Collision theory, 532 table

Table 4.1 shows the remarkably good predictions made by transition state theory, and can be compared with the much poorer predictive value of collision theory, Table 4.2, demonstrating the considerable superiority of transition state theory. 

Table 11.3 compares observed rate constants for several reactions with those predicted by collision theory, arbitrarily taking p = 1. As you might expect, the calculated k s are too high, suggesting that the steric factor is indeed less than 1. 

Some of the rate constants discussed above are summarized in Table VI. The uncertainties (often very large) in these rate constants have already been indicated. Most of the rate constants have preexponential factors somewhat greater than the corresponding factors for neutral species reactions, which agrees with theory. At 2000°K. for two molecules each of mass 20 atomic units and a collision cross-section of 15 A2, simple bimolecular collision theory gives a pre-exponential factor of 3 X 10-10 cm.3 molecule-1 sec.-1... 

Collins and Jameson11 found that for small air bubbles (20 to 100 jzm), varying the particle zeta potential from +30 mV to +60 mV resulted in an order of magnitude change in the observed rate constants for each drop size. Table 9 shows the values of the calculated and observed first-order rate constants for the data of Collins and Jameson obtained when their particles (polystyrene) had the minimum stability (zeta potential + 30 mV). The observed rate constants are much smaller than those calculated from collision theory. Their data indicate that between 1 in 40 to I in 100 collisions results in the particles sticking to bubbles. This is consistent with the particle-collision removal mechanism. 

Table 4.2 Comparison of experimental A factors with collision numbers, Z, calculated from collision theory...

Table 7.1 lists values of log10 A for some ionic reactions, and shows qualitative agreement of experiment with this electrostatically modified collision theory. At first sight this indicates the correctness of the electrostatic treatment. 

We see in Table XII. 1 that we cannot separately identify the terms in the rate-constant expression for the thermodynamics equation or the collision theories without special assumptions. A complete identification of all the terms, frequencies, energies of activation and entropies of activation from experimental data is possible only for the Arrhenius equation and the transition-state theory. 

In this last expression, the preexponential factors are all similar in containing a product of two collision frequencies, a steric factor, and a mean lifetime. The latter may be approximated in a number of ways, each of which yields about 10 sec. Since bimolecular collision frequencies are about 10 liters/mole-sec, this would make Z V about 10 liters /mole -sec. The collision theory thus leads to a frequency of termolecular collisions of about 10 liters /mole -sec, which as we shall see from Table XII.9, is about the order of magnitude observed for the fastest reactions. 

Have you ever seen a demolition derby in which the competing vehicles are constantly colliding Each collision may result in the demolition of one or more vehicles as shown in Figure 17-2a. The reactants in a chemical reaction must also come together in order to form products, as shown in Figure 17-2b. The collision theory states that atoms, ions, and molecules must collide in order to react. The collision theory, summarized in Table 17-2, explains why reactions occur and how the rates of chemical reactions can be modified. 

We can extend the collision theory to calculate the rate constant for bimolecular reactions of two species, A and B. Comparing observed and predicted rate constants gives the values of P shown in Table 18.1. As the colliding molecules become larger and more complex, P becomes smaller because a smaller fraction of collisions is effective in causing reaction. The steric factor is an empirical correction that has to be identified by comparing results of the simple theory with experimental data. It can be predicted in more advanced theories but only for especially simple reactions. 

Since the collision theory is the older and simpler, Eq. (1) has been used in the analysis of most of the published results. Table 13-2 lists the values of constants for this equation for some typical hydrolytic rea,ctions. 

The only exception to this general conclusion is in the case of reactions which, according to all the available evidence, are elementary. This is discussed in more detail in Section 7. However, for now it can be noted, as demonstrated by the results in Table 4.1, that a simple collision theory can predict the form of the experimental rate equation for an elementary reaction involving two reactant species. For reactions which are not elementary, such as those in Table 4.2, no such theoretical approach is available. Indeed, if it were, then a large area of experimental chemical kinetics would never have come into existence. 

Table 7.1 A comparison of experiment with collision theory for a selection of gas-phase bimolecular reactions...

The ratio of collision numbers, (H2/O2) = 2.3 at 373 K. Note that the ratio obtained from Table 2.2b at 298°K is just about the same—even a little smaller. The weak dependence of collision number per unit volume on temperature is due to a compensation between collision frequency (increasing) and number density (decreasing). This should tell us that dramatic increases in reaction rate with temperature as observed in experiment surely cannot be explained solely on the basis of simple collision theory. 

The values for (AA°) in Table 2.5e are obtained from pre-exponential factor measurements, values for p determined from equation (2-33a) or (2-34a), and the estimation procedure suggested in Illustration 2.5. In general, these are not elementary steps, although for many years it was believed that the hydrogen/iodine reaction was a true bimolecular reaction, since both collision theory and TST estimates of pre-exponential factors were in good agreement with experiment. This view, however, has changed (J.H. Sullivan, J. Chem. Phys., 46, 73 (1967)]. ... 

A useful comparison between the predictions of simple collision theory and experiment can be made, since if the activation energy is determined, the experimental frequency factor can be directly compared with that predicted by Eq. (2-33). The hard-sphere diameter can be estimated from transport properties, although the choice of this parameter is somewhat arbitrary. In Table 2-1 a comparison between theory and experiment is presented for several well-studied bimolecular reactions (cf. Benson [10] for a more complete compilation). The tabulated steric factor is that value which makes the experimental and theoretical values coincide. In view of the assumptions involved, many of the steric factors are surprisingly close to unity. However, marked deviations in the form of unreasonably small steric factors do occur, especially if polyatomic molecules are involved. This often indicates that quantum-mechanical effects may be important or that a different classical theory may be required. 

Table 3-1 gives a comparison of the experimental results with the predictions of the collision theory. Since the entries in the third column are the elastic-hard-sphere results for the preexponential factor it would appear... 

The corrections to Eyring s theory in Tables I-IV are smaller than those to the simple collision theory. This is easily understood by means of the relation (68.Ill), which yields... 

Tables 2.1 to 2.3 contain the data needed for the application of the collision theory to the reactions of combination and disproportionation of two free radicals.

The pre-exponential factors for the reactions of ozone with alcohols, calculated according to the activated complex method (ACT) and collision theory (CT) are represented in Table 5. 

The effect of a catalyst on the rate equation is to increase the value of the rate constant. Table 16.11 summarizes the changes that affect the rate of reaction and the rate constant. Rate constants are unaffected by changes in concentration and are only affected by temperature (as described by the Arrhenius equation) or the presence of a catalyst, which provides a new pathway or reaction mechanism. Rates increase with concentration and pressure (if gaseous reactants are involved), which can be accounted for by simple collision theory (Chapter 6). 

In the temperature range 300-700 K the Arrhenius parameters, given in Table 8.1, are 2x 10 cm mol sec" and 2 kJ mol. The -factor, which is about 20% of that estimated using collision theory, may be estimated using (9.14)-(9.16) if reasonable assumptions about the structure of the activated complex of HIg are made. Both geometry and vibrational frequencies must be estimated. 

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