Question

According to Le Châtelier's principle, how would increasing the volume of the reaction vessel affect the equilibrium $2{\mathrm{SO}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\to 2{\mathrm{SO}}_3(\mathrm{g})?(\text{Chapter }17)$

Short answer

According to Le Châtelier's principle, increasing the volume of the reaction vessel for the equilibrium $2{\mathrm{SO}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\to 2{\mathrm{SO}}_3(\mathrm{g})$ will cause the reaction to shift towards the side with more moles of gas, the reactant side, to counteract the change. This results in an increase in the concentrations of ${\mathrm{SO}}_2(\mathrm{g})$ and ${\mathrm{O}}_2(\mathrm{g})$, and a decrease in the concentration of ${\mathrm{SO}}_3(\mathrm{g})$.

Step-by-step solution

Identify shift direction

In order to determine which direction the equilibrium will shift, we must consider the number of moles of gaseous reactants and products. For the reaction, the total number of moles of gas in the reactant side is $2+1=3$, and in the product side, it's just $2$. Since there are more moles of gas in the reactants, increasing the volume of the container will lead to a decrease in partial pressures of all the gases according to the equation $V=nRT/P$ (at constant temperature). To compensate for this change and reach equilibrium again, the reaction will favor the direction with a higher number of moles of gas.

Shift direction according to Le Châtelier's principle

According to Le Châtelier's principle, increasing the volume will shift the reaction towards the side with more moles of gas to counteract the change. In this case, the reaction will favor the formation of more reactants: $2{\mathrm{SO}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})$. Therefore, when the volume of the reaction vessel is increased, the equilibrium will shift towards the formation of more reactants, resulting in an increase in the concentrations of ${\mathrm{SO}}_2(\mathrm{g})$ and ${\mathrm{O}}_2(\mathrm{g})$, and a decrease in the concentration of ${\mathrm{SO}}_3(\mathrm{g})$.

Key concepts

Chemical Equilibrium

Understanding chemical equilibrium is essential when studying the behavior of reactions. It is the state reached by a reversible chemical reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentration of reactants and products over time. At equilibrium, a particular ratio of reactant to product concentrations is maintained, known as the equilibrium constant (K).

It's important to remember that equilibrium does not mean the reactants and products are in equal concentrations, but rather that their ratios remain constant. This state is dynamic rather than static, meaning that the reactant and product molecules continue to react with each other; they simply do so at equal rates, creating a balance.

Reaction Vessel Volume

The volume of a reaction vessel plays a crucial role in gaseous reactions and their equilibrium states. According to the ideal gas law (PV=nRT), where P is the pressure, V the volume, n the number of moles of gas, R the gas constant, and T the temperature, a change in the volume of the container will affect the pressure of the gases involved, assuming temperature and number of moles of gases remain constant.

When the volume of the reaction vessel is increased, the pressure of the gases decreases. This decrease in pressure impacts how the reaction proceeds. Under these conditions, Le Châtelier's principle predicts that the equilibrium will shift to increase the pressure, often by forming more molecules of gas if the reaction allows it.

Shift in Equilibrium

A shift in equilibrium occurs when an external change, such as a change in vessel volume, temperature, pressure, or concentration of reactants or products, is applied to a system in chemical equilibrium. Le Châtelier's principle helps us predict the direction of the shift as the system attempts to counteract the change.

In the context of changing volume, if the system contains gases, increasing volume decreases pressure and causes the equilibrium to shift towards the side with more moles of gas, as seen in the provided exercise. This shift allows the system to increase the pressure and restore a new equilibrium state. Conversely, decreasing volume would shift equilibrium towards the side with fewer moles of gas to lower the pressure.

Gaseous Reactions

Gaseous reactions are particularly sensitive to changes in volume and pressure due to the properties of gases. Gas molecules are far apart and move rapidly, occupying space according to the volume of their container. As a result, changes to the volume of the reaction vessel have direct and significant effects on gas pressure and thus on the equilibrium position of gaseous reactions.

In summary, when the volume increases, the gas molecules have more space to spread out, resulting in lower pressure. According to the exercise discussed, the reaction will shift to increase the number of gas molecules to counter this change, aligning with Le Châtelier's principle. This behavior is a distinctive feature of gaseous reactions and equilibrium.