Question

Consider the gas-phase reaction: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftarrows 2 \mathrm{NH}_{3}(g)\) Suppose it is at equilibrium inside of a closed vessel. Next, the volume of the closed vessel is suddenly decreased, increasing the overall pressure inside the flask. According to Le Châtelier's principle, which way will the reaction shift, and why? Then explain why the reaction \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}(g)\) would not shift when exposed to the same type of disturbance.

Short answer

The equilibrium of the reaction N2(g) + 3H2(g) ⇄ 2NH3(g) will shift to the right, favoring the formation of NH3(g), in response to an increase in pressure. This is because the system will try to counteract the pressure increase by favoring the side with fewer moles of gas, which is the right side (products) in this case. On the other hand, the reaction N2(g) + O2(g) ⇄ 2NO(g) does not shift when exposed to an increase in pressure because both sides of the equilibrium have the same number of moles of gas (2 moles); therefore, there is no shift that would counteract the change in pressure according to Le Châtelier's principle.

Step-by-step solution

Understand Le Châtelier's principle

Le Châtelier's principle states that if a change is applied to a system at equilibrium, the system will shift its equilibrium position to counteract the effect of the change. Changes that can affect a system at equilibrium include concentration of reactants or products, pressure, and temperature. In the context of our problem, an increase in pressure prompts the system to shift the equilibrium in a way that minimizes the pressure increase. This typically means favoring the side of the reaction with fewer moles of gas, as reducing the number of moles of gas would lead to decreased pressure.

Determine how pressure change affects the first reaction: N2(g) + 3H2(g) ⇄ 2NH3(g)

In this reaction, we have 1 mole of N2(g) reacting with 3 moles of H2(g) to form 2 moles of NH3(g). On the left side of the equilibrium (reactants), there are a total of 4 moles of gas - while on the right side (products), there are only 2 moles of gas. When the volume of the closed vessel is decreased, and the overall pressure increases, according to Le Châtelier's principle, the reaction will shift to the side with fewer moles of gas to counteract the pressure increase. In this case, the reaction will shift towards the right, favoring the formation of NH3(g).

Analyze the second reaction: N2(g) + O2(g) ⇄ 2NO(g)

In the second reaction, 1 mole of N2(g) reacts with 1 mole of O2(g) to form 2 moles of NO(g). The number of moles of gas is the same on both sides of the equilibrium (2 moles). Therefore, an increase in pressure does not favor either side of the reaction, as both sides have an equal number of moles of gas. According to Le Châtelier's principle, the equilibrium position will not change in response to a pressure increase, since there is no shift that would counteract the change in pressure. Hence, the reaction N2(g) + O2(g) ⇄ 2NO(g) does not shift when exposed to an increase in pressure.

Key concepts

Chemical Equilibrium

In the world of chemistry, understanding how reactions reach a state of balance is crucial. This state of balance is known as chemical equilibrium. At equilibrium, the rate of the forward reaction, where reactants are transformed into products, is exactly equal to the rate of the reverse reaction, where products revert to reactants. Importantly, even though the rates are equal, the amounts of reactants and products do not have to be the same; they simply remain constant over time.

Le Châtelier's principle provides insight into the predictability of such a system when it's disturbed. If, for example, more reactants are added to a system at equilibrium, the reaction will shift to produce more products until a new equilibrium is established. This balancing act is a dance between molecules that students must understand to fully grasp the dynamic yet stable nature of chemical equilibrium.

Reaction Shift Due to Pressure Change

Pressure changes are one of the disturbances that can cause a shift in chemical equilibrium. According to Le Châtelier's principle, an increase in pressure will shift the reaction toward the side with fewer moles of gas. This is because the system aims to reduce the pressure, and by favoring the reaction that produces fewer gas molecules, the overall volume and therefore pressure can be reduced.

This principle comes alive when we consider the reaction involving nitrogen and hydrogen gases forming ammonia. A decrease in volume or, conversely, an increase in pressure will shift the reaction to produce more ammonia, as this side has fewer gas molecules. On the other hand, for a reaction like the formation of nitrogen monoxide from nitrogen and oxygen, pressure change doesn't alter the direction of the reaction since the number of gas molecules remains the same on both sides of the equation.

Mole Ratio in Chemical Reactions

The mole ratio details the relative quantities of reactants and products in a chemical reaction and plays a critical role in predicting how pressure changes can affect equilibrium. In a balanced chemical equation, the coefficients indicate the mole ratio, which in turn shows how many moles of each substance are involved.

For example, in the ammonia synthesis reaction, the mole ratio between nitrogen, hydrogen, and ammonia is 1:3:2. When the system's pressure is increased, the reaction favors the production of ammonia not only because it moves to a state of lower pressure but also because the conversion of four moles of reactants to two moles of products aligns with the desire to have fewer moles of gas present. In reactions where the mole ratio results in the same number of gas molecules on each side, pressure changes have no impact on the equilibrium position. Students need to grasp this concept to predict the effects of pressure on various chemical equilibria accurately.