How is the Activation Energy of the Arrhenius equation related to the exponents in rate laws?
Rate Law

For the reaction:

$\ce{aA + bB -&gt; cP}$

The rate law is as follows:

$R = k[A]^x[B]^y$

where:


  $a$,$b$,and $c$ are stoichiometric constants which have integer values
   $[A]$ is the concentration of species A
   $x$ is the order with respect to species A
   $[B]$ is the concentration of species B
   $y$ is the order with respect to species B
   $k$ is the rate constant.


(1) Neither $x$ nor $y$ depend on $a$, $b$, or $c$. 

(2) Neither $x$ nor $y$ is required to be an integer value. 

(3) k is measured for a specific temperature. The Arrhenius Equation would predict how k would change with temperature. So k does not depend on any of $x$, $y$, $a$, $b$, or $c$. 

Say the reaction was for some sort of gas reaction. I now add a catalyst. I get a new rate:

$R_2 = k_2[A]^{x_2}[B]^{y_2}$

There isn't any way to use the first rate equation to predict what the second rate equation will be. (You could of course try to analyze the function of the catalyst to make predictions on what the best catalyst would be...)