Question

Le Chatelier's principle is stated (Section 13.7\()\) as follows: "If a change is imposed on a system at equilibrium, the position of the equilibrium will shift in a direction that tends to reduce that change." The system \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g)\) is used as an example in which the addition of nitrogen gas at equilibrium results in a decrease in \(\mathrm{H}_{2}\) concentration and an increase in \(\mathrm{NH}_{3}\) concentration. In the experiment the volume is assumed to be constant. On the other hand, if \(\mathrm{N}_{2}\) is added to the reaction system in a container with a piston so that the pressure can be held constant, the amount of \(\mathrm{NH}_{3}\) actually could decrease and the concentration of \(\mathrm{H}_{2}\) would increase as equilibrium is reestablished. Explain how this can happen. Also, if you consider this same system at equilibrium, the addition of an inert gas, holding the pressure constant, does affect the equilibrium position. Explain why the addition of an inert gas to this system in a rigid container does not affect the equilibrium position.

Short answer

In summary, the addition of N₂ to the equilibrium reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g) affects the equilibrium position based on whether the volume or pressure is held constant. When the volume is constant, adding N₂ shifts the equilibrium to the right, increasing NH₃ concentration and decreasing H₂ concentration. When the pressure is held constant using a piston, adding N₂ causes the equilibrium to shift left, decreasing NH₃ concentration and increasing H₂ concentration. Adding an inert gas to the system does not affect the equilibrium position because it does not change the partial pressures or concentrations of the reacting species. These observations are consistent with Le Chatelier's principle, which states that the equilibrium will shift in a direction that tends to reduce the imposed change in the system.

Step-by-step solution

1. Identifying the Reaction and Components

First, let's write the balanced chemical equation for the reaction: \[N_{2}(g) + 3 H_{2}(g) \rightleftharpoons 2 NH_{3}(g) \] With this reaction, adding N₂ can cause two possible behaviors: the equilibrium could shift to the right (toward the production of more NH₃) or shift to the left (toward the consumption of NH₃). We will analyze each scenario as we progress through the solution.

2. Scenario 1: Adding N₂ at constant volume

According to Le Chatelier's principle, when we introduce more N₂ into the system, the pressure will temporarily increase, causing the equilibrium to shift in a direction that reduces this increase. Since the volume is constant, the shift will be towards the side with fewer moles of gas. In this case, the reaction shows that 4 moles of gas (1 mole N₂ and 3 moles H₂) are on the left side, and 2 moles of NH₃ gas are on the right side. Thus, the equilibrium will shift to the right, increasing the concentration of NH₃ and decreasing the concentration of H₂, as mentioned in the example.

3. Scenario 2: Adding N₂ with a piston and keeping the pressure constant

When we add more N₂ into the system, the increase in gas will cause the pressure to rise as well. However, since the pressure is held constant by adjusting the piston, the increase in N₂ will be accompanied by an increase in volume to maintain the pressure. As the volume increases, the gas concentrations decrease. In this case, the equilibrium will attempt to shift to counteract the decrease in pressure by moving towards the side with more moles of gases. Thus, the equilibrium will shift to the left, decreasing the concentration of NH₃ and increasing the concentration of H₂. This behavior is consistent with Le Chatelier's principle since the equilibrium adjusts itself in response to the added N₂.

