where C is given by
p

∆C = ∆a +( ∆b T) + ( ∆c T ) + ( ∆d T ) (2-103)
3
2
•
•
•
p
and ∆C is in cal/mol K, J/mol K, using T in degrees Kelvin.
p
The constants for the equation are found by
∆a = ∑ α products a • products − ∑ α reactants a • reactants (2-104)
∆b= ∑ α products b • products ∑ α reactants b • reactants (2-105)
−

∆c= ∑ α products c • products ∑ α reactants c • reactants (2-106)
−

−
∆d = ∑ α products d • products ∑ α reactants d • reactants (2-107)

So that

T T
∫ ∆CdT = ∫ { ∆a +( ∆b T)+( ∆c T ) +( ∆d T )} dT (2-108)
2
3
•
•
•
p
298 298
Integrating Equation 2-108 yields
T ∆b
(
∫ ∆CdT = ∆a T − 298 )+ ( T −298 2 )
2
p
298 2
(2-109)
∆d
∆c
3
4
+ ( T −298 3 ) + ( T −298 4 )
3 4
The heat of reaction at the system temperature is therefore given by