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The Kinetic Theory of Gases relates the temperature of a gas and the average mechanical energies of its individual molecules.
To derive this equation, we will be assuming that our container holds a statistically large sample of molecules of an ideal gas [remember NA= 6.02 x 1023] that are moving simultaneously in three dimensions.
We can also assume that the majority of their velocities will have non-zero x-, y-, and z-components. But remember, that a particle's average velocity is the vector sum of its three components and that no velocity component is statistically more likely, or more prevalent, than another. In chapter 2 we saw that if we had ?rA as a function of X, [?rA= f(X)] we could size many reactors and reactor sequences and systems.

The larger the activation energy, the more temperature sensitive k and thus the reaction rate.
In our development of collision theory we assumed all molecules had the same average energy. By increasing the temperature we increase the kinetic energy of the reactant molecules which can in turn be transferred to internal energy to increase the stretching and bending of the bonds causing them to be in an activated state, vulnerable to bond breaking and reaction. We see that as the temperature is increased we have greater number of molecules have energies E A or greater and hence the reaction rate will be greater. The activation energy is a measure of the minimum energy a that the reacting molecules must have in order for the reaction to occur.

Note that the phrase "average" velocity has also been replaced with the expression "root mean square" or rms velocity, vrms. However, all the molecules don?t have the same energy, rather there is distribution of energies where some molecules have more energy than others.
The distraction function f(E,T) describes this distribution of the energies of the molecules.

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