Question

Two statements, one Assertion (A) and the other Reason (R) are given. Choose the correct option. Assertion: The rate constant (\(k\)) for a chemical reaction gets nearly doubled for a \(10^\circ\) rise in temperature. Reason: The number of bimolecular collisions between reactant molecules increases with increase in temperature.

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

Hint:

Temperature increases reaction rate mainly by increasing the number of molecules with energy greater than activation energy, not just by increasing collision frequency.

Answer 1

The Correct Option is B

Step 1: Understand the Assertion (A).
The assertion states that the rate constant \(k\) nearly doubles for every \(10^\circ C\) rise in temperature.
This is an empirical rule observed for many reactions and is explained by the Arrhenius equation.
\[ k = A e^{-\frac{E_a}{RT}} \] Thus, assertion (A) is correct.

Step 2: Understand the Reason (R).
The reason states that the number of bimolecular collisions increases with temperature.
As temperature increases, the kinetic energy of molecules increases, leading to more frequent collisions.
Hence, statement (R) is also correct.

Step 3: Examine whether R explains A.
Although collisions increase with temperature, this is not the primary reason for the sharp increase in rate constant.
The major factor is the increase in the number of molecules having energy greater than activation energy \(E_a\).

Step 4: Role of activation energy.
According to the Arrhenius equation, a small increase in temperature causes a large increase in the fraction of molecules crossing the energy barrier.
This leads to a significant increase in rate constant.

Step 5: Compare both effects.
Increase in collision frequency contributes slightly to rate increase.
However, the exponential increase in high-energy molecules is the dominant factor.
Therefore, the reason given does not correctly explain the assertion.

Step 6: Final conclusion.
Both Assertion (A) and Reason (R) are correct, but Reason (R) is not the correct explanation of Assertion (A).
Final Answer:
The correct option is:
\[ \boxed{\text{(B) Both A and R are correct but R is not the correct explanation of A}} \]