Page 101 - Modeling of Chemical Kinetics and Reactor Design

Thermodynamics of Chemical Reactions 71

Since the composition is constant, dlny = 0 and Equation
i
2-59 becomes

 f   RT
RTd ln  i  =  V −  dp (2-60)
i
 p   p 
i
where V is the partial molar volume. For a single gas, Equation 2-60
i
reduces to give

f    RT
RTd ln   =  V −  dp (2-61)
 p  p 

where V is the specific volume. If we integrate at constant temperature
and constant composition from p = 0 to the particular pressure p = p′,
which is required to calculate the fugacity, the following is obtained:

 f   f  p′  V  1
ln  i  − ln  i  =  ∫ −  dp (2-62)
 p  pp′  p  p=0 0  RT p
=
i
i
f /p = 1 at p = 0, which yields
i
i
f   p′  V  1
i
ln   =  ∫ −  dp
 p pp′ 0  RT p (2-63)
=
Equation 2-63 gives the fugacity at p′ and T in terms of an integral
that is evaluated from experimental data.
Equation 2-63 can be expressed in terms of the compressibility factor

Z = pV (2-64)
RT

and Equation 2-63 now becomes

 f  p′  Z −  1
=
ln   ∫   dp (2-65)
 p′  p 
0