Question

For which system at equilibrium, at constant temperature will the doubling of the volume cause a shift to the right? (1) \(\mathrm{II}_{2}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{IICl}(\mathrm{g})\) (2) \(2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{CO}_{2}(\mathrm{~g})\) (3) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\) (4) \(\mathrm{PCl}_{5}(\mathrm{~g}) \rightleftharpoons \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})\)

Short answer

Reaction 4: \(\text{PCl}_{5}(\text{g}) \rightleftharpoons \text{PCl}_{3}(\text{g}) + \text{Cl}_{2}(\text{g})\)

Step-by-step solution

Identify the Effect of Volume Change

When the volume of a system at equilibrium is doubled, the pressure in the system is halved. According to Le Chatelier's Principle, the system will shift in the direction that counteracts this change, favoring the side with more moles of gas to increase the pressure.

Analyze Reaction 1

For the reaction \(\text{II}_{2}(\text{g}) + \text{Cl}_{2}(\text{g}) \rightleftharpoons 2 \text{IICl}(\text{g})\), the reactants are 2 moles of gas (1 mole of II\text{Cl}_{2} and 1 mole of Cl_{2}) and the products are 2 moles of gas (2 moles of IICl). The number of moles of gas on both sides is the same, so volume change will not affect the equilibrium position.

Analyze Reaction 2

For the reaction \(2 \text{CO}(\text{g}) + \text{O}_{2}(\text{g}) \rightleftharpoons 2 \text{CO}_{2}(\text{g})\), the reactants have 3 moles of gas (2 moles of CO and 1 mole of O_2) and the products have 2 moles of gas (2 moles of CO_2). Doubling the volume will shift the equilibrium to the left.

Analyze Reaction 3

For the reaction \(\text{N}_{2}(\text{g}) + 3 \text{H}_{2}(\text{g}) \rightleftharpoons 2 \text{NH}_{3}(\text{g})\), the reactants have 4 moles of gas (1 mole of N_2 and 3 moles of H_2) and the products have 2 moles of gas (2 moles of NH_3). Doubling the volume will shift the equilibrium to the left.

Analyze Reaction 4

For the reaction \(\text{PCl}_{5}(\text{g}) \rightleftharpoons \text{PCl}_{3}(\text{g}) + \text{Cl}_{2}(\text{g})\), the reactant has 1 mole of gas (PCl_5) and the products have 2 moles of gas (1 mole of PCl_3 and 1 mole of Cl_2). Doubling the volume will shift the equilibrium to the right.

Conclusion

Based on the analysis, among the provided reactions, the equilibrium for reaction 4 will shift to the right when the volume is doubled.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle explains how a system at equilibrium responds to external changes. If a change is made to the conditions (like pressure, volume, or temperature), the system adjusts to counteract that change.
This principle helps predict the shift in equilibrium when conditions change.
For example, if the volume increases, the system will shift towards the side with more gas moles to increase pressure and restore balance.

Reaction Quotient (Q)

The reaction quotient, Q, is essential in understanding where a reaction stands concerning equilibrium. Q is calculated similarly to the equilibrium constant, K, but it doesn't assume the system is at equilibrium.
If Q < K, the reaction shifts right to produce more products.
If Q > K, the reaction shifts left to produce more reactants.
By comparing Q to K, we predict the direction of the reaction to reach equilibrium.

Gas Laws

Gas laws are vital in chemical equilibrium, especially under changing volume and pressure. Boyle's Law states that gas volume and pressure are inversely related at constant temperature: \(P_1 V_1 = P_2 V_2\).
According to this, doubling the volume of a gas halves its pressure if temperature is constant.
These changes directly affect equilibrium according to Le Chatelier's Principle, causing the system to adjust the amount of gas to stabilize the new pressure.