Reaction Kinetics: Homogeneous Gas Reactions

By Keith J. Laidler, Robert Robinson, H. M. N. H. Irving and L. A. K. Staveley

Reactions Kinetics: Volume I: Homogeneous Gas Reactions presents a general introduction to the subject of kinetics, including the basic laws of kinetics and the theoretical treatment of reaction rates. This four-chapter book deals mainly with homogeneous reactions in the gas phase. Chapter 1 presents the kinetic laws based on experimental results in terms of their simple concepts, with a special consideration of the way in which rates depend on concentration, while Chapter 2 deals with the interpretation of rates in terms of more fundamental theories. Chapter 3 covers the overall reactions that are believed to be elementary, such as the reaction between hydrogen and iodine, the reverse decomposition of hydrogen iodide, the corresponding reactions involving deuterium instead of hydrogen, and the dimerizations of butadiene and cyclopentadiene, as well as a few elementary termolecular reactions, all involving nitric oxide. This chapter also includes a general account of some of the elementary reactions that occur as steps in more complex mechanisms. Chapter 4 examines the reaction rates of numerous complex gas reactions. Undergraduate physical chemistry and chemical kinetics students, as well as advanced students in other fields, such as biology and physics, will find this book invaluable.

• Language: English
• Publisher: Elsevier Science
• Release date: Oct 22, 2013
• ISBN: 9781483222417

Book preview

LAIDLER

CHAPTER 1

Basic Kinetic Laws

Publisher Summary

This chapter presents basic kinetic laws and experimental results in terms of simple concepts. The subject of chemical kinetics is concerned with the rates of chemical reactions and with the factors upon which the rates depend. The most important of these factors are concentration, temperature, and hydrostatic pressure. By making systematic studies of the effects of these factors on rates, it is possible to draw conclusions about the detailed mechanisms by which chemical reactions proceed. The ultimate objective of a kinetic study is to arrive at a reaction mechanism. The studies of a nonkinetic nature, such as stereochemical studies, provide valuable information regarding mechanism. The rate of a chemical reaction, which may also be referred to as its velocity or speed, may be expressed in various ways. In a kinetic investigation, one measures, in some direct or indirect fashion, concentrations at various times. The method of integration is more widely used in the interpretation of kinetic data than is the differential method.

The subject of chemical kinetics is concerned with the rates of chemical reactions, and with the factors upon which the rates depend. The most important of these factors are concentration, temperature and hydrostatic pressure. By making systematic studies of the effects of these factors on rates it is possible to draw conclusions about the detailed mechanisms by which chemical reactions proceed. It is probably true to say that the ultimate objective of a kinetic study is to arrive at a reaction mechanism. Studies of a non-kinetic nature, such as stereochemical studies, may also provide valuable information as to mechanism, and must always be taken into account in a kinetic investigation.

In any branch of science it is convenient to distinguish between the phenomenological, or empirical, laws that are obeyed, and the theories that are formulated in order to provide an explanation for these laws. The present chapter is mainly concerned with the kinetic laws, and with the analysis of experimental results in terms of simple concepts; it is almost entirely devoted to a consideration of the way in which rates depend on concentration. Chapter 2, on the other hand, deals with the interpretation of rates in terms of more fundamental theories.

RATE OF REACTION

The rate of a chemical reaction, which may also be referred to as its velocity or speed, may be expressed in various ways. In some investigations it is convenient to measure the concentration x of a product of reaction at various times, and curve a in Fig. 1 shows schematically how such a concentration may vary with the time. The slope dx/dt of such a curve at any time then provides a measure of the rate at that time. If the units of concentration are moles per litre the units of the rate are clearly moles litre−1 sec−1.

FIG. 1 Schematic curves showing the concentration of a product, and the concentration of a reactant, as functions of time.

Alternatively, one may measure the concentration of a reactant, and curve b of Fig. 1 shows how such a concentration may vary with time. The slopes, dc/dt, are now all negative; it is convenient to drop the negative sign and define the rate as −dc/dt.

It is important to note that the rate of a chemical reaction may have a different numerical value according to the way it is defined and measured. Consider, for example, the reaction

Since every time one molecule of nitrogen reacts two molecules of ammonia are formed it is evident that the rate of formation of ammonia, υNH2, is twice the rate of disappearance of nitrogen, υN2:

(1)

Similarly the rate of disappearance of hydrogen, υH2, is three times the rate of disappearance of nitrogen,

(2)

Order of Reaction

In some reactions the rates are proportional to the concentrations of reactants raised to some power; in such cases, and only in such cases, it is convenient to speak of the order of a reaction. Thus if a rate is directly proportional to a single concentration,

(3)

the reaction is said to be of the first order. An example of such a reaction is the decomposition of ethane in the gas phase,

Under the usual experimental conditions the rate of appearance of ethylene, equal to the rate of disappearance of ethane, is proportional to the first power of the ethane concentration or pressure.

