JEE Chemistry 2025 Question with Solution

Given: Statements about the temperature dependence of rate constants are to be checked using the Arrhenius equation.

Find: Which statements are correct.

The Arrhenius equation is

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

where $k$ is the rate constant, $A$ is the pre-exponential factor, $E_a$ is the activation energy, $R$ is the gas constant, and $T$ is the absolute temperature.

Now examine each statement:

1. Statement A: "The Arrhenius equation holds true only for an elementary homogeneous reaction."

This is incorrect. The Arrhenius equation is used more generally and is not restricted only to elementary homogeneous reactions.

2. Statement B: "The unit of $A$ is same as that of $k$ in Arrhenius equation."

This is correct because the exponential factor

$$e^{-E_a/RT}$$

is dimensionless, so $A$ and $k$ must have the same units.

3. Statement C: "At a given temperature, a low activation energy means a fast reaction."

This is correct. From

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

a smaller $E_a$ gives a larger value of $k$ at the same temperature, so the reaction is faster.

4. Statement D: "$A$ and $E_a$ as used in Arrhenius equation depend on temperature."

This is incorrect in the basic Arrhenius treatment. They are generally taken as temperature-independent constants over a limited temperature range.

5. Statement E: "When $E_a \gg RT$. $A$ and $E_a$ become interdependent."

This is incorrect. There is no such direct interdependence implied by the condition $E_a \gg RT$.

Therefore, the correct statements are B and C only.

The correct option is C.

Given: A multiple-statement question based on the Arrhenius equation.

Find: The true statements among A to E.

Use the relation

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

• $k$ = rate constant
• $A$ = frequency factor or pre-exponential factor
• $E_a$ = activation energy
• $R$ = gas constant
• $T$ = temperature in kelvin

Analysis of statement A: The claim that the Arrhenius equation is valid only for an elementary homogeneous reaction is false. It is experimentally useful for many reactions, including complex ones.

Analysis of statement B: Since the exponential term is dimensionless,

$$\frac{E_a}{RT}$$

must be dimensionless, and hence

$$e^{-E_a/RT}$$

is dimensionless. Therefore, $A$ must carry the same units as $k$. So this statement is true.

Analysis of statement C: At fixed temperature, decreasing $E_a$ makes the exponent less negative, increasing $k$. A larger rate constant corresponds to a faster reaction. Hence this statement is true.

Analysis of statement D: In the elementary treatment of the Arrhenius equation used here, $A$ and $E_a$ are treated as constants over the temperature range considered. Thus the statement is false.

Analysis of statement E: The condition $E_a \gg RT$ does not make $A$ and $E_a$ interdependent. They remain separate parameters in the Arrhenius expression. So this statement is false.

Hence, only B and C are correct.

Therefore, the correct option is C.