Question

According to Collision Theory, the rate constant of a chemical reaction depends on activation energy. If the activation energy of a reaction increases, then the value of the rate constant \(k\) will:

• A. Increase exponentially
• B. Remain unchanged
• C. Decrease exponentially
• D. Become zero

Hint:

Remember: \[ k = A e^{-E_a/RT} \]
• Larger activation energy \(\Rightarrow\) smaller rate constant
• Higher temperature \(\Rightarrow\) larger rate constant

Answer 1

The Correct Option is C

Concept: According to Arrhenius equation: \[ k = A e^{-E_a/RT} \] where:
• \(k\) = Rate constant
• \(A\) = Frequency factor
• \(E_a\) = Activation energy
• \(R\) = Universal gas constant
• \(T\) = Absolute temperature The equation clearly shows that the rate constant depends exponentially on activation energy.

Step 1: Analyze the exponential term.
The exponential factor is: \[ e^{-E_a/RT} \] When activation energy \(E_a\) increases: \[ -\frac{E_a}{RT} \] becomes more negative. As a result: \[ e^{-E_a/RT} \] decreases rapidly. Hence: \[ k \] also decreases exponentially.

Step 2: Physical interpretation.
Higher activation energy means reactant molecules require more energy to cross the energy barrier. Therefore:
• Fewer molecules can form activated complex
• Number of effective collisions decreases
• Reaction becomes slower Hence, rate constant decreases. Therefore, the correct answer is: \[ \boxed{\text{(C) Decrease exponentially}} \]