Question

For a reversible reaction A ⇌ B, the ΔH_{forward reaction} = 20 kJ mol^-1. The activation energy of the uncatalysed forward reaction is 300 kJ mol^-1. When the reaction is catalysed keeping the reactant concentration same, the rate of the catalysed forward reaction at 27°C is found to be same as that of the uncatalysed reaction at 327°C. The activation energy of the cataysed backward reactoion is ____ kJ mol^-1.

Hint:

Catalysts lower activation energies equally for forward and backward reactions without altering ∆H

Answer 1

Correct Answer: 130

Activation Energy Calculation

Step 1: Activation energy for the uncatalyzed backward reaction:

\( E_a(\text{backward}) = E_a(\text{forward}) - \Delta H \)

\( E_a(\text{backward}) = 300 - 20 = 280 \, \text{kJ/mol} \)

Step 2: Using the given temperatures and equal rates, calculate \( E_a(\text{forward, catalyzed}) \):

\( \frac{E_a(\text{forward, catalyzed})}{E_a(\text{forward, uncatalyzed})} = \frac{T_c}{T_u} \)

\( \frac{E_a(\text{forward, catalyzed})}{300} = \frac{300}{600} \)

\( E_a(\text{forward, catalyzed}) = 150 \, \text{kJ/mol} \)

Step 3: Calculate \( E_a(\text{backward, catalyzed}) \):

\( E_a(\text{backward, catalyzed}) = E_a(\text{forward, catalyzed}) - \Delta H \)

\( E_a(\text{backward, catalyzed}) = 150 - 20 = 130 \, \text{kJ/mol} \)

Final Results:

• Uncatalyzed Backward Reaction: \( 280 \, \text{kJ/mol} \)
• Catalyzed Forward Reaction: \( 150 \, \text{kJ/mol} \)
• Catalyzed Backward Reaction: \( 130 \, \text{kJ/mol} \)