Page 145 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 115

experimental data fit the expressions in the form of Equation 3-13,
the exponents will vary slightly with temperature. In these cases, the
observed correlation should be applied only in a restricted tem-
perature interval.
Not all reactions can be expressed to have a specific order. A
specific example is the synthesis of ammonia expressed as

k 1
N + 3 H { 2 NH 3
2
2
k 2
The Temkin-Pyzhev equation describes the net rate of synthesis over
promoted iron catalyst as:


+ ( r ) = k C  C 3 H 2   a − k  C 2 NH 3   b

NH 3 1 N 2 2 2 3 (3-15)
net  C NH 3   C H 2 
where a and b are empirical exponents that vary with reaction condi-
tions such as temperature, pressure, and conversion. Equation 3-15
does not describe the initial rate at zero partial pressure of NH .
3
The units of the reaction rate constant k vary with the overall order
of the reaction. These units are those of a rate divided by the nth
power of concentration as evident from Equations 3-13 and 3-14.
r − ( A ) moles volume time)
(
−
k = = n (3-16)
C n ( moles volume)

or

k = time ( moles) 1 − n 1
−1
( volume) 1 − n

n
= time −1  moles  −+1 (3-17)
 volume 

Consider a reaction involving a reactant such that A → products.
The rate equations corresponding to a zero, first, second, and third
order reaction together with their corresponding units are: