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340 Nonelernentary Reaction Kinetics Chap. 7
The rate law for this reaction is
For rate expressions similar or equivalent to those given by Equation (7-3),
reaction orders cannot be defined. That is, for rate laws where the denominator
is a polynomial function of the species concentrations, reaction orders are
described only for limiting values of the reactant and/or product concentra-
tions. Reactions of this type are nonelementary in that there is no direct cove-
spondence between reaction order and stoichiometry.
PSSH, Polymers, In this chapter we discuss four topics: the pseudo-steady-state hypothe-
Enzymes, Bacteria sis, polymerization, enzymes, and bioreactors. The pseudo-steady-state hypoth-
esis (PSSH) plays an important role in developing nonelementary rate laws.
Consequently, we will first discuss the fundamentals of the PSSH, followed by
its use of polymerization reactions and enzymatic reactions. Because enzymes
are involved in all living organisms, we close the chapter with a discussion on
bioreactions and reactors.
7.1 Fundamentals
Nonelementary rate laws similar to Equations (7-2) and (7-3) come about as a
result of the overall reaction taking place by a mechanism consisting of a
series of reaction steps. In our analysis, we assume each reaction step in the
reaction mechanism to be elementary; the reaction orders and stoichiometric
coefficients are identical.
To illustrate how rate laws of this type are formed, we shall first consider
the gas-phase decomposition of azomethane, AZO, to give ethane and nitrogen:
(CH3)2N2 CZH6+N2 (7-4)
Experimental observations show that the rate law for N2 is first-order with
respect to AZO at pressures greater than 1 atm (relatively high concentrations)
rN,
and second-order at pressures below 50 mmHg (low concentrations): I
7.1.1 Active Intermediates
This apparent change in reaction order can be explained by the theory
developed by Lindemann., An activated molecule, [(CH3),N2] *, results from
collision or interaction between molecules:
H. C. Ramsperger, J. Am. Gem. SOC., 49, 912 (1927).
7. A. Lindemann, Trans. Faraday SOC., 17, 598 (1922).