Page 94 - Modeling of Chemical Kinetics and Reactor Design

64 Modeling of Chemical Kinetics and Reactor Design

Thus, for any small reversible displacement at equilibrium, dG = 0,
if dP = 0, dT = 0. Similarly:

If dT = 0, dV = 0 then dA = 0
If dP = 0, dS = 0 then dH = 0
If dV = 0, dS = 0 then dU = 0

REACTION EQUILIBRIUM

Considering any generalized reversible chemical reaction, such that
at dT = 0 and dP = 0:

aA + bB [ cC + dD (2-27)
If the reaction mixture is large enough that the mole numbers
corresponding to the stoichiometric numbers react, then the composi-
tions remain unchanged. If these mole numbers react at equilibrium,
then the overall change in Gibbs function is

dG = cµ + dµ – aµ – bµ = 0 at equilibrium (2-28)
A
C
D
B
Since
∂ G
µ = A
A n ∂ A (2-29)
The chemical potential as a function of composition can be
expressed as

µ = µ + RT ln a i (2-30)
o
i
where a is the activity of i. Introducing Equation 2-30 into the change
i
in the Gibbs statement, and separating the standard state terms on the
right side, gives

c
a • a d D o o o o
C
RT ln =− c { µ C + dµ D − aµ A − bµ B} (2-31)
a
a • a b B
A


c
a • a d  − c ( µ o C + dµ o D − aµ o A − bµ o B)
C D = exp  
a
a • a b B  RT  (2-32)


A