Page 110 - Elements of Chemical Reaction Engineering 3rd Edition

82 Rate Laws and Stoichiometry Chap. 3

3/2
- ~CH,CHO = ~CCH,CHO (3-19)
In many gas-solid catalyzed reactions it is sometimes preferable to write
the rate law in terms of partial pressures rather than concentrations. One such
example is the reversible catalytic decomposition of cumene, C, to form ben-
zene, B, and propylene, P:
+
H6
c6 H&H(CH3)2 e H6
c3
c6
The reaction can be written symbolically as

It was found experimentally that the reaction follows Langmuir-Hinshelwood
kinetics and the rate law is (see Chapter 10)

(3-20)

where K, is the pressure equilibrium constant with units of atm (or kPa); K,
and K, are the adsorption constants with units of atm-' (or Wa'); and the
specific reaction rate, k, has units of
mol cumene
[kl = kg cat s atm

We see that at equilibrium (-r& = 0) the rate law for the reversible reaction is
indeed thermodynamically consistent:

Solving for K, yields

pBepPe
Kp = -
PCe
which is identical to the expression obtained from thermodynamics.
To express the rate of decomposition of cumene -rk as a function of
conversion, replace the partial pressure with concentration, using the ideal gas
law:

P, = C,RT (3-21)

and then express concentration in terms of conversion.
The rate of reaction per unit weight of catalyst, -ra, and the r$e of
reaction per unit volume, -rA, are related through the bulk density ph of the
catalyst particles in the fluid media: