Question

For $\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}$ $\mathrm{E}_{\mathrm{a}}$ for forward and backward reaction are 180 and $200 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If catalyst lowers $\mathrm{E}_{\mathrm{a}}$ for both reaction by $100 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Which of the following statement is correct?

• A. Catalyst does not alter the Gibbs energy change of a reaction.
• B. Catalyst can cause non-spontaneous reactions to occur.
• C. The enthalpy change for the reaction is $+20 \mathrm{~kJ} \mathrm{~mol}^{-1}$.
• D. The enthalpy change for the catalysed reaction is different from that of uncatalysed reaction.

Hint:

Catalysts lower the activation energy but do not change the thermodynamic properties of the reaction.

Answer 1

The Correct Option is A

To answer the given question, we need to understand the role of a catalyst in chemical reactions, particularly how it affects activation energy and reaction spontaneity but not Gibbs free energy or enthalpy change.

1. The chemical reaction given is: \(\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}\).
2. The activation energy \((\mathrm{E}_{\mathrm{a}})\) for the forward reaction is: 180 kJ/mol, and for the backward reaction, it is: 200 kJ/mol.
3. The enthalpy change \(\Delta{H}\) for the reaction can be calculated using the formula: \(\Delta H = \mathrm{E}_{\mathrm{a \, forward}} - \mathrm{E}_{\mathrm{a \, backward}} = 180 \, \text{kJ/mol} - 200 \, \text{kJ/mol} = -20 \, \text{kJ/mol}\).
4. The given options discuss the impact of a catalyst on Gibbs energy, spontaneity, enthalpy change, and comparison between catalyzed and uncatalyzed reactions.
5. A catalyst lowers the activation energy of both the forward and reverse reactions by the same amount (given as 100 kJ/mol here), hence it does not alter the net enthalpy change \((\Delta H)\) of the reaction nor the Gibbs free energy \((\Delta G)\).
6. Analyzing the options:
   • Option 1: "Catalyst does not alter the Gibbs energy change of a reaction."
     This is correct because a catalyst does not affect \(\Delta G\).
     Correct Answer: Catalyst does not alter the Gibbs energy change of a reaction.
   • Option 2: "Catalyst can cause non-spontaneous reactions to occur."
     While a catalyst can increase the rate of a reaction, it does not alter the spontaneous nature determined by \(\Delta G\).
   • Option 3: "The enthalpy change for the reaction is +20 kJ/mol."
     This is incorrect; calculation shows it as -20 kJ/mol.
   • Option 4: "The enthalpy change for the catalysed reaction is different from that of uncatalysed reaction."
     This is incorrect; the enthalpy change remains the same regardless of catalysis.
7. Therefore, the correct statement is that a catalyst does not alter the Gibbs energy change of a reaction.

Hence, the correct answer confirms that a catalyst does not change the Gibbs free energy of a reaction, focusing instead on lowering activation energy for both the forward and backward reactions without affecting the reaction's thermodynamics.

Answer 2

1. Given: - $\mathrm{A}_{2}+\mathrm{B}_{2} \rightleftharpoons 2 \mathrm{AB}$ - $\mathrm{E}_{\mathrm{f}} = 180 \mathrm{~kJ} \mathrm{~mol}^{-1}$ - $\mathrm{E}_{\mathrm{b}} = 200 \mathrm{~kJ} \mathrm{~mol}^{-1}$ 
2. Calculate the enthalpy change ($\Delta \mathrm{H}$): \[ \Delta \mathrm{H} = \mathrm{E}_{\mathrm{f}} - \mathrm{E}_{\mathrm{b}} = 180 \mathrm{~kJ} \mathrm{~mol}^{-1} - 200 \mathrm{~kJ} \mathrm{~mol}^{-1} = -20 \mathrm{~kJ} \mathrm{~mol}^{-1} \] 
3. Effect of catalyst: - Catalyst lowers the activation energy but does not change the Gibbs free energy change ($\Delta \mathrm{G}$) or the enthalpy change ($\Delta \mathrm{H}$) of the reaction. 
Therefore, the correct answer is (1) Catalyst does not alter the Gibbs energy change of a reaction.