The term second order is applied to two types of reactions: those in which the rate is proportional to the square of a single concentration,

(4)

and those in which it is proportional to the product of two concentrations of different reactants,

(5)

An example of the first type is the decomposition of gaseous hydrogen iodide,

for which the rate from left to right is proportional to the square of the hydrogen iodide concentration. The rate of the reverse reaction,

is proportional to the product of the concentrations of hydrogen and iodine, and the reaction is therefore also of the second order. It is, in fact, first order in hydrogen and first order in iodine.

Third-order reactions are also known; an example is the reaction between nitric oxide and chlorine,

the rate of which is proportional to the square of the nitric oxide concentration and to the first power of the chlorine concentration:

(6)

The reaction is thus second-order in nitric oxide and first-order in chlorine; its over-all order is three.

One may generalize the situation as follows. If the rate of a reaction is proportional to the αth power of the concentration of a reactant A, to the βth power of the concentration of B, etc.,

(7)

it is said to be of the αth order in A, of the βth order in B, and so forth. The over-all order of the reaction is

(8)

Several points are worth emphasizing in connection with the consideration of the order of a reaction. In the first place, by no means all reactions can be spoken of as having an order.

The rate of the reaction between hydrogen and bromine, for example, obeys the rate equation

(9)

This complex rate equation arises as a result of the complexity of the reaction, the details of which are considered later. For such a reaction one should not speak of the order of the reaction, but should express the dependence by using the rate equation (9).

Secondly, one should never attempt to deduce the order of a reaction from the stoichiometric equation. If the mechanism happens to be a very simple one such a deduction may be correct; thus the reaction

is indeed second-order (first order in hydrogen and first order in iodine), as suggested by the equation. However the reaction

is not, as indicated above, second-order, since it occurs by a complex mechanism.

It should be clear from this discussion that the order of reaction is strictly an experimental quantity, being concerned solely with the way in which rate depends on concentration. The term order should not be used to mean molecularity or vice versa; the latter term, which is discussed in the next chapter, represents a deduction from the kinetics and from other evidence, and refers to the number of molecules entering into an elementary reaction.

Finally, it may be noted that non-integral orders are possible. Thus the thermal conversion of para-hydrogen into ortho-hydrogen is a reaction of the three-halves order,

(10)

Such non-integral orders suggest a complex type of mechanism, as will be considered.

Rate Constant

The constant k occurring in the above equations for reactions having a simple order (i.e. excepting eqn. (9)) is known as the rate constant for the reaction. Sometimes, especially when it shows some variation with the experimental conditions, it is known as the rate coefficient. It is numerically equal to the rate when the reactant concentrations are all unity, and it is therefore also called the specific rate.

The units of the rate constant are readily deduced from the rate equation, and vary with the order of reaction. Thus for a first-order reaction, for which

(11)

the units of k are those of v (mole litre−1 sec−1) divided by concentration (mole litre−1), and are therefore sec−1. For a second-order reaction

(12)

and k is therefore rate divided by the square of a concentration; the units are thus litre mole−1 sec−1. In general, for a reaction of the nth order,

(13)

the units are mole¹-n litren-1 sec−1.

It was noted previously that the rate of a reaction sometimes varies with the species that is under consideration. It follows that the rate constant varies in the same way. Consider, for example, the dissociation of ethane into two methyl radicals,

The rate of formation of methyl radicals is twice the rate of disappearance of ethane, and the rate constant for the formation of radicals is equal to twice that for the disappearance of ethane. The rate constant in such a case may be defined in either way, according to convenience.

ANALYSIS OF KINETIC RESULTS

In a kinetic investigation one measures, in some direct or indirect fashion, concentrations at various times. The problem is then to express the rate in terms of an equation which relates the rate to the concentrations of reactants, and sometimes of products or other substances present (e.g. of catalysts). If the reaction has a simple order one must determine what the order is, and also the rate constant. If it does not, as with the reaction between hydrogen and bromine (eqn. (9)), the form of the rate equation, and the magnitudes of the constants (e.g. k and k′ in eqn. (9)), must be determined.

There are two main methods for dealing with such problems; they are known as

(1) the method of integration

(2) the differential method.

In the method of integration one starts with a rate equation which one thinks may be applicable; for example, if the reaction is believed to be a first-order reaction one starts with

(14)

where c is the concentration of reactant. By integration one converts this into an equation giving c as a function of t, and then compares this with the experimental variation of c with t. If there is a good fit one can then, by simple graphical procedures, determine the value of the rate constant. If there is not one must try another rate equation and go through the same procedure until the fit is satisfactory. The method is seen to be something of a hit-and-miss one, but is nevertheless very valuable, especially where no special complications arise.

The second method, the differential method, employs the rate equation in its differential, un-integrated, form. Values of dc/dt are obtained from a plot of c against t, by taking slopes, and these are directly compared with the rate equation. The main difficulty with this method is that slopes cannot be obtained very accurately; in spite of this drawback the method is on the whole the more reliable one, and unlike the integration method does not lead to any particular difficulties when there are complexities in the kinetic