Comparison between Collision theory, Transition state theory and Arrhenius law

In general, the three theories can be combined into a single expression that demonstrates the overall dependence of the reaction rate constants on temperature;
             ➩ k ∝ Tⁿ exp(-Eₐ/RT) 
                                     ----------------(1) 
Where, 
      the value of 'n' ranges between '0 and 1'.
                 ( 0 ≤ n ≥ 1 ) 
For some variations in temperature, the changes in the exponential term is more compare to the power term therefore the Exponential term is more sensitive compare to the power term. 

⛤If n=0, then the equation(1) reduces in the following form, 
      ➩ k ∝ T°.exp(-Eₐ/RT) 
      ➩ {k ∝ exp(-Eₐ/RT)} -------(2) 
Which is nothing but the Arrhenius law or Arrhenius equation. 

⛤If n=½, then the equation(1) reduces in the following form, 
     ➩{k ∝ T½ .exp(-Eₐ/RT)} -------(3) 
Which is nothing but the result of Collision theory. 

⛤If n=1, then the equation(1) reduces in the following form, 
     ➩ k ∝ T¹.exp(-Eₐ/RT)
     ➩ {k ∝ T exp(-Eₐ/RT)} --------(4) 
Which is nothing but the result of Transition state theory or Absolute rate theory. 

➛All three theories show that the value of the reaction rate constant changes with changes in the activation energy and the reaction's temperature.

➛let's see a picture which shows that how temperature affect the reaction rate constant, 
Fig:- Showing temperature dependency on the reaction rate constant
This suggests that Arrhenius law is a good approximation for the temperature dependence of both collision and transition state theories. 

Comparison between theories
  1. Collision theory, {k ∝ T½ .exp(-Eₐ/RT)} Transition state theory,{k ∝ T exp(-Eₐ/RT)} Arrhenius law, {k ∝ exp(-Eₐ/RT)}
  2. Depending on the expression, in the case of Transition state theory, the reaction rate constant is proportional to the first power of the temperature, while in the case of Collision theory, the reaction rate constant is proportional to the square root of the temperature and whereas in the case of Arrhenius law, there is no direct dependence of the reaction rate constants on temperature. 
  3. Collision theory tells us that a reaction occurs when reactive molecules collide with each other, while transition state theory tells us that a reaction occurs when reactive molecules have enough energy to form an intermediate complex.
  4. Collision theory is applied only to the gas phase reaction (because it is based on the kinetic theory of gases) while the transition state theory applies to reactions occurring in solution as well as reactions occurring in the gas phase.
  5. Resultant equation of transition state theory is more reliable than either the Arrhenius equation and the resultant equation of Collision theory. 
  6. In terms of accuracy, the transition state theory gives higher accuracy than collision theory.

Hope you have found this article helpful!! Feel free to comment if you have any queries.!!

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