Consider the following statements related to temperature dependence of rate constants. Identify the correct statements:
A. The Arrhenius equation holds true only for an elementary homogenous reaction.
B. The unit of A is same as that of k in Arrhenius equation.
C. At a given temperature, a low activation energy means a fast reaction.
D. A and Ea as used in Arrhenius equation depend on temperature.
E. When $$E_a \gg RT$$, A and $$E_a$$ become interdependent.
Choose the correct answer  from the options given below :

The empirical Arrhenius equation for the temperature dependence of a rate constant is
$$k = A \; e^{-\;E_a/RT}$$
where $$k$$ is the rate constant, $$A$$ is the pre-exponential (frequency) factor, $$E_a$$ is the activation energy, $$R$$ is the gas constant and $$T$$ is the absolute temperature.

Statement A: “The Arrhenius equation holds true only for an elementary homogeneous reaction.”
The equation is observed to describe a very wide range of reactions—elementary as well as complex, homogeneous as well as heterogeneous. Hence Statement A is incorrect.

Statement B: “The unit of $$A$$ is same as that of $$k$$ in the Arrhenius equation.”
In $$k = A\,e^{-E_a/RT}$$ the exponential factor is dimensionless. Therefore $$A$$ must possess exactly the same units as $$k$$ so that the product on the right retains the units of a rate constant. Statement B is correct.

Statement C: “At a given temperature, a low activation energy means a fast reaction.”
For fixed $$T$$, the exponential term is $$e^{-E_a/RT}$$. A smaller $$E_a$$ gives a larger value of the exponential term, hence a larger $$k$$ and therefore a faster reaction. Statement C is correct.

Statement D: “$$A$$ and $$E_a$$ as used in the Arrhenius equation depend on temperature.”
In the usual Arrhenius treatment, both $$A$$ and $$E_a$$ are taken to be temperature-independent over a moderate temperature range. They may vary slightly in reality, but the statement that they depend on temperature is not accepted in the standard model. Statement D is incorrect.

Statement E: “When $$E_a \gg RT$$, $$A$$ and $$E_a$$ become interdependent.”
Even if $$E_a$$ is much larger than $$RT$$, the Arrhenius parameters remain independent constants obtained from the intercept and slope of an Arrhenius plot. Statement E is incorrect.

Therefore, only Statements B and C are correct.

Correct answer: Option C (B and C Only).