Van't Hoff argued that the temperature  of a reaction and the standard equilibrium constant  exhibit the relation:
where  denotes the apposite standard internal energy change value.
Let  and  respectively denote the forward and backward reaction rates of the reaction of interest, then
, an equation from which  naturally follows.
Substituting the expression for  in eq.(), we obtain .
The preceding equation can be broken down into the following two equations:
and 
where  and  are the activation energies associated with the forward and backward reactions respectively, with .
Experimental findings suggest that the constants in eq.() and eq.() can be treated as being equal to zero, so that  and 
Integrating these equations and taking the exponential yields the results  and , where each pre-exponential factor  or  is mathematically the exponential of the constant of integration for the respective indefinite integral in question.