Question

In Arrhenius equation, $k=A{{e}^{{-{{E}_{a}}}/{RT}\;}}$ A may be termed as the rate constant at:
This question has multiple correct options
(A) Very low temperature
(B) Very high temperature
(C) Zero activation energy
(D) The boiling temperature of the reaction mixture

Answer 1

Hint: The Arrhenius equation can be described as the effect of temperature on the velocity of a chemical reaction and is used for calculating the rate constants for a reaction. A is the frequency factor and k is the rate constant in the equation and at certain conditions both these values become equal and these conditions can be found by examining the exponential factor in Arrhenius equation.

Complete step by step answer:
  - The Arrhenius equation was formulated by a Swedish chemist Svante Arrhenius. He combined the Boltzmann distribution law and concepts of activation energy to derive the Arrhenius equation which is shown below
\[k=A{{e}^{{-{{E}_{a}}}/{RT}\;}}\]
  Where k is the rate constant
              A is the pre-exponential factor or frequency factor
              e is the mathematical quantity (exponential)
             ${{E}_{a}}$ is the activation energy
              R is the gas constant
              T is the temperature in kelvin.

-The pre-exponential factor or frequency factor (A) is specifically related to the molecular collision which can be determined experimentally as it varies with different reactions. As we know the activation energy (${{E}_{a}}$) is the threshold energy which the reactants must attain before reaching the transition state.
- We are asked to find the condition at which the frequency factor A may be termed as the rate constant k. From the Arrhenius equation it’s clear that for k becoming equal to A, the value of the term ${{e}^{{-{{E}_{a}}}/{RT}\;}}$ must be one. For this condition to be satisfied the term ${-{{E}_{a}}}/{RT}\;$must be zero.
- In the above respect, when T becomes infinity (T=∞) the term${-{{E}_{a}}}/{RT}\;$ become zero and also when the activation energy is zero (${{E}_{a}}$=0), the term${-{{E}_{a}}}/{RT}\;$ becomes zero and thus the frequency factor A become equal to rate constant k.
Hence we can easily conclude that at the conditions of very high temperature and zero activation energy, the A becomes equal to rate constant k.
So, the correct answer is “Option B and C”.

Note: Bear in mind that, according to the Arrhenius equation, larger the activation energy of a reaction, smaller will be the rate constant and greater is the influence of temperature on rate constant. At the lower temperature range, increase in the temperature will cause more change in the value of rate constant than the same increase in temperature at higher temperature range.