Page 372 - Elements of Chemical Reaction Engineering Ebook

Ssc. 7.1 Fundamentals 343
its high reactivity (i.e., large specific reaction rates). We shall also consider it
to be present only in low concentrations. These two conditions lead to the
pseudo-steady-st ate approximation, in which the rate of formation of the active
intermediate is assumed to be equal to its rate of di~appearance.~ As a result,
The PSSH assumes
that the net rate ,,f the net rate of formation of the active intermediate, r*, is zero:
formation of A’ is
zero r* = 0
We found that the rate of formation of the product, nitrogen, was

(7-1 1)
‘Nz = k3 ‘AZO*
and that the rate of formation of AZO* was

(7-14)
‘AZO* = k, ‘.&o - k2 ‘AZO ‘AZO* k3 ‘AZO
[Jsing the pseudo-steady-state hypothesis (PSSH), Equations (7- 11) and
(7-14) can be combined to obtain a rate law for N2 solely in terms of the con-
centration of azomethane. First we solve for the concentration of the active inter-
mediate=@ in terms of the concentration of azomethane, AZO. From the PSSH,

TAZ0* = 0 (7-15)

k3
-
rAZO* = kl - k2 CAZO cAzo% CAzo* = 0 (7-16)
we can1 solve Equation (7-16) for CAzo* in terms of e,,,:

(7-17)

Substituting Equation (7-17) into Equation (7-1 1) gives

The final form of the
rate law (7-18)

At low concentrations

k2C.420 4 k3
for which case we obtain the following second-order rate law:

‘N2 = k,CiZO (7-19)

At high concentrations
k2cAZ0 % k3

4F~r further elaboration on this section, see R. Aris, Am. Sci., 58, 419 (1970).