Chemical reaction rates, collision equilibrium rate constant

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

Each of the rate terms, k+ and k, in Eq. (9.16) is related to concentrations in a way that one would predict if the probability of reaction were dependent on the collision of randomly moving particles the rate is proportional to the product of the number of entities involved in the reaction. All other factors that determine the reaction rate (energy barriers, temperature dependence, the effect of other species in solution, catalysis, etc.) are represented in the rate constant, k, which has units necessary to balance the left- and right-hand sides of the rate expression. Because ion interaction effects that are accounted for by activity coefficients in chemical equilibrium calculations (Chapter 3) are all incorporated into the rate constant, concentrations and not activities are used on the right-hand side of the reaction rate equation. 

The Collision Theory of Chemical Reactions Energy Changes During a Molecular Collision Conditions That Affect the Rate of a Chemical Reaction The Development of a Chemical Equilibrium Le Chatelier s Principle The Equilibrium Constant The Significance of the Value of K... 

How can reactions take place starting with bulk thermal reactants for which the proportion of molecules in the higher vibrational states is exponentially small It is a requirement of chemical kinetics that reaction rates be measured for reactants that are maintained in thermal equilibrium. If necessary, a buffer gas is added whose role is to insure that thermal equilibrium is maintained, hy collisions. In the bulk the very few vibrationally hot, i.e., excited, HCl molecules react with I atoms produced by thermal dissociation of I2. This displaces the remaining HCl molecules from their thermal equilibrium because the mean vibrational energy is now lower. Collisions with the buffer gas restore the thermal equilibrium or, on a molecular level, collisions repopulate the higher vibrational states of HCl and also dissociate I2 molecules. Next, the vibrationally hot HCl molecules are preferentially removed by reaction with I atoms. Equilibrium needs to be restored, and so on. All this is hidden when we just focus attention on the thermal reaction rate constant. 

In his 1920 article on reaction kinetics, Polanyi noted that existing kinetic theories could not be quite correct, as the ratio of forward to backward reaction rates failed to yield the equilibrium constants obtained on the basis of thermodynamics. In 1925, in a rejoinder to a paper in which Max Bom and James Franck argued that it would be nearly impossible for a collision of molecules to incite chemical reactions, Polanyi and Wigner managed to resolve the discrepancy between forward and reverse reaction rates for the case of two-body capture and its reverse. 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

A mixture of electrons, ions, and atoms forms a system similar to that which we considered in Chap. X, dealing with chemical equilibrium in gases. Equilibrium is determined, as it was there, by the mass action law. This law can be derived by balancing the rates of direct and inverse collisions, but it can also be derived from thermodynamics, and the equilibrium constant can be found from the heat of reaction and the chemical constants of the various particles concerned. The heats of reaction can be found from the various ionization potentials, quantities susceptible of independent measurement, and the chemical constants are determined essentially as in Chap. VIII. Thus there are no new principles involved in studying the equilibrium of atoms, electrons, and ions, and we shall merely give a qualitative discussion in this section, the statements being equivalent to mathematical results which can be established immediately from the methods of Chap. X. 

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