Correct statements regarding Arrhenius equation
Q. Correct statements regarding Arrhenius equation among the following are :

A. Factor $e^{-E_a/RT}$ corresponds to fraction of molecules having kinetic energy less than $E_a$.

B. At a given temperature, lower the $E_a$, faster is the reaction.

C. Increase in temperature by about $10^\circ$C doubles the rate of reaction.

D. Plot of $\log k$ vs $\dfrac{1}{T}$ gives a straight line with slope $= -\dfrac{E_a}{R}$.
A. A and B Only
B. B and D Only
C. B and C Only
D. A and C Only
Correct Answer: B and C Only

Explanation

Arrhenius equation is given by:

$$ k = A e^{-E_a/RT} $$

Statement A: The factor $e^{-E_a/RT}$ represents the fraction of molecules having kinetic energy greater than or equal to activation energy $E_a$, not less. Hence, statement A is incorrect.

Statement B: At a fixed temperature, a lower activation energy $E_a$ means a larger fraction of molecules can cross the energy barrier, resulting in a faster reaction. Hence, statement B is correct.

Statement C: Empirically, for many reactions, an increase in temperature by about $10^\circ$C approximately doubles the reaction rate. Hence, statement C is correct.

Statement D: From Arrhenius equation:

$$ \log k = \log A - \frac{E_a}{2.303R}\left(\frac{1}{T}\right) $$

So, slope of $\log k$ vs $\dfrac{1}{T}$ is $-\dfrac{E_a}{2.303R}$, not $-\dfrac{E_a}{R}$. Hence, statement D is incorrect.

Therefore, the correct statements are:

B and C only

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