Absolute expression of the reaction rate

We will now calculate the number of mass points that cross the pass per time unit in order to express the reaction rate. 

It is presumed that the activated complex is located witliin a box of arbitraiy width 5, which is located at the top of the barrier. The net reaction rate is defined by the average speed at which the activated complex surmounts the barrier. The probability p(v) for our mass point to have a speed between v and v + dv along a degree of freedom, with kg being the Boltzman s constant, is  

The average mass point speed of the activated complex at the top of the barrier, in the sense of crossing, is  

The integration limits of the denominator are between and +oo because the mass point can move in both directions, but only one direction is efficient so the nnmerator integration limits are between 0 and + . The calcnlation of the average passing speed of our mass point at the top of the barrier is  

The duration of the passage t is given by the average lifetime of our activated complex, which is defined by the quotient of the length of the barrier over the average speed of passage  

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