Collision theory gases

On the other hand, equation (i), based on the simple gas collision theory, gives Z, = n X 1.5 X 10". This discrepancy between the two methods must now be examined in detail, as the question of using the correct collision formula is fundamental to the interpretation of the kinetics of surface reactions. 

The major problem is how to calculate the kinetics of these reactions. There are several proposals and one of them is gas collision theory, because they are of the same order of magnitude. Collisions occur repeatedly with high frequency, so they constitute multiple collisions. It is estimated that the distances between the molecules in the liquid phase are approximately equal, whereas in the gas phase are quite different. Moreover, besides the attractive forces, there are also repulsive forces, but the important thing is that for the reaction to occur it is necessary to overcome the energy barrier E. Differently from the reactions in the gas phase, the collisions in the liquid phase are 10-1000 times higher, but depend on other properties such as the viscosity. 

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

From what we know about molecular sizes, we can calculate that a particular CH4 molecule collides with an oxygen molecule about once every one-thousandth of a microsecond (1(M seconds) in a mixture of household gas (methane, formula CH4) and air under normal conditions. This means that every second this methane molecule encounters 10 oxygen molecules Yet the reaction does not proceed noticeably. We can conclude either that most of the collisions are ineffective or that the collision theory is not a good explanation. We shall see that the former is the case—we can understand why most collisions might be ineffective in terms of ideas that are consistent with the collision theory. 

Now that we have a model, we must check its consistency with various experiments. Sometimes such inconsistencies result in the complete rejection of a model. More often, they indicate that we need to refine the model. In the present case, the results of careful experiments show that the collision model of reactions is not complete, because the experimental rate constant is normally smaller than predicted by collision theory. We can improve the model by realizing that the relative direction in which the molecules are moving when they collide also might matter. That is, they need to be oriented a certain way relative to each other. For example, the results of experiments of the kind described in Box 13.2 have shown that, in the gas-phase reaction of chlorine atoms with HI molecules, HI + Cl — HC1 I, the Cl atom reacts with the HI molecule only if it approaches from a favorable direction (Fig. 13.28). A dependence on direction is called the steric requirement of the reaction. It is normally taken into account by introducing an empirical factor, P, called the steric factor, and changing Eq. 17 to... 

According to the collision theory of gas-phase reactions, a reaction takes place only if the reactant molecules collide with a kinetic energy of at least the activation energy, and they do so in the correct orientation. 

A gas composed of molecules of diameter 0.5 nm takes part in a chemical reaction at 300. K and 1.0 atm with another gas (present in large excess) consisting of molecules of about the same size and mass to form a gas-phase product at 300. K. The activation energy for the reaction is 25 kj-mol. Use collision theory to calculate the ratio of the reaction rate at 320. K relative to that at 300. K. 

The case of m = Q corresponds to classical Arrhenius theory m = 1/2 is derived from the collision theory of bimolecular gas-phase reactions and m = corresponds to activated complex or transition state theory. None of these theories is sufficiently well developed to predict reaction rates from first principles, and it is practically impossible to choose between them based on experimental measurements. The relatively small variation in rate constant due to the pre-exponential temperature dependence T is overwhelmed by the exponential dependence exp(—Tarf/T). For many reactions, a plot of In(fe) versus will be approximately linear, and the slope of this line can be used to calculate E. Plots of rt(k/T" ) versus 7 for the same reactions will also be approximately linear as well, which shows the futility of determining m by this approach. 

How useful is the rate expression derived from collision theory for describing adsorption For cases in which adsorption is not activated, i.e. E = 0, the collision frequency describes, in essence, the rate of impingement of a gas on a surface. This is an upper limit for the rate of adsorption. In general, the rate of adsorption is lower, because the molecules must, for example, interact inelastically with the sur-... 

Primary Ionization—(1) In collision theory the ionization produced by the primary particles as contrasted to the "total ionization" which includes the "secondary ionization" produced by delta rays. (2) In counter tubes the total ionization produced by incident radiation without gas amplification. 

Termolecular Reactions. If one attempts to extend the collision theory from the treatment of bimolecular gas phase reactions to termolecular processes, the problem of how to define a termolecular collision immediately arises. If such a collision is defined as the simultaneous contact of the spherical surfaces of all three molecules, one must recognize that two hard spheres will be in contact for only a very short time and that the probability that a third molecule would strike the other two during this period is vanishingly small. 

An increase in the concentration of a reactant (or reactants) in solution, or an increase in the pressure on a gas-phase reaction, increases the rate of reaction. In terms of the collision theory ... 

The science of reaction kinetics between molecular species in a homogeneous gas phase was one of the earliest fields to be developed, and a quantitative calculation of the rates of chemical reactions was considerably advanced by the development of the collision theory of gases. According to this approach the rate at which the classic reaction... 

Simple Collision Theory (SCT) of Bimolecular Gas-Phase Reactions... 

Simple collision theory recognizes that a collision between reactants is necessary for a reaction to proceed. Does every collision result in a reaction Consider a 1 mL sample of gas at room temperature and atmospheric pressure. In the sample, about 10 collisions per second take place between gas molecules. If each collision resulted in a reaction, all gas phase reactions would be complete in about a nanosecond (10 s)—a truly explosive rate As you know from section 6.2, however, gas phase reactions can occur quite slowly. This suggests that not every collision between reactants results in a reaction. 

The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed for orienting molecules prior to collision (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) bmte force orientation of polar molecules in extremely strong electric fields. Several chemical reactions have been studied with one of the reagents oriented prior to collision. ... 

Most treatments encountered in discussions of collision theory primarily are concerned with reactions in the gas phase. However, most of the reactions in chemistry and biochemistry occur in solutions. In solutions, the molecules are moving in the potential field of their neighbors rather than freely as in the gas phase. Thus, the potential energy varies and holes in the solvation shell permits displacement of the molecule from its original position. There are also rapid collisions with molecules that make up the solvent cage as the molecule makes its series of discontinuous displacements. Two molecules in solution that become neighbors will tend to collide a number of times (often referred to as an encounter) before they separate (or before they react). 

Trimolecular reactions (also referred to as termolecular) involve elementary reactions where three distinct chemical entities combine to form an activated complex Trimolecular processes are usually third order, but the reverse relationship is not necessarily true. AU truly trior termolecular reactions studied so far have been gas-phase processes. Even so, these reactions are very rare in the gas-phase. They should be very unhkely in solution due, in part, to the relatively slow-rate of diffusion in solutions. See Molecularity Order Transition-State Theory Collision Theory Elementary Reactions... 

The rate of collision of gas molecules is given by gas kinetic theory. Molecules have an average kinetic energy given by the expression... 

Collision theory is based on the concept that molecules behave like hard spheres during a collision of two species, a reaction may occur. To estimate a rate constant for a bimolecular reaction between reactants A and B based on this theory, one needs first to calculate the number of collisions occurring in a unit volume per second (ZA1 ) when the two species, A and B, having radii rA and ru, are present in concentrations jVa and Aru, respectively. From gas kinetic theory, this can be shown to be given by Eq. (I) ... 

Instead, we must turn to the kinetic molecular theory of gases for an estimate of the frequency with which molecules collide with a solid surface. We shall not be misled, however, if we anticipate that this pressure is low. Example 9.6 is a numerical examination of gas collisions with walls. 

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