Page 90 - Introduction to chemical reaction engineering and kinetics

72 Chapter 4: Development of the Rate Law for a Simple System

and the following increases of pressure (AP) were noted (in part) with increasing time:

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AP/kFa 4.5 9.9 17.9 25.9 32.5 37.9
From these results, determine the order of reaction, and calculate the value of the rate
constant in pressure units (kFa) and in concentration units (mol L-l).

SOLUTION

It can be shown that the experimental data given do not conform to the hypothesis of a
first-order reaction, by the test corresponding to that in Example 4-3. We then consider
the possibility of a second-order reaction. From equation 4.2-6, we write the combined
assumed form of the rate law and the material balance equation (for constant volume), in
terms of CHsCHO (A), as

( -rAp) = -dp,ldt = kApp;

The integrated form is

’ ‘+kt
- - PAo Ap
PA
so that l/PA is a linear function of t. Values of PA can be calculated from each value of
AP, since P, = pAo, and

AP = P - P, = PA + PCH, + Pco - PAo

= PA + 2@,, - PA) - PAo = PAo - PA = 48*4 - PA (3)
Values of PA calculated from equation (3) are:

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pAlkPa 43.9 38.6 30.6 22.6 15.9 10.5

These values are plotted in Figure 4.2 and confirm a linear relation (i.e., n = 2). The
value of kAp calculated from the slope of the line in Figure 4.2 is

k = 5.07 X 10e5 kPa-’ s-l
AP
and, from equation 4.2-8 for kA in (-IA) = kAci,

kA = RTkAp = 8.314(791)5.07 X 10m5 = 0.334 L mole1 s-l

4.3.3 Third-Order Reactions

The number of reactions that can be accurately described as third-order is relatively
small, and they can be grouped according to:

(1) Gas-phase reactions in which one reactant is nitric oxide, the other being oxygen
or hydrogen or chlorine or bromine; these are discussed further below.
(2) Gas-phase recombination of two atoms or free radicals in which a third body
is required, in each molecular act of recombination, to remove the energy of