For the reversible reaction,

2NH₃(g) ⇌ N₂(g) + 3H₂(g); ΔH = 92.5 kJ,

the reaction shifts in the forward direction by

Solution:

The given reaction is 2NH₃(g) ⇌ N₂(g) + 3H₂(g) with ΔH = 92.5 kJ. This indicates that the forward reaction (decomposition of ammonia) is endothermic. The number of moles of gaseous products (1 mole N₂ + 3 moles H₂ = 4 moles) is greater than the number of moles of gaseous reactants (2 moles NH₃).

According to Le Chatelier's Principle:

1. Decreasing temperature: Since the forward reaction is endothermic (ΔH > 0), decreasing the temperature will shift the equilibrium in the backward (exothermic) direction to counteract the change. Thus, option (1) is incorrect.

2. Addition of inert gas at constant volume: When an inert gas is added at constant volume, the total pressure of the system increases, but the partial pressures (and thus concentrations) of the reacting gases remain unchanged. Therefore, the equilibrium position is not affected. Thus, option (2) is incorrect.

3. Addition of inert gas at constant pressure: When an inert gas is added at constant pressure, the total volume of the system increases. To maintain the partial pressures of the reacting gases, the equilibrium will shift towards the side with a greater number of moles of gas. In this reaction, the product side has 4 moles of gas, while the reactant side has 2 moles of gas. Hence, the equilibrium will shift in the forward direction. Thus, option (3) is correct.

4. Addition of catalyst: A catalyst increases the rate of both the forward and backward reactions equally, helping the system reach equilibrium faster but not altering the equilibrium position. Thus, option (4) is incorrect.