Activation energy collision numbers

Number of collisions with the activation energy = (total number of collisions)e " ... 

The reaction constant k was related to a collision number Z, the number of reactant molecules colliding/unit time, and an activation energy E by the Anhenius equation... 

A typical value of the collision number is 10 °s in gases at one atmosphere pressure and room temperature, and the number of successful collisions which can bring about the chemical reaction is equal to this number multiplied by the Anhenius or probability factor, exp(— /f 7 ), where E is the activation energy, the critical collision energy needed for reaction to occur. 

If hvQ is small compared with kT, the partition function becomes kT/hvQ. The function kT jh which pre-multiplies the collision number in the uansition state theoty of the bimolecular collision reaction can therefore be described as resulting from vibration of frequency vq along the transition bond between the A and B atoms, and measures the time between each potential n ansition from reactants to product which will only occur provided that die activation energy, AEq is available. 

The temperature dependence of a rate is often described by the temperature dependence of the rate constant, k. This dependence is often represented by the Arrhenius equation, /c = Aexp(- a/i T). For some reactions, the temperature relationship is instead written fc = AT" exp(- a/RT). The A term is the frequency factor for the reaction, which reflects the number of effective collisions producing a reaction. a is known as the activation energy for the reaction, and is a measure of the amount of energy input required to start a reaction (see also Benson, 1960 Moore and Pearson, 1981). 

By increasing the temperature T, we have not changed the magnitude of the activation energy, nor have we changed the value of AH of reaction. The increased rate is a kinetic result we have enhanced the number of successful reaction collisions per unit time. 

With all other factors held constant, decreasing the number of molecules decreases the chance of collision. Adding an accelerating catalyst has no effect on the rate of collisions. It lowers the activation energy, thereby increasing the chance for effective molecular collisions. Furthermore, it increases the rate of production. 

In a purely photochemical reaction the absorption of radiant energy is plainly responsible for the activation. This suggested the possibility that thermal reactions are also due to activation by the thermal radiation which is present at every temperature. The argument was very forcibly presented by Perrin who showed that if the specific rate of a imimolecular gas reaction remains constant, with indefinite diminution in pressure, activation must be by radiation since the number of opportunities for activation by collision also diminishes without limit. In fact, the decomposition of nitrogen pentoxide, the first gas reaction shown to be unquestionably unimolecular, was found to have a specific reaction rate constant over a wide range of pressure, and apparently increasing at very low pressures. ... 

If we compare the rate constants for the recombination of alkyl radicals ( 1010,5 liter/mole-sec.) with collision frequencies of these same radicals (1011-3 liter/mole-sec.) we are struck by the very high efficiency (1 in 6 collisions) of these recombination processes. For the younger generation of kineticists these values are by now well established and occasion no surprise. However, one has only to turn back in the literature some 15 or more years to discover that the older generation was quite prepared for recombination efficiencies of the order of 10 a to 10 4 while a number of respected workers anticipated activation energies of the order of 3 to 15 kcal. What was the origin of such speculations and why was the range so broad ... 

The velocity constant of a reaction can be expressed in the form xe E RT- With bimolecular reactions the variations in x> which depends on the collision number, are small from reaction to reaction compared with the variations of many powers of ten in the exponential term. Similarly, even in termolecular reactions the exponential term appears to play the principal part in determining the region of temperature in which the velocity of reaction shall attain an assigned value. The gaining of the energy of activation appears to be the principal determining factor in simple reactions, and it is often roughly true to... 

A catalyst increases the rate of a chemical reaction by providing an alternative reaction path which has a lower activation energy. A catalyst does not increase the number of collisions between the reactant particles but only causes more of the collisions to become successful collisions, so increasing the rate of the reaction. 

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