Collision theory, of bimolecular

There is an inunediate coimection to the collision theory of bimolecular reactions. Introducing internal partition functions excluding the (separable) degrees of freedom for overall translation. 

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. 

The Collision Theory of Bimolecular Gaseous Reactions. This is the earliest theory of reaction rates. Since reaction between two species takes place only when they are in contact, it is reasonable to suppose that the reactant species must collide before they react. Since our knowledge of molecular collisions is more complete for the gaseous phase than for the liquid phase (in the latter case we speak of encounters rather than collisions), we will restrict our discussion to bimolecular reactions in the gaseous phase. 

Present, R.D. (1955) Note on the simple collision theory of bimolecular reactions Proc. Natl. Acad. Sci. USA 41, 415-417. 

A deeper understanding of what the Arrhenius parameters mean can be developed from the collision theory of bimolecular gas phase reactions, which itself is based upon kinetic gas theory. The requirement for two particles like H2 and I2 or two HI particles to react with each other is that they encounter each other, i.e., that they collide. It has been found, however, that the frequency of collisions in an ideal gas (which is of the order of 10 s at standard conditions) by far surpasses the... 

Both sets of data, k and (it the Arrhenius equation veiy well and hence are consistent with the collision theory of bimolecular gas-phase reactions which provides an equation 24.19 compatible with the Arrhenius equation. The numerical values for k and A may be compared to the results of Exercise 24.7(a) and are in rough agreement at 647 K, as is the value of E. ... 

The Collision Theory of Bimolecular Elementary Processes in Gases... 

The empirical Arrhenius formula for the temperature dependence of elementary rate constants was presented. This empirical formula was based on an idea that activated molecules with high energy are necessary for the reaction to occur and that the population of molecules with a characteristic activation energy is given by the Boltzmann probability distribution. We presented the collision theory of bimolecular reaction rates, using first the assumption that all collisions with a relative kinetic energy greater than a critical value would lead to reaction. 

The basis of the collision theory of bimolecular reactions is the idea that molecular encounters that lead to reaction are associated with reactive cross sections. Consider a general reaction between species A and B moving with velocities and... 

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