Arrhenius equation: Increasing temperature increases the rate reaction

The rate of reaction of a particular reaction often increases as one increase the temperature. However, how can this belief be proved using Arrhenius equation? According to the Arrhenius equation, the rate constant (k) is obtained by the ratio of Ea to RT, in which Ea denotes required energy while RT is the available thermal energy. The Arrhenius Equation is given by:

k=Ae^-(Ea/RT)

When Ea is larger, it results in slower reactions. On the other hand, when RT is large, it leads to faster rate of reaction. Larger Ea gives smaller rate constant k, but larger RT produces larger rate constant (k). Larger rate constant increases the rate of reactions. 

By using Arrhenius equation, one can easily see that when the temperature is increased, the rate constant will also increase.

Let us consider these two scenarios. In the first scenario, Ea=120,000 Joules/mole, R=8.31 mol^-1 K^-1, and K=373K.In the second scenario, Ea=120,000Joules/mole, R=8.31 mol^-1 K^-1, and K=423K.

Substituting these numbers into Arrhenius equation when keeping A and k values constant gives a fraction of collision as follows:
Fraction of collisions=e^{-(120,000Joules/mole)/ (273K x 8.31 mol-1 K-1)}…………………………Scenario 1

Fraction= e^-(38.7)

= 1 x 10^-17

Fractions of collisions= e^{-(120,000Joules/mole)/ (423K x 8.31mol-1K-1)} ……………………...Scenario 2

= 1.5 X 10^-15

In scenarios 1 and two show that increasing temperature of the reaction from 373K to 423K increases fraction of collisions from 1 x 10^-17 to 1.5 X 10^-15. Therefore, increasing temperature increases the number of useful collisions of components participating in a chemical reaction.