At several points in this chapter, and especially in Section 14-4, an experimental rate law has been explained in terms of a mechanism invoking reactive intermediates.
These may be radicals, such as C H3 or C O C H3, or relatively unstable com
pounds, such as H2I . Although the lifetime of such species is short in a reacting system, they usually survive enough collisions to come to equilibrium with the surroundings, that is, to reach the equilibrium Boltzmann distribution of transla
tional, rotational, and vibrational energy. They thus have definite physical and thermodynamic properties. They are perfectly " g o o d " chemical species.
Organic free radicals have been known for some time. F . Paneth and co-workers showed around 1930 that the thermal decomposition of lead tetraethyl or of mer
cury dimethyl produced ethyl and methyl radicals. These could be swept along by a flow of inert gas to react downstream with a film of lead or other metal, to regenerate metal alkyl compounds. The triphenylmethyl radical, produced by the dissociation of hexaphenylethane, is stable enough in solution to be observed both spectro-photometrically and through its paramagnetism.
The world of chemistry now includes a vast number of compounds that are too reactive to be stored in bottles but at whose properties the physical chemist can arrive by various contemporary means. F o r example, modern mass spectrometers routinely measure trace quantities of all kinds of molecular fragments produced either in a chemical reaction or by induced decomposition by light or by electron impact. In this last approach one determines the energy of impinging electrons needed to produce a given fragment, the threshold value being called the appearance potential. Methane produces C H4 + when 12 V electrons are passed through the gas, and at 14 V, C H3 + results. Methyl radicals generated in a chemical reaction and then electron bombarded give C H3 + again, but now with only 10 V electrons and the difference between 14 and 10 V must correspond to the energy for the process C H4 - > C H3 + H. Thus the energies of formation of unstable species can be estimated.
The kineticist contributes much information. F o r example, the activation energy for the recombination of two radicals, · R + · R' - > R R ' , is often zero or very small, which means that the activation energy for the reverse process gives the ΔΕ for the overall reaction (note Fig. 14-7) and hence that bond energy. Extensive tables
(c)
FIG. 14-14. (a) Molecular beam apparatus used for the study of the reaction of fluorine atoms with hydrocarbons. [From J. M. Parson, K. Shobatake, Υ. T. Lee, and S. A. Rice, Disc. Far. Soc. 5 5 , 344 (1973).] (b) The cone containing most of the KI product intensity for the reaction K + I2- * I + K I . (c) Velocity-angle contour map for the CsCl product of the C s + R b C l reaction. (From R. D. Levine andR. B. Bernstein, "Molecular Reaction Dynamics,"
Oxford Univ. Press, London and New York, 1974.)
COMMENTARY AND NOTES, SECTION 3 585 of bond energies and entropies make possible the fairly reliable calculation of activation energies and frequency factors for most reactions involving small mole
cules and radical fragments [see Benson (1968)].
Another facet of modern kinetics is the study of the intimate details of just how elementary reactions occur. An important technique is that using molecular beams, and a representative apparatus is illustrated in Fig. 14-14(a). Collimated beams of the two reactants impinge, and the angular distribution of product molecules is determined. A mass spectrometer may be used in front of the detector to select only that product desired. The beams emerge from a nozzle or an aperture in an oven with a thermal velocity distribution, but velocity selectors (see Fig. 2-12) can be used to limit the beam to a particular kinetic energy range. One of the beams may be made intermittent by means of a chopper so that the time lag before the appearance of product can be measured. It is, in brief, possible to obtain the kinetic energy as well as the angular distribution for the reaction products. One can thus calculate how much of the available energy (impact energy plus energy of reaction) appears as kinetic energy in the products, and therefore how much remains in the form of vibrational excitation. Also, ion-molecule reactions can be studied by using an ion source.
Some reactions that have been studied are
(1) Κ + H B r - > Η + K B r , (5) Κ + I C H8 - > K I + C H8, (2) C s + R b C l - > R b + CsCl, (6) F + C2H4 - * Η + C2H8F , (3) K + I2- > I + K I , (7) C s + S Fe- > C s F + S F6, (4) A r+ + D2 — D + A r D + , (8) Oa + + D2 - > D + 02D + .
Since reactant energy can be specified, Eq. (14-70) takes the more general form
where σ denotes the effective cross section or target area of a molecule for a reactive collision and is considered to be a function of the relative kinetic energy Ε and of temperature. Equation (14-90) reduces to Eq. (14-70) if σ , which corresponds to πσ2, is taken to be a constant. Treated on this basis, σ is 127 A2 for reaction (3).
The angular distribution of the products is of great interest, however, because it is informative as to how the reaction occurs. At one extreme is a "stripping" process whereby one reactant simply pulls off an atom from the other as it goes by. This appears to happen in the case with reaction (3). The resulting angular distribution of the KI product is shown in Fig. 14-14(b)+ (the other product, I, would have the complementary distribution required by momentum conservation). Alternatively, the reactants may form a weak association complex. This will have angular momen
tum and rotate in the plane defined by the two reactant beams. When the complex breaks up, the products will be concentrated in this plane but will otherwise be random in direction. This is the case for reaction (2). Figure 14-14(c) shows the angular distribution of the CsCl product, plotted as isoprobability contours in a polar plot, distance from the origin being proportional to velocity.1 Note that
+ Figure 14-14(b,c) s h o w s angular distributions taking the center o f mass as the frame o f reference. T h e experimental data, o f course, give angular distributions in the laboratory frame o f reference, and w o u l d be skewed in the direction toward which the t w o product b e a m s travel.
T h e conversion t o the center-of-mass frame o f reference is not a trivial process and can s o m e times be d o n e only with s o m e approximations.
(14-90)
there is now about equal probability for the CsCl to appear in the forward as in the backward direction.
Still more fundamental is the complete distribution of reaction "trajectories."
The term is used here to denote not just the angular distributions but also those of product kinetic and vibrational energies. For example, in reaction (6), the product CsF appears with a distribution of vibrational excitation. The relative probability falls off exponentially with increasing vibrational quantum number, but CsF in, say, the v = 4 state, is still quite probable. The understanding of reaction kinetics at this level of detail has become a challenging and difficult exercise in wave mechanics.
14-CN-4 Explosions
An explosion is a reaction which proceeds at an accelerating rate; once initiated it goes to completion very quickly and essentially cannot be stopped. The subject is obviously one of very great practical importance, ranging from the engineering of internal combustion engines to the devising of commercial and military explo-sives. The subject is alsa a very difficult one for the gas kineticist. A mixture of hydrogen and oxygen at about 500°C will react slowly and in a well-behaved way at a low pressure, say a few Torr. If the pressure is raised to about 10 Torr, an explosion occurs and this behavior continues up to a pressure of perhaps 20 Torr, above which the mixture again reacts in a normal, nonexplosive fashion. If the pressure is raised further to about 10 atm pressure, the mixture is again explosive!
A diagram showing these explosion limits is given in Fig. 14-15. The problem is to explain the behavior.
One general explanation for explosive reaction is simply that if the process is exothermic, the heat released may not be able to escape rapidly enough, and so the reaction mixture heats up, thereby increasing all reaction rates, which then increases the rate of heat production, which further accelerates the rise in tempera-ture and speed of reaction. Such an explosion is called a thermal explosion. There
Explosion region
t, °C
FIG. 14-15. Explosion limits of a stoichiometric mixture ofH2 + 02. (From S. W. Benson,
"The Foundations of Chemical Kinetics" Copyright I960, McGraw-Hill, New York. Used with permission of McGraw-Hill Book Co.)