Question

In the Arrhenius equation, \[K=A{{\exp }^{{{-E}_{a}}/RT}}\]. At zero activation energy or infinite temperature, A may be termed as:
(a) time constant
(b) rate constant
(c) reaction rate
(d) none of the above

Answer 1

Hint:Chemical kinetics are an integral part of physical chemistry. They help us determine how a reaction proceeds in the given circumstances. It tells us whether the reaction is fast, slow or spontaneous.

Complete step by step solution:
Arrhenius collected reaction-rate data of many reaction and observed that it followed a particular pattern based on three factors:
(1) The number of collisions per unit time.
(2) The fraction of collisions that occur with the correct orientation.
(3) The fraction of the colliding molecules that have an energy greater than or equal to Ea.
Based on these observations he gave the famously know Arrhenius equation, written as:
\[K=A{{\exp }^{{{-E}_{a}}/RT}}\]
where, K = rate constant,
\[{{E}_{a}}\] = activation energy,
R = gas constant,
A = constant called the pre-exponential factor,
T = temperature.
This formula is a general comparison between the energy of the molecules (RT) and the activation energy (\[{{-E}_{a}}\]). Here, the pre-exponential factor is a constant, specific to the reaction.
Now from the formula we can observe that:
When activation energy approaches zero,
\[{{E}_{a}}\to 0,\,\dfrac{{{-E}_{a}}}{RT}\to 0,\,\exp \to 1\]
\[K=A{{\exp }^{{{-E}_{a}}/RT}}=A\]
When temperature approaches infinity,
\[T\to \infty ,\dfrac{{{-E}_{a}}}{RT}\to 0,\,\exp \to 1\]
\[K=A{{\exp }^{{{-E}_{a}}/RT}}=A\]

We can conclude that at zero activation energy or infinite temperature, A may be termed as rate constant (K). So, the correct option is (b).

Note: Both of the cases are not practical. By the very definition of chemical reaction, it must involve change in energy during the phase of reaction. Thu, activation energy can never be zero.
Similarly, infinite temperature is also not feasible.