Question

The volume of the reaction vessel containing an equilibrium mixture in the reaction \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons\) \(\mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) is increased. When equilibrium is re-established, (a) the amount of \(\mathrm{Cl}_{2}\) will have increased; (b) the amount of \(\mathrm{SO}_{2}\) will have decreased; (c) the amounts of \(\mathrm{SO}_{2}\) and \(\mathrm{Cl}_{2}\) will have remained the same; (d) the amount of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) will have increased.

Short answer

(a) The amount of Cl2 will have increased. (b) Incorrect, the amount of SO2 will have increased. (c) Incorrect, the amounts of SO2 and Cl2 will have increased. (d) Incorrect, the amount of SO2Cl2 will have decreased.

Step-by-step solution

Identifying The Reaction Direction

In the given reaction, \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\), the number of moles of gas on the products side (SO2 and Cl2) is more than the reactants side (SO2Cl2). So, when the volume of the reaction vessel increases, the reaction will proceed in the forward direction to increase the number of moles of gas and thus, counteract the change.

Changes in the amounts of the gases

Now, as the reaction proceeds in the forward direction, the amount of SO2Cl2 which is the reactant will decrease. As a result, the amount of both Cl2 and SO2 will increase as they are the products of the forward reaction. This is in accordance with Le Chatelier's principle as it occurs to counteract the increase in volume and decrease in the pressure of the system.

Conclusion for each statement

On analyzing the scenario, (a) the amount of Cl2 will have increased, which is correct. (b) The amount of SO2 will have decreased, which is incorrect as the amount of SO2 will have increased. (c) The amounts of SO2 and Cl2 will have remained the same, which is incorrect as both will have increased. (d) The amount of SO2Cl2 will have increased. This statement is also incorrect as the amount of SO2Cl2 will have decreased.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a handy tool in understanding how a system at equilibrium reacts to external changes. The principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change and restore balance.
In the context of chemical reactions, this often involves changes in concentration, temperature, or pressure. To simplify:

• If you add a substance, the system shifts to use it.
• If you remove a substance, the system shifts to replace it.
• If pressure increases, the system shifts to reduce it by favoring the side with fewer gas moles.

In gas reactions, like our given example involving \\(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\), Le Chatelier's Principle predicts the direction of the shift when the volume changes.

Reaction Direction

Determining the direction of a chemical reaction when equilibrium is disturbed is essential. For the reaction between \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g})\) and its products, \(\mathrm{SO}_{2}(\mathrm{g})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\), know that the reaction moves towards the side with more gas molecules if the volume of the container is increased.
Since gas occupies more volume, increasing the reaction vessel's size decreases pressure. Le Chatelier's Principle advises that the reaction will adjust by shifting towards the side with more moles of gas, thereby increasing the volume again.
This means the forward reaction is favored, converting more \(\mathrm{SO}_{2} \mathrm{Cl}_{2}(\mathrm{g})\) into \(\mathrm{SO}_{2}(\mathrm{g})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\). In our example:

• Moles increase from one to two as you shift to the right.
• This adjustment isn't just theoretical; it's a direct response to the change in conditions.

Gas Reactions

Gas reactions provide a practical context for exploring equilibrium concepts, especially in changing conditions like volume and pressure. Gas reactions, like our given example \(\mathrm{SO}_{2}\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{SO}_{2}(\mathrm{g}) + \mathrm{Cl}_{2}(\mathrm{g})\), are significant due to their immediate reaction to volume changes.
In a gas reaction, when you change the volume of the reaction vessel, it directly affects the pressure. According to Le Chatelier's Principle, the reaction shifts in a direction to balance this pressure change.
Consider these points:

• Volume Increase: If you increase the volume, the reaction shifts towards the side with more gas molecules, as this helps increase pressure again.
• Volume Decrease: Conversely, if the volume is reduced, the reaction shifts toward fewer gas molecules.

Explorations of gas reactions can help one visualize the dynamic nature of equilibria and their dependence on the physical context of the reaction environment.