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ORDER OF REACTION, AND RATE CONSTANT

The term order of reaction can be applied to any elementary reaction considered in one direction only, and to certain composite reactions.

For an elementary reaction occurring in one direction the order of reaction is equal to the molecularity, but it describes the kinetics not the mechanism. Thus, for the unimolecular elementary process

EA E + A

the rate of reaction is proportional to the concentration of the reactant EA:

v = k [EA]........ (5)

As the concentration [EA] is raised to the first power the order is unity and the reaction is said to be first order. The constant k is known as the rate constant of the reaction.

For the bimolecular elementary process

E + A EA

the rate is proportional to the product of the reactant concentrations:

v = k [E] [A]........ (6)

The reaction is first-order in E, first-order in A, but second-order overall, and k is again the rate constant. The orders for the individual reactants, unity for E and unity for A, are known as partial orders and the sum of all the partial orders of a reaction is the overall order.

Second-order rate constants, such as k in Eqn (6), have the dimensions of reciprocal concentration multiplied by reciprocal time, whereas first-order rate constants, such as k in Eqn (5), have the dimensions of reciprocal time. This difference in dimensions is not normally evident from the symbols used to represent rate constants, and care must therefore be taken to avoid making improper comparisons between rate constants of different orders. It is sometimes convenient to multiply a second-order rate constant by an appropriate concentration to produce a quantity with the dimensions of a first-order rate constant, e.g. k [A] from Eqn (6); such a product is called a pseudo-first-order rate constant. The units of rate constants vary with the order of reaction in the same way that their dimensions vary. For a first-order rate constant, such as k in Eqn (5), the units are s^-1. For a second-order rate constant, such as k in Eqn (6), the units are dm³ mol^-1 s^-1 or L mol^-1 s^-1 or M^-1 s^-1.

The concept of order of reaction (but not molecularity) can also be applied to certain reactions that occur by composite mechanisms, provided that the rate is proportional to reactant concentrations raised to powers (which need not be integral). However, this is rarely the case with enzyme-catalysed reactions and the concept of order cannot therefore be applied strictly to such reactions overall. Nonetheless the individual steps of composite reactions have orders when considered in one direction. For processes that do not have a true order it is sometimes convenient to define an apparent order with respect to a reactant A as (or as , which is equivalent). For many enzyme-catalysed reactions the true order with respect to any substrate approximates to unity at very low concentrations and to zero at very high concentrations, but is not defined at intermediate concentrations. The apparent order, on the other hand, exists at any concentration.

It is sometimes useful to consider the rates of unidirectional elementary steps of a composite reaction in isolation. When the use of the term rate of reaction for such rates would cause ambiguity the term chemical flux or chemiflux may be used instead. For a full discussion of this terminology, see the IUPAC recommendations [3]. In enzyme kinetics the need for an unambiguous terminology occurs mainly in discussions of the use of rates of transfer of isotopic labels as probes of the chemical fluxes in different parts of the composite reaction.

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