Analysis of Assertion (A) and Reason (R)

The Assertion (A) states that the Arrhenius equation predicts that the rate constant ($k$) decreases with increasing temperature or decreasing activation energy ($E_a$). The Reason (R) discusses the relative ease of changing temperature versus reducing activation energy.

Evaluating Assertion (A)

The Arrhenius equation is given by:

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

Where:

• $k$ = rate constant
• $A$ = pre-exponential factor
• $E_a$ = activation energy
• $R$ = ideal gas constant
• $T$ = absolute temperature

Let's analyze the effects stated in Assertion (A):

• Effect of Temperature ($T$): As temperature ($T$) increases, the term $E_a / (RT)$ decreases. Consequently, the exponent $-E_a / (RT)$ becomes less negative (closer to zero). Since the exponential function $e^x$ increases as $x$ increases, $e^{-E_a / (RT)}$ increases. Therefore, the rate constant ($k$) increases with increasing temperature. Assertion (A) incorrectly states it decreases.
• Effect of Activation Energy ($E_a$): As activation energy ($E_a$) decreases, the term $E_a / (RT)$ decreases. Similar to the temperature effect, the exponent $-E_a / (RT)$ becomes less negative, leading to an increase in the rate constant ($k$). Assertion (A) incorrectly states that $k$ decreases with decreasing $E_a$.

Therefore, Assertion (A) is incorrect.

Evaluating Reason (R)

Reason (R) states:

• "Changing the temperature of a reaction mixture is easy to do" - This is generally true as heating or cooling are standard laboratory operations.
• "reducing the activation energy is more challenging in a reaction" - This is also generally true. Reducing $E_a$ often requires catalysts or altering the reaction pathway, which can be complex compared to temperature adjustments.

Therefore, Reason (R) is correct.

Conclusion

Based on the analysis, Assertion (A) is incorrect, while Reason (R) is correct. This corresponds to Option D.