Question

State whether reactants or products will be favored by an increase in the total pressure (resulting from compression) on each of the following equilibria. If there is no change, explain why that is so. (a) \(2 \mathrm{O}_{3}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{O}_{2}(\mathrm{~g})\) (b) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{C}(\mathrm{s}) \rightleftharpoons \mathrm{H}_{2}\) (g) \(+\mathrm{CO}(\mathrm{g})\) (c) \(4 \mathrm{NH}_{3}(\mathrm{~g})+5 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (d) \(2 \mathrm{HD}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{~g})+\mathrm{D}_{2}\) (g) (e) \(\mathrm{Cl}_{2}\) (g) \(\rightleftharpoons 2 \mathrm{Cl}(\mathrm{g})\)

Short answer

For (a), (c), and (e), increased pressure favors reactants. For (b) and (d), there is no change in the equilibrium position due to an increase in pressure.

Step-by-step solution

Understanding Le Châtelier's Principle

Le Châtelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change. Increasing total pressure by compression usually favors the side of the equilibrium with fewer moles of gas.

Analyzing Equilibrium (a)

For the reaction \(2 \mathrm{O}_{3}(\mathrm{g}) \rightleftharpoons 3 \mathrm{O}_{2}(\mathrm{g})\), there are 2 moles of ozone on the reactant side and 3 moles of oxygen on the product side. Increasing pressure favors the formation of reactants because there are fewer gas moles on that side.

Analyzing Equilibrium (b)

For the reaction \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) + \mathrm{C}(\mathrm{s}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{g}) + \mathrm{CO}(\mathrm{g})\), the number of moles of gas is the same on both sides of the equilibrium (2 moles of gas each). Thus, changing the pressure has no effect on the position of equilibrium.

Analyzing Equilibrium (c)

For the reaction \(4 \mathrm{NH}_{3}(\mathrm{g}) + 5 \mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 4 \mathrm{NO}(\mathrm{g}) + 6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\), there are 9 moles of gas on the reactant side and 10 moles of gas on the product side. Increasing pressure favors the reactants due to their fewer gas moles.

Analyzing Equilibrium (d)

For the reaction \(2 \mathrm{HD}(\mathrm{g}) \rightleftharpoons \mathrm{H}_{2}(\mathrm{g}) + \mathrm{D}_{2}(\mathrm{g})\), there are 2 moles of HD on the reactant side and 2 moles of gas on the product side. A change in pressure will not favor either side due to an equal number of gas moles.

Analyzing Equilibrium (e)

For the reaction \(\mathrm{Cl}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{Cl}(\mathrm{g})\), there is 1 mole of chlorine gas on the reactant side and 2 moles of Cl on the product side. Increasing pressure favors the formation of reactants as they have fewer moles of gas.

Key concepts

Le Châtelier's Principle

Le Châtelier's Principle is a foundational concept in chemistry that helps predict how a system at equilibrium responds to external changes. When a dynamic equilibrium is disturbed, such as by a change in pressure, concentration, or temperature, the system adjusts to minimize the disturbance and restore balance. As we encounter gas phase reactions, we often see this principle in action. The system tends to favor the direction that compensates for the change. For instance, if pressure is increased by compression, the system will shift toward the side with fewer moles of gas, effectively reducing the pressure. Understanding this principle allows us to predict the direction of shift and whether reactants or products will be favored under different conditions.

Let's consider a practical illustration of how Le Châtelier's Principle operates in the real world. Imagine a bottle of soda that is sealed tight at equilibrium. Once opened, the pressure is reduced, and according to Le Châtelier's Principle, the system shifts to increase pressure again, resulting in the release of carbon dioxide gas as bubbles—a common everyday example of equilibrium at work.

Reaction Quotient

The reaction quotient, or Q, is like a snapshot of a reaction at any point before it reaches equilibrium. It's calculated using the same formula as the equilibrium constant (K), but with the current concentrations or partial pressures of the reactants and products instead of their equilibrium values. The value of Q is pivotal in predicting the direction of the reaction. If Q is less than K, the system will shift toward the products to reach equilibrium. Conversely, if Q is greater than K, the system will shift toward the reactants.

In using the reaction quotient, students can get immediate insights into the behavior of a reaction that is not at equilibrium. Knowing both Q and K helps determine the actions required to nudge a system back to its balanced state. For example, if the Q value is higher than expected, introducing more reactants or removing some products could help re-establish equilibrium according to Le Châtelier's Principle.

Equilibrium Constant

The equilibrium constant, K, is a vital number in chemistry that indicates the extent to which reactants are converted into products in a reaction at equilibrium. For gas phase reactions, K can be expressed in terms of partial pressures (Kp) or concentrations (Kc). The value of K is temperature specific and remains constant as long as the temperature is maintained. High K values mean that, at equilibrium, products are favored, while low K values suggest reactants are favored.

Understanding K allows chemists to design reactions more efficiently, predicting the yield of products under given conditions. However, it's crucial to recognize that the equilibrium constant does not provide information about the rate of reaction—it solely describes the position of equilibrium. This concept is particularly potent when combined with Le Châtelier's Principle to predict how changes in pressure, volume, or other factors might shift the equilibrium position, thereby altering the concentrations or pressures of the reactants and products.

Gas Phase Reactions

Gas phase reactions are fascinating as the behavior of gases provides additional factors to consider when looking at chemical equilibrium. In these reactions, the number of moles of gaseous reactants and products can significantly affect the reaction conditions and outcome, especially when the system is subject to changes in pressure or volume. The Ideal Gas Law tells us that for gases, volume, temperature, pressure, and the number of moles are all tightly interlinked.

When examining gas phase reactions through the lens of Le Châtelier's Principle, changes in pressure by compression or expansion can have a pronounced effect. A reaction with a decrease in the number of moles of gas will be favored by an increase in pressure, and vice versa. For educators and students alike, interpreting these reactions requires a solid grip on concepts like partial pressures, mole ratios, and the nature of how gaseous molecules interact within a closed system. Moreover, the introduction of inert gases or changes in the volume of the containment vessel can also shift the equilibrium position, showcasing the dynamism and responsiveness of gas phase reactions.