Q39 / 180 · COMEDK 2025 (10 May Shift 1) · Chemistry
Two statements, One Assertion (A) and the other Reason (R) are given. Choose the right option.
Assertion: The rate constant $(\mathrm{k})$ for a chemical reaction gets nearly doubled for a $10^{\circ}$ rise in temperature.
Reason: The number of bimolecular collisions between reactant molecules increase with increase in temperature
- AA is wrong but $R$ is correct.
- Correct answerBBoth $A$ and $R$ are correct but $R$ is not the correct explanation of $A$.
- CBoth $A$ and $R$ are correct and $R$ is the correct explanation of $A$.
- DA is correct but R is wrong.
Solution
The rate constant $k$ of a reaction is given by the Arrhenius equation $k = A e^{-E_a / RT}$. For most reactions, a $10^{\circ}C$ rise in temperature leads to a doubling or tripling of the rate constant. This is primarily due to the increase in the fraction of molecules possessing energy greater than or equal to the activation energy $E_a$, which is represented by the term $e^{-E_a / RT}$.
The number of bimolecular collisions between reactant molecules does increase with an increase in temperature because the average kinetic energy and velocity of the molecules increase. However, the increase in the total number of collisions is proportional to $\sqrt{T}$, which is very small compared to the exponential increase in the fraction of effective collisions (those with energy $\ge E_a$).
Therefore, while both statements are factually correct, the increase in the number of collisions is not the primary reason for the doubling of the rate constant; the primary reason is the exponential increase in the fraction of molecules with energy greater than the activation energy. Thus, R is not the correct explanation of A.
Answer: Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$.
The number of bimolecular collisions between reactant molecules does increase with an increase in temperature because the average kinetic energy and velocity of the molecules increase. However, the increase in the total number of collisions is proportional to $\sqrt{T}$, which is very small compared to the exponential increase in the fraction of effective collisions (those with energy $\ge E_a$).
Therefore, while both statements are factually correct, the increase in the number of collisions is not the primary reason for the doubling of the rate constant; the primary reason is the exponential increase in the fraction of molecules with energy greater than the activation energy. Thus, R is not the correct explanation of A.
Answer: Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$.
Hence, the correct answer is option: 'B'.