Page 52 - The engineering of chemical reactions

36 Reaction Rates, the Batch Reactor, and the Real World

We can now return to our reaction system and examine the situation near chemical
equilibrium. For a reversible reaction we have

r = rf - rb = kf~,,,,,,,c~~f’ - kb~prodUCtsc~b’ = 0
because the rate is zero at chemical equilibrium. Rearranging this equation, we obtain

Since we just noted that

we can immediately identify terms in these equations,

and
Vj = Wlbj - mfj
at equilibrium. There is an apparent problem in the preceding equations in that K,, is di-
mensionless, while kf and kb can have different dimensions if the orders of forward and back
reactions are not identical. However, as noted, we implicitly divide all concentrations by
the standard state values of 1 mole/liter, so that all these expressions become dimensionless.
From the preceding equations it can be seen that the rate coefficients and the equilib-
rium constant are related. Recall from thermodynamics that
AG; = AH, - T AS;
where AH, is the standard state enthalpy change and AS; is the standard state entropy
change in the reaction. Both AH; and AS: are only weakly dependent on temperature. We
can therefore write
K,, = exp(-AGi/RT) = exp(AS,O/R)exp(-AHi/RT)
kf
- = 5 exp[-(Rf - &/RT]
kb
Therefore, we can identify
Ef - Eb = AH;
and
ho
- = exp(AS;/R)
ho
[While AGa and AG: can have very different values, depending on T and P, AHR and
A Hi are frequently nearly independent of T and P, and we will use AHR from now on to
designate the heat of a reaction in any state. We will therefore frequently omit the superscript
o on AHa.]
These relationships require that reactions be elementary, and it is always true that
near equilibrium all reactions obey elementary kinetics. However, we caution once again