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Homogeneous Reactions

In homogeneous reactions the reaction mixture contains one single phase (gas, liquid or solid). When materials react to form products, there may be a single reaction or multiple reactions occurring. There are ways to determine whether a single stoichiometric equation and single rate equation ( single reaction), or multiple equations (multiple reactions) should be used to characterize the process (for example, examining the stoichiometry at more than one temperature). We first consider a single reaction

  equation98

Here a note of caution is appropriate. We can call (1.7) an elementary reaction if tex2html_wrap_inline305 molecules of tex2html_wrap_inline307 collide with tex2html_wrap_inline309 molecules of B, they join by some exchange mechanism (possibly with energy release or absorption), and tex2html_wrap_inline313 molecules of tex2html_wrap_inline315 result. This is true in some cases, but more often than not there are a number of intermediate species produced by intermediate elementary reactions that constitute the mechanism of the reaction. For example, the reaction

displaymath385

was for a long time thought to be an elementary bimolecular reaction. But this was later demonstrated not to be the case. The reaction

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involves several elementary steps, some of which are

eqnarray105

For most reactions, the sequence of elementary steps that constitute their mechanism is not known. Sometimes only a single reaction is observed. The reason is that the amount of the intermediate species formed is very small and escapes detection. The speed with which these intermediate species are created and destroyed also makes them difficult to detect. The general scheme is as follows:

reactants tex2html_wrap_inline407 several intermediate species tex2html_wrap_inline407 products

Based on experimental observation (also explained by collision theory) the law of mass action states that the rate of an elementary reaction (at a constant temperature) is proportional to the product of the concentrations of the reactants. Thus, for a single elementary reaction (1.7), the reaction rate as given by the law of mass action is

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where tex2html_wrap_inline411 is called the rate constant and is empirically determined (dependent on temperature). In this case, the system of equations describing the evolution of each species is

eqnarray115

and the reaction is said to be of order 2. In general, the mechanism of the reaction is more complicated. Nevertheless, in many cases it is found that the reaction rate is well approximated as being proportional to the product of powers of the concentrations of the reactants. For (1.7) such a rate law would be written as

  equation125

where tex2html_wrap_inline413 is called the order of the reaction in A, tex2html_wrap_inline417 is called the order of the reaction in B, and the sum of the exponents, tex2html_wrap_inline421 , is called the order of the reaction. The rate constant, k, of an tex2html_wrap_inline425 -order reaction has dimensions tex2html_wrap_inline427 .

It should be noted that not all reactions are order reactions as defined above. For example, the rate law for the reaction between hydrogen and bromine,

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is

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In the case of a non-elementary reaction, we may postulate a sequence of elementary reactions as its mechanism. This is usually suggested by the chemistry of the species involved (see Levenspiel). The test of the validity of the mechanism proposed is whether the predicted kinetics corresponds to experimental observation. Sometimes reactions may proceed by more than one mechanism, or else their kinetics can be explained by several mechanisms. This makes the discovery truly a detective's work!




next up previous
Next: Zero Order Processes Up: Reaction Rates Previous: Reaction Rates

Mon Apr 28 17:54:28 EDT 1997
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