4. Effect of adding an inert gas

If we add an inert gas into the reaction mixture at constant pressure, the total pressure of the system will increase, but the individual partial pressures of N₂, H₂, and NH₃ will not change. Since the equilibrium position is dependent on the concentrations (or partial pressure) of the reactants and products, adding an inert gas at constant pressure will not affect the equilibrium position because it does not change the partial pressures of the reacting species. However, if we add an inert gas to the system in a rigid container (constant volume), the total pressure of the system will increase, but the relative concentrations of N₂, H₂, and NH₃ will also remain unchanged. In this case, the addition of an inert gas does not affect the equilibrium position because the ratio of the concentrations of the reactants and products does not change. This observation is also consistent with Le Chatelier's principle, as there is no change in concentration to counteract.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reaction where the rate of the forward reaction equals the rate of the backward reaction. In simpler terms, it means that the concentrations of the reactants and products remain constant over time.
This occurs because the formation of products from reactants occurs at the same speed as the formation of reactants from products. The equilibrium does not mean that the reactants or products are in equal amounts. Instead, the equilibrium position tells you the ratio of their concentrations once the system is in balance.
Le Chatelier's Principle helps us predict the effect of changes within this state of balance. If a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the system will adjust to minimize the impact of that change.
A classic example is the reaction of nitrogen gas (\(N_2(g)\)) with hydrogen gas (\(3H_2(g)\)) to form ammonia (\(2NH_3(g)\)). This reaction helps to illustrate how equilibrium can shift when variables like pressure and concentration change.

Effect of Pressure Changes

Pressure changes can significantly impact a chemical reaction at equilibrium, especially if gases are involved. In the equation \(\displaystyle N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)\), changes in pressure will shift the equilibrium position.
When pressure is increased by reducing the volume, equilibrium will shift towards the side with fewer gas molecules. Here, the right side of the equation has fewer moles of gas (2 moles of \(NH_3\)) compared to the left side (4 moles total of \(N_2\) and \(H_2\)).
Conversely, if the pressure decreases, like when the volume increases, the equilibrium shifts towards the side with more moles of gas. In the example reaction, this means shifting left to produce more \(N_2\) and \(H_2\), since it results in more gas molecules.
Understanding this concept is crucial because it helps predict how a system will respond to physical changes in pressure, maintaining balance as described by Le Chatelier's Principle.

Effect of Volume Changes

Volume changes directly influence pressure in a gas system at equilibrium. When volume decreases, pressure increases. When volume increases, pressure decreases.
In a container with gases, changing the volume affects the concentration of the gases. In our reaction example with \(N_2,\) \(H_2,\) and \(NH_3,\):

• Decrease in volume (increase in pressure): Equilibrium shifts to reduce the number of gas molecules, favoring the formation of \(NH_3\).
• Increase in volume (decrease in pressure): Equilibrium shifts towards producing more gas molecules, favoring \(N_2\) and \(H_2\).

The change in equilibrium position occurs because the system attempts to counterbalance the change, illustrating the principle beautifully. Volume changes are particularly impactful in reactions involving gases because they alter both concentration and pressure simultaneously.

Inert Gas Addition

The addition of an inert gas to a system at equilibrium can seem confusing. An inert gas, which does not react chemically with the species in the reaction, affects the system differently depending on how the pressure is maintained.
In a fixed volume system, adding an inert gas increases the total pressure by adding more gas molecules. However, because the inert gas doesn't interact with \(N_2,\) \(H_2,\), or \(NH_3,\), the partial pressures and concentrations of the reacting species remain unchanged. Thus, the equilibrium position doesn't shift.
When pressure is constant, such as with a moveable piston, adding an inert gas also doesn't change the equilibrium position. The reason is that the addition doesn't change the partial pressures of reactants and products. Since equilibrium depends on these partial pressures, inert gases don't disrupt the balance due to the lack of chemical interaction.

Reaction Dynamics

Reaction dynamics describe how fast or slow reactions occur and how systems achieve equilibrium. Dynamics also involve understanding how changes in conditions can alter the rates of forward and backward reactions.
For example, in the system \(N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g),\) changes due to external factors like pressure or volume affect the route to equilibrium.
If you introduce more \(N_2\) while the volume remains constant, the system dynamically adjusts by accelerating the reaction that consumes \(N_2\) and \(H_2\) to form \(NH_3\), temporarily altering concentrations until a new equilibrium is met.
Reaction dynamics encompass not just rate but also how a system responds to alteration in equilibrium pressures, concentrations, and other conditions. It plays a crucial role in understanding how and when shifts occur, providing insights into the behavior of chemical systems under varying circumstances.