Page 108 - Elements of Chemical Reaction Engineering 3rd Edition

80 Rate Laws and Stoichiometry Chap. 3

Comparing Equations (3-16) and (3-17), we see the relationship between the
specific reaction rate with respect to diphenyl and the specific reaction rate
with respect to benzene is

Example 3-3 Formulating a Reversible Rate Law

The exothermic reaction
Af2B ___) 2D (E3-3.1)

is virtually irreversible at low temperatures and the rate law is

-rA = k,Cy2CB (E3-3.2)
Suggest a rate law that is valid at high temperatures, where the reaction is revers-
ible:
A+2B e (E3-3.3)
2D

Solution
These criteria must The rate law for the reversible reaction must
be satisfied
1. satisfy thermodynamic relationships at equilibrium, and
2. reduce to the irreversible rate law when the concentration of one or more of
the reaction products is zero.

We know from thermodynamics that the equilibrium relationship for Reaction
(E3-3.1) as written is
c2, dm3
Kc= - [K,] = (E3-3.4)
with units
cAecie
Rearranging Equation (E3-3.4) in the form\

suggests that we try a reversible rate law of the form
-r, = k, [ CACi - g] (E3-3.5)

Equation (E3-3.5) satisfies the equilibrium conditions but does not simplify to the
initial, irreversible rate when C, = 0. Substituting C, = 0 into the equation being
tested yields