Problem 78 - Chemistry: An Atoms-Focused Approach

Question

Ammonia is added to a gaseous reaction mixture containing \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) that is at chemical equilibrium. How will the addition of ammonia affect the relative concentrations of \(\mathrm{H}_{2}, \mathrm{Cl}_{2},\) and \(\mathrm{HCl}\) if the cquilibrium constant of reaction 2 is much greater than the cquilibrium constant of reaction \(1 ?\) (1) \(\quad \mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) $$ \text { (2) } \quad \mathrm{HCl}(g)+\mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(s) $$

Step-by-Step Solution

Answer

Answer: The addition of ammonia will result in a decrease in the relative concentrations of H₂, Cl₂, and HCl. This occurs due to the effect of ammonia on the second reaction which consumes HCl, causing the first reaction to shift right and consume more H₂ and Cl₂ to produce more HCl.

Step 1: Identify the Relevant Equilibria

Both reactions 1 and 2 are related to the concentrations of H₂, Cl₂, and HCl in the system. Therefore, both reactions are relevant to understanding the problem. Keep in mind that the equilibrium constant of Reaction 2 is much greater than the equilibrium constant of Reaction 1.

Step 2: Apply Le Chatelier's Principle to Reaction 1

Le Chatelier's Principle states that when a system at equilibrium is subject to a change, the system will adjust itself to minimize the effect of that change. In the case of Reaction 1, adding NH₃ does not directly affect the equilibrium since it is not involved in Reaction 1. Therefore, Le Chatelier's Principle does not apply to Reaction 1 in this case.

Step 3: Apply Le Chatelier's Principle to Reaction 2

When NH₃ is added to the system, the equilibrium of Reaction 2 will be disturbed. According to Le Chatelier's Principle, the system will shift to minimize the stress caused by the addition of NH₃. Since the equilibrium constant of Reaction 2 is much larger than Reaction 1, Reaction 2 will shift significantly to the right, consuming more HCl to form NH₄Cl.

Step 4: Analyze the Effect on the Concentrations of H₂, Cl₂, and HCl

As more NH₃ is added, Reaction 2 shifts right, consuming more HCl and producing NH₄Cl. Due to the consumption of HCl, the concentration of HCl decreases. This change in concentration will, in turn, affect the equilibrium of Reaction 1. Since the concentration of HCl decreases, Reaction 1 will shift to the right as well, to produce more HCl. Therefore, this process consumes H₂ and Cl₂, decreasing their concentrations as the reaction proceeds.

Step 5: State the Final Result

In conclusion, the addition of ammonia to the reaction mixture will result in a decrease in the relative concentrations of H₂, Cl₂, and HCl. This is due to the effect of ammonia on Reaction 2, which consumes HCl, causing Reaction 1 to shift right and consume more H₂ and Cl₂ to produce more HCl.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is an essential concept in chemical equilibrium, particularly when analyzing how systems respond to changes. If you modify the conditions of a system at equilibrium, it will adjust to counteract the change and restore balance. In the context of the exercise, adding ammonia (\(\text{NH}_3\)) represents a change to the equilibrium system.
Let's break this down with Reaction 2: Ammonia reacts with hydrochloric acid (\(\text{HCl}\)) to form ammonium chloride (\(\text{NH}_4\text{Cl}\)). Here, Le Chatelier's Principle tells us the system will shift to reduce the stress of adding extra ammonia, causing the equilibrium position to shift to the right.

• Reaction 2: \(\text{HCl}(g) + \text{NH}_3(g) \rightleftharpoons \text{NH}_4\text{Cl}(s)\)
• Added stress: Increase in \(\text{NH}_3\)
• System response: Shift to produce more \(\text{NH}_4\text{Cl}\)

This principle serves as a predictive tool, allowing us to foresee how the concentrations of \(\text{H}_2\), \(\text{Cl}_2\), and \(\text{HCl}\) will change.

Equilibrium Constant

The equilibrium constant, represented as \(K \), is a crucial factor in determining how far a reaction will proceed. A large \(K \) value indicates that the reaction strongly favors product formation, whereas a small \(K \) suggests a preference for reactants.
In our exercise, Reaction 2 has a much larger equilibrium constant compared to Reaction 1. This significant difference strongly influences the behavior of the chemical system when disturbed, like with the addition of ammonia.

• Reaction 1: \(\text{H}_2(g) + \text{Cl}_2(g) \rightleftharpoons 2 \text{HCl}(g)\)
• Reaction 2: \(\text{HCl}(g) + \text{NH}_3(g) \rightleftharpoons \text{NH}_4\text{Cl}(s)\)
• Effect: \(K_2 > K_1\) means Reaction 2 is more product-favored

This difference suggests that when ammonia is added, Reaction 2's stronger tendency to shift right significantly influences the concentration of \(\text{HCl}\), thereby also affecting Reaction 1.

Reaction Shifts

Understanding reaction shifts involves analyzing how equilibrium positions change in response to a disturbance. If ammonia is added to the equilibrium mixture, Reaction 2 shifts to the right to form more \(\text{NH}_4\text{Cl}\), using extra \(\text{HCl}\).
This shift decreases the concentration of \(\text{HCl}\), prompting Reaction 1 to respond. Reaction 1 then shifts to the right as well, consuming more \(\text{H}_2\) and \(\text{Cl}_2\) to produce more \(\text{HCl}\) and balance the decrease.

• Additional \(\text{NH}_3\) triggers Reaction 2 to absorb \(\text{HCl}\)
• Resulting decreased \(\text{HCl}\) affects Reaction 1
• Balances by shifting Reaction 1 right, reducing \(\text{H}_2\) and \(\text{Cl}_2\)

Ultimately, understanding these shifts helps us predict changes in all reactant and product concentrations, providing clarity on how the system adapts to maintain equilibrium.