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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).
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