Page 97 - Modeling of Chemical Kinetics and Reactor Design

Thermodynamics of Chemical Reactions 67

ratio K can then be determined from the equilibrium constant. This
f
step is necessary in determining the equilibrium conversion from free
energy data.
The steps in the process are:

o
1. Calculate the standard change of free energy, ∆G .
o
∆G = –RT ln K f (2-43)
or

o
∆G = –RT ln K p (2-44)
o
where ∆G is the difference between the free energies of the
products and reactants when each is in a given standard state.
2. Determine the equilibrium constant K using Equation 2-43.
f
3. Evaluate K from Equation 2-42.
y
4. Calculate the conversion from K .
y
Steps 1 and 2 require thermodynamic data. Figure 2-1 shows the
equilibrium constants of some reactions as a function of temperature.
The Appendix at the end of this chapter gives a tabulation of the
o
standard change of free energy ∆G at 298 K.

REAL GASES

If φ is the fugacity coefficient, and is defined by

φ= f i (2-45)
p

Then

f = φp (2-46)
i
Substituting Equation 2-45 into Equation 2-39 gives

c
c
φ • φ d D • p • p d D = K
C
C
a
a
φ • φ b p • p b f (2-47)
A B A B