Question

Consider the following system at equilibrium: $$ \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) $$ Will the number of moles of reactants or products change if we increase the volume of the reaction container? Explain your answer.

Short answer

No, the number of moles of reactants or products will not change if the volume of the reaction container is increased. This is due to the fact that there are an equal number of moles of gas on both sides of the equilibrium equation.

Step-by-step solution

Identify number of moles on each side of the reaction

The equation for the reaction is: \( CO(g) + H_2O(g) \leftrightarrow CO_2(g) + H_2(g) \). There are 2 moles of gas on both sides of the equation, one from the CO and one from the H2O on the left, and one from CO2 and one from H2 on the right.

Apply Le Châtelier's Principle

According to Le Châtelier's Principle, when the volume of the container increases (thus decreasing the pressure), the system will try to oppose the change by shifting to the side of the reaction that has more moles of gas. However, both the reactants and products sides of the reaction have the same number of moles of gas, meaning the system will not shift and the number of moles of reactants and products will remain constant.

Conclusion

So, increasing the volume of the reaction container will not change the number of moles of reactants or products in this system. The equilibrium will remain as it is.

Key concepts

Le Châtelier's Principle

When studying chemical reactions, Le Châtelier's Principle is a fundamental concept that predicts how a system at equilibrium will respond to changes in concentration, temperature, pressure, or volume. In essence, this principle states that if an external stress is applied to a system in equilibrium, the system will adjust in a way to counteract that change.

For example, imagine a sealed container holding a mixture of gases that are reacting with each other. If we were to increase the pressure inside that container—perhaps by decreasing its volume—the reaction would shift to reduce the pressure. It does this by favoring the production of fewer gas molecules, if such a path is available. Conversely, if we decrease the pressure by increasing the container’s volume, the system attempts to increase the pressure, typically by shifting the reaction to the side that produces more gas molecules.

In the exercise provided, the reaction volume change does not prompt a shift in the equilibrium because both sides of the reaction have the same number of gas moles. This illustrates a subtlety of Le Châtelier's Principle: it predicts the direction of shift based on the stress applied, but if the stress does not result in an imbalance of moles, there will be no shift.

Reaction Volume Change

The volume of a reaction can significantly influence the position of equilibrium according to Le Châtelier's Principle. In scenarios where changing the volume also changes the pressure of the system, the reaction can shift to the side with more or fewer moles of gas, attempting to restore equilibrium. However, this behavior hinges on whether there is a difference in the number of moles of gas on each side of the balanced equation.

In the exercise we're looking at, an increase in volume translates to a decrease in pressure, as there is the same amount of space for the gas molecules to occupy. Typically, if there had been a difference in the number of gas moles on either side of the equation, we would anticipate a shift in the equilibrium. However, because the number of gas moles is equal on both sides—two moles each—the change in volume doesn't drive the equilibrium to favor the formation of reactants or products. This serves as a clear example of how reaction volume change impacts chemical equilibrium when considering gaseous components.

Moles of Gas

In chemical reactions, particularly those involving gases, the number of moles of gas on each side of a balanced equation plays a critical role. Each mole of a gas occupies a set volume under the same conditions of temperature and pressure, according to Avogadro's Law. Hence, the total volume of gases involved in a reaction is directly related to the number of moles.

When discussing the equilibrium of a gas-phase reaction, if one side of the reaction has more moles of gas than the other, a change in volume will likely shift the equilibrium to the side with more moles of gas. This tendency aims to balance out the change in pressure caused by the volume change. In the context of our exercise, the fact that there are equal moles of gas on both sides of the reaction means that a change in reaction volume does not affect the equilibrium position. Understanding the concept of moles of gas in this manner is crucial for predicting and explaining the behavior of reactions under varying conditions.