Question:
The reaction rate constants of two reactions follow Arrhenius' law. The activation energies of Reaction 1 and Reaction 2 are \(E_1\) and \(E_2\), respectively, and \(E_1 < E_2\). Assuming the same value of the frequency factor for both reactions, which one of the following statements is CORRECT?
The reaction rate constants of two reactions follow Arrhenius' law. The activation energies of Reaction 1 and Reaction 2 are \(E_1\) and \(E_2\), respectively, and \(E_1 < E_2\). Assuming the same value of the frequency factor for both reactions, which one of the following statements is CORRECT?
Show Hint
Compare \(d(\ln k)/dT = E/(RT^2)\) for the two reactions at the same T; the T-dependent part cancels out when you take the ratio between reactions.
Updated On: Jul 17, 2026
- Reaction 1 and Reaction 2 are less temperature sensitive at lower temperature than at higher temperature.
- Reaction 1 and Reaction 2 have the same temperature sensitivity at all temperatures.
- Reaction 1 is more temperature sensitive than Reaction 2 at all temperatures.
- Reaction 2 is more temperature sensitive than Reaction 1 at all temperatures.
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Write the Arrhenius equation for the rate constant.
\[ k = A_0 \exp\left(-\frac{E}{RT}\right) \]
Step 2: Define temperature sensitivity mathematically.
\[ \frac{d(\ln k)}{dT} = \frac{E}{RT^2} \]
Step 3: Check how temperature affects sensitivity of a single reaction.
For fixed E, sensitivity decreases as T increases. Option A claims the opposite and is incorrect.
Step 4: Compare the two reactions at the same temperature.
\[ \frac{(d(\ln k)/dT)_2}{(d(\ln k)/dT)_1} = \frac{E_2}{E_1} > 1 \]
Since E1<E2, this ratio always exceeds 1, at every temperature.
Step 5: Eliminate the remaining options.
Option B is wrong since the activation energies differ. Option C is the reverse of the correct conclusion.
Step 6: Final answer.
\[ \boxed{\text{Reaction 2 is more temperature sensitive than Reaction 1 at all temperatures}} \]Was this answer helpful?
0
0
Top GATE CH Chemical Reaction Engineering Questions
- Choose correct option (Chlor-Alkoli Industry)
- The ratio of the activation energy of a chemical reaction to the universal gas constant is 1000 K. The temperature-dependence of the reaction rate constant follows the collision theory. The ratio of the rate constant at 600 K to that at 400 K is
- The rate of a reaction \( A \rightarrow B \) is \( 0.2 \) mol m\(^{-3}\) s\(^{-1}\) at a particular concentration \( C_{A1} \). The rate constant of the reaction at a given temperature is \( 0.1 \) m\(^3\) mol\(^{-1}\) s\(^{-1}\). If the reactant concentration is increased to \( 10 C_{A1} \) at the same temperature, the reaction rate, in mol m\(^{-3}\) s\(^{-1}\), is
- Two parallel first-order liquid phase reactions \( A \xrightarrow{k_1} B \) and \( A \xrightarrow{k_2} C \) are carried out in a well-mixed isothermal batch reactor. The initial concentration of A in the reactor is \( 1 \) kmol m\(^{-3}\), while that of B and C is zero. After 2 hours, the concentration of A reduces to half its initial value, and the concentration of B is twice that of C. The rate constants \( k_1 \) and \( k_2 \), in h\(^{-1}\), are, respectively,
- For the electrolytic cell in a chlor-alkali plant, which of the following statements is/are correct?
View More Questions
Top GATE CH Questions
- Consider a Leniar Homogeneous system AX = 0, where A is N × N matrix and X is N × 1 vector. When we solve this 0 is null matrix of N × 1. Let R be the rank matrix for a for a Non-trivial solution.
- Which are true for Petroleum / Petrochemicals?
- F(x) = ex - 5x and the value of X0 = 1 then what will be the value of X1?
- The first non-zero term in the taylor series expansion of (1 - x) - e- x, about x = 0
- \(\frac{P}{Q}\) is not equal 1, \(\left(\frac{P}{Q}\right)^{\frac{P}{Q}} = P^{\frac{P}{Q} - 1}\)
View More Questions