Page 84 - Introduction to chemical reaction engineering and kinetics

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

Furthermore, extrapolations of the rate law outside the range of conditions used to gen-
erate it can be made with more confidence, if it is based on mechanistic considerations.
We are not yet in a position to consider fundamental rate laws, and in this chapter we
focus on empirical rate laws given by equation 4.1-3.

4.1.3 Separability versus Nonseparability of Effects
In equation 4.1-3, the effects of the various reaction parameters (ci, T) are separable.
When mechanistic considerations are taken into account, the resulting rate law often
involves a complex function of these parameters that cannot be separated in this man-
ner. As an illustration of nonseparability, a rate law derived from reaction mechanisms
for the catalyzed oxidation of CO is

(--Tco) = w-) ccoc;;/[l + K(T)+, + K’(T)cE].

In this case, the effects of cco, co*, and T cannot be separated. However, the simplifying
assumption of a separable form is often made: the coupling between parameters may be
weak, and even where it is strong, the simpler form may be an adequate representation
over a narrow range of operating conditions.

4.2 GAS-PHASE REACTIONS: CHOICE OF CONCENTRATION UNITS

4.2.1 Use of Partial Pressure
The concentration ci in equation 4.1-3, the rate law, is usually expressed as a molar
volumetric concentration, equation 2.2-7, for any fluid, gas or liquid. For a substance in
a gas phase, however, concentration may be expressed alternatively as partial pressure,
defined by

pi = xip; i = 1,2, . . . , Ng (4.2-1)

where Ng is the number of substances in the gas phase, and xi is the mole fraction of i
in the gas phase, defined by

xi = niln,; i = 1,2, . . . , Ng (4.2-2)
where IZ, is the total number of moles in the gas phase.
The partial pressure pi is related to ci by an equation of state, such as

pi = z(n,IV)RT = zRTc,; i = 1,2,...,N, (4.2-3)

where z is the compressibility factor for the gas mixture, and depends on T, P, and
composition. At relatively low density, z =l, and for simplicity we frequently use the
form for an ideal-gas mixture:
pi = RTc,; i = 1,2, . . . , Ng (4.2-3a)

For the gas-phase reaction 2A + 2B + C + 2D taking place in a rigid vessel at a certain
T, suppose the measured (total) pressure P decreases initially at a rate of 7.2 kPa min-’ .
At what rate is the partial pressure of A, PA, changing? State any assumptions made.