Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The Arrhenius equation predicts that the rate constant of a reaction can be decreased by increasing the temperature or by decreasing the activation energy.
Reason (R) : Changing the temperature of a reaction mixture is easy to do, however reducing the activation energy is more challenging in a reaction.
In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

When evaluating mathematical relationships like $y = e^{-x}$, remember that as $x$ (which acts as a stand-in for $E_a/T$) decreases, the overall value of $y$ increases. Thus, higher $T$ or lower $E_a$ strictly increases reaction rates.

Answer 1

The Correct Option is D

Step 1: Concept:
This is an Assertion-Reason type question focusing on chemical kinetics, specifically the Arrhenius equation and the practical manipulation of reaction rates.

Step 2: Key Formula or Approach:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
Where:
- $k$ is the rate constant
- $A$ is the pre-exponential factor
- $E_a$ is the activation energy
- $R$ is the universal gas constant
- $T$ is the absolute temperature

Step 3: Step-by-step Explanation:

• Evaluating Assertion (A): The statement claims that the rate constant ($k$) can be decreased by increasing temperature ($T$) or by decreasing activation energy ($E_a$).
Let's analyze the math: If $T$ increases, the term $\frac{E_a}{RT}$ becomes smaller. Because of the negative sign, $-\frac{E_a}{RT}$ becomes less negative (i.e., it increases). Therefore, the exponential $e^{-E_a/RT}$ increases, causing $k$ to increase.
Similarly, if $E_a$ is decreased, the magnitude of the negative exponent becomes smaller, again causing $k$ to increase.
Therefore, increasing $T$ or decreasing $E_a$ both result in a higher reaction rate, contradicting Assertion (A). Assertion (A) is explicitly false.

• Evaluating Reason (R): Modifying the temperature of a reaction requires only simple physical apparatus (like a heat bath). Conversely, decreasing the activation energy fundamentally changes the reaction pathway, which typically requires discovering and utilizing an appropriate catalyst. Finding a stable, efficient, and cost-effective catalyst is inherently much more challenging than merely turning up a thermostat. Therefore, Reason (R) is a fundamentally correct statement of fact.

Step 4: Final Answer:
Since (A) is false and (R) is true, the correct choice is option (D).