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5.3 Reversible Reactions 95

In this form, the sets of exponents czi and a/ are related to each other by restrictions
imposed by thermodynamics, as shown in the next section.

5.3.2 Thermodynamic Restrictions on Rate and on Rate Laws

Thermodynamics imposes restrictions on both the rate r and the form of the rate law
representing it. Thus, at given (T, P), for a system reacting spontaneously (but not at
equilibrium),
AG,,, < 0 and r > 0 (5.3-5)

At equilibrium,

A%, = 0 and r = 0 (5.3-6)

The third possibility of r < 0 cannot arise, since AG,,, cannot be positive for sponta-
neous change.
Equation 5.3-6 leads to a necessary relation between (Y~ and aj in equation 5.3-4. From
this latter equation, at equilibrium,

kf(T) fI4~
i = l
-=- (5.3-7)
k,(T)
fi c;:,
i = l
Also, at equilibrium, the equilibrium constant is

(5.3-8)

Since kf/k, and Kc,eq are both functions of T only, they are functionally related (Den-
bigh, 1981, p. 444):
k, (0 (5.3-9)
- = w&q)
4 m

or

(5.3-10)

i=l
It follows necessarily (Blum and Luus, 1964; Aris, 1968) that 4 is such that

(5.3-11)

$$ = (Kc,eJ (n ’ 0)
r
where
II = (a; - cqyvi; i = 1,2,. . . (5.3-12)