Page 96 - Modeling of Chemical Kinetics and Reactor Design

66 Modeling of Chemical Kinetics and Reactor Design

is ammonia synthesis where the operating pressure may be as high as
1,500 atm.
The real gas can be expressed as

c
f • f d
C D = K
a
f • f b f (2-39)
A B
The fugacity in Equation 2-39 is that of the component in the
equilibrium mixture. However, fugacity of only the pure component
is usually known. It is also necessary to know something about how
the fugacity depends on the composition in order to relate the two,
therefore, assumptions about the behavior of the reaction mixture must
be made. The most common assumption is that the mixture behaves
as an ideal solution. In this case, it is possible to relate the fugacity,
f, at equilibrium to the fugacity of the pure component, f′, at the same
pressure and temperature by

f = y f′ (2-40)
i
i
Equation 2-40 is known as the Lewis Randall rule, where f′ is the
fugacity of pure component i at the same temperature and total
pressure as the mixture.
Substituting Equation 2-40 into Equation 2-39 gives

c
y • y d D = K • f′ ( ) a •( f′ ) b
A
B
C
a
y • y b f f′ ( ) c •( f′ ) d (2-41)
A B C D
where
c
K = y • y d D (2-42)
C
y
a
y • y b
A B
The f′ , f′ , f′, and f′ are determined for the pure gas at the pressure
A B C D
of the mixture and depend on the pressure and the temperature. In
gaseous mixtures, the quantity K as defined by Equation 2-38 is used.
p
For an ideal gas reaction mixture, K = K . For a non-ideal system,
f p
Equation 2-39 can be used to calculate K from the measured
p
equilibrium compositions K using Equation 2-42. The composition
y