Page 107 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 3.1 Basic Definitions 79

where

kB
- K, = concentration equilibrium constant
=
k-B
The equilibrium constant decreases with increasing temperature for exotlhermic
reactions and increases with increasing temperature for endothermic reactions.
We need to check to see if the rate law given by Equation (3-14) is ther-
modynamically consistent at equilibrium. Using Equation (3- 10) and substitut-
ing the appropriate species concentration and exponents, thermodynamics tells
us that

(3-15)

At equilibrium, -rB = 0, and the rate law given by Equation (3-14) becomes
At equilibrium the
rate law mwt
reduce to an - rB~O=k C
equation
consistent with
thermodynamic Rearranging, we obtain
equilibrium

which is identical to Equation (3-15).
A further discussion of the equilibrium constant and its thermodynamic
relationship is given in Appendix C.
Finally, we want to rewrite the rate of formation of diphenyl and hydro-
gen in terms of concentration. The rate of formation of these species must have
the same functional dependence on concentrations as does the rate of disap-
pearance of blenzene. The rate of formation of diphenyl is

(3-16)
L J
Using the relationship given by Equation (2-20) for the general reaction

(2-20)

we can obtain the relationship between the various specific reaction rates,
k,, k,:

(3-17)