Chemical reactions molecular collisions, frequency

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

In chemiluminescence, some of the chemical reaction products developed remain in an excited state and radiate light when the excitation is discharged. This is particularly so at low pressures, when the collision frequency is low the excitation is discharged as light radiation. The extra energy bound to the excited molecule can discharge through impact or molecular dissociation. 

Molecular collisions are a fundamental requirement for chemical reactions, and concentrations are important because they determine the frequency of these collisions. Nevertheless, most collisions do not result in a chemical reaction, because the energy of collision is insufficient to surmount the barrier to reaction. This barrier, the energy required to rearrange atoms in going from reactants to products, is very substantial for most reactions it is called the activation energy, or the enthalpy of activation (A//a). 

According to the first postulate the cause of activation is radiation. Perrin was impressed by the fact that reaction rate in a uni-molecular reaction does not depend on the collision frequency, and so he sought for some source of energy other than collisions. Radiation is a natural source to consider. Furthermore, he pointed out that the temperature coefficient of the emission of monochromatic light from a heated solid is the same as the temperature coefficient of most chemical reactions. The similarity might be coincidence, but at the time it seemed significant. 

The chemical reaction is characterized on the one hand by the kinetic mechanism, that is to say the dependence on the concentrations of the participants in the reaction, on the other hand by the reaction (velocity) constant. This latter in the simplest form is k — Ae EIRT in which E is the energy of activation and A the frequency factor. The latter is in the classical collision theory equal to where Z the collision number ( io11) and P the probability factor or steric factor. The latter can be much larger than unity if the activation energy is divided over several internal degrees of freedom (mono-molecular reactions) but it can also be as low as io 8, e.g., in cases where steric hindrance plays a role. 

Collisions lie at the very heart of chemistry, because chemical reactions can occur only when molecules collide with one another. The kinetic theory of gases provides methods for estimating the frequency of molecular collisions and the average distance traveled by a molecule between collisions, both important in understanding the rates of chemical reactions (See Chapter 18). 

The kinetic molecular theory of gases (p. 178) postulates that gas molecules frequently collide with one another. Therefore, it seems logical to assume—and it is generally true—that chemical reactions occur as a result of collisions between reacting molecules. In terms of the collision theory of chemical kinetics, then, we expect the rate of a reaction to be directly proportional to the number of molecular collisions per second, or to the frequency of molecular collisions ... 

Both linear and nonlinear Raman spectroscopy can be combined with time-resolved detection techniques when pumping with short laser pulses [8.781. Since Raman spectroscopy allows the determination of molecular parameters from measurements of frequencies and populations of vibrational and rotational energy levels, time-resolved techniques give information on energy transfer between vibrational levels or on structural changes of short-lived intermediate species in chemical reactions. One example is the vibrational excitation of molecules in liquids and the collisional energy transfer from the excited vibrational modes into other levels or into translational energy of the collision partners. These processes proceed on picosecond to femtosecond time scales [8.77,8.79]. 

Therefore, E can easily be calculated, plotting the experimentally measured In k versus 1/T. According to the simple collision theory, an act of chemical reaction can only occur if colliding molecules have the kinetic energy which exceeds the activation barrier, The frequency factor. A, is the number of collisions of reacting molecules per unit time. The exponential term in (2.21) determines a portion of those collisions which can lead to the chemical transformation. Note that (2.21) postulates the fulfillment of the Boltzmann equilibrium distribution of molecular energies in the reaction mixture. 

In this first phase of development, the theories of chemical kinetics tried to resolve the problem of the calculation of the pre-exponential factor and activation energy in the Arrhenius equation. The difficulties in calculating A stemmed in large part from the confusion that had existed ever since the first quarter of the nineteenth century over the role of molecular colhsions on the rates of reaction. Today, we know that molecular collisions lead to the distribution of energy between molecules, but the rate of chemical reactions is determined both by the frequency of these colhsions and the factors associated with the distribution of energy. 

Arrhenius established equation (20.22) by fitting experimental data into his equation. This was before the collision theory of chemical reactions had been developed, but his equation is consistent with the collision theory. In the preceding section, we discussed the importance of (1) the frequency of molecular collisions, (2) the fraction of collisions energetic enough to produce a reaction. 

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