Nonelementary rate laws

Note The rate constant, k. and aciisation cnergie.s for a number of the reactions in these examples are given in the Data Ba.se on the CD-ROM and Summary Notes. 

A large number of both homogeneous and heterogeneous reactions do not follow simple rate laws. Examples of reactions that don t follow simple elementary rate laws are discussed below. 

Homogeneous Reactions The overall order of a reaction does not have to be an integer, nor does the order have to be an integer with respect to any individual component. As an example, consider the gas-phase synthesis of phosgene. 

This reaction is first order with respect to carbon monoxide, three-halves order with respect to chlorine, and five-halves order overall. 

Sometimes reactions have complex rate expressions that cannot be separated into solely temperature-dependent and concentration-dependent portions. In the decomposition of nitrous oxide. 

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In this chapter we discuss four topics the pseudo-steady-state hypothesis, polymerization, enzymes, and bioreactors. The pseudo-steady-state hypothesis (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. 

Nonelementary Rate Laws and Reactions Present Status of Our Approach to Reactor Sizing and Design 83 Stoichiometric Table 84... 

Sec. 7.1 Active Intermediates and Nonelementary Rate Laws Example 7-2 FSSH Applied to Thermal Cracking of Ethane... 

Examples of reactions that follow nonelementary rate laws Homogeneous... 

Sectioo 9.1 Active Intermediates arxJ Nonelementary Rate Laws... 

Reaction rate laws are determined experimentally. For reactions known to be elementary reactions, it is necessary to experimentally determine the rate constant. For other reactions that may or may not be elementary, it is necessary to experimentally determine the reaction rate law and the rate constant. If the reaction rate law conforms to that of an elementary reaction, i.e., for reaction aA + pB products, the reaction rate law is d /dt=k[A] [B], then the reaction is considered consistent with an elementary reaction, but other information to confirm that no other steps occur is necessary to demonstrate that a reaction is elementary. It is possible that a reaction has the "right" reaction rate law, but is shown later to be nonelementary based on other information. 

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 concenha-tions. Reactions of this type are nonelementary in that there is no direct coite-Spondence between reaction order and stoichiometry. 

Another nonelementary reaction that follows an elementary rate law is the gas-phase reaction between hydrogen and iodine... 

Caspar and Showalter identify five overall stoichiometric processes that make up the total reaction. These are summarized in Table 5.1. The rate laws used for processes A, B, and C have been simplified from the full empirical multiterm rate laws (Reynolds, 1958 von Bunau and Eigen, 1962 Liebhafsky and Roe, 1979) by taking into account the conditions of the oscillatory EOE reaction. When the stoichiometries of the model equations for processes A and D are simplified by dividing by 3, we obtain the following set of p.seudo-elementary reactions as our final empirical rate law model. By chance, the model obeys mass action kinetics, though the rate constants are products of rate constants for the nonelementary component processes and the constant concentrations. 

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