Page 100 - Modeling of Chemical Kinetics and Reactor Design

70 Modeling of Chemical Kinetics and Reactor Design

K is not independent of pressure because it is a function of the
L
chemical potentials of pure i at the temperature T and pressure P of
the mixture or of the infinite dilution state of i.

DETERMINING THE FUGACITY
AND FUGACITY COEFFICIENT

For any single component fluid at constant temperature and composition,

 ∂µ i 
  = V i
∂ 
 p (2-54)
,
i ,
Tn n j
or

dµ= Vdp (2-55)
i
where µ is the chemical potential of the pure gas at temperature T
i
o
and pressure P. The fugacity f of the gas in which µ is a function of
the temperature is
o
µ = µ + RT ln f i (2-56)
i
i
Differentiating Equation 2-56 at constant temperature and compo-
sition gives

dµ = RTd ln f (2-57)
i i
Combining Equations 2-55 and 2-57 gives

[ RTd ln f = V dp] (2-58)
i
i
T
Subtracting RTd ln p from both sides of Equation 2-58 gives
i

 f 
RTd ln  i  = Vdp − RT d ln p i
i
 p 
i
(2-59)
= V dp RTd ln p − RTd ln y i
−
i
i