Write the Arrhenius equation

The Arrhenius equation is $k = A e^{-E_a/(RT)}$ where:

• $k$ = rate constant
• $A$ = pre-exponential (frequency) factor
• $E_a$ = activation energy
• $R$ = gas constant
• $T$ = temperature

Check each statement

Statement A

"The Arrhenius equation holds true only for an elementary homogeneous reaction."

This is false.

The Arrhenius equation is an empirical relation and is widely applicable to many reactions, not only elementary homogeneous reactions.

Statement B

"The unit of $A$ is same as that of $k$ in Arrhenius equation."

This is true.

Since in $k = A e^{-E_a/(RT)}$ the exponential term is dimensionless, $A$ must have the same units as $k$.

Statement C

"At a given temperature, a low activation energy means a fast reaction."

This is true.

From $k = A e^{-E_a/(RT)}$ for fixed $T$, a smaller $E_a$ gives a larger value of $k$, hence the reaction is faster.

Statement D

"$A$ and $E_a$ as used in Arrhenius equation depend on temperature."

This is false in the usual JEE treatment.

In the Arrhenius equation, for a given reaction over a moderate temperature range, $A$ and $E_a$ are treated as constants.

Statement E

"When $E_a \gg RT$, $A$ and $E_a$ become interdependent."

This is false.

In the standard Arrhenius formulation, $A$ and $E_a$ are taken as independent parameters. The condition $E_a \gg RT$ does not imply such interdependence.

List the correct statements

The correct statements are: $\boxed{B \text{ and } C}$

Match with options

Option C says: B and C Only.

Hence the correct option is $\boxed{\text{C}}$

Compare with stored correct answer

Stored correct answer: C

Our derived answer matches the stored answer.