Problem 52 - Chemistry: The Central Science

Question

Consider \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) \(\Delta H=-904.4 \mathrm{~kJ}\). How does each of the following changes affect the yield of \(\mathrm{NO}\) at equilibriun?? Answer increase, decrease, or no change: (a) increase [NII \(\left._{3}\right]\); (b) increase \(\left[\mathrm{H}_{2} \mathrm{O}\right]\); (c) decrease \(\left[\mathrm{O}_{2}\right] ;\) (d) decrease the volume of the container in which the reaction occurs; \((e)\) add a catalyst; (f) increase temperature.

Step-by-Step Solution

Answer

(a) Increase in the concentration of NH₃ will result in an increase in the yield of NO at equilibrium. (b) Increase in the concentration of H₂O will result in a decrease in the yield of NO at equilibrium. (c) Decrease in the concentration of O₂ will result in a decrease in the yield of NO at equilibrium. (d) Decreasing the volume of the container will result in a decrease in the yield of NO at equilibrium. (e) Adding a catalyst has no effect on the yield of NO at equilibrium. (f) Increasing temperature will result in a decrease in the yield of NO at equilibrium.

Step 1: (a) Increase [NH₃]:

According to Le Châtelier's principle, when the concentration of a reactant (NH₃, in this case) is increased, the equilibrium will shift in the direction that consumes the added substance. In this reaction, the consumption of NH₃ leads to the formation of more NO and H₂O. Thus, an increase in the concentration of NH₃ will result in an increase in the yield of NO at equilibrium.

Step 2: (b) Increase [H₂O]:

Similarly, as per Le Châtelier's principle, increasing the concentration of a product (H₂O) will shift the equilibrium in the direction that reduces the concentration of the added substance. In this case, the consumption of H₂O will produce more NH₃ and O₂. Thus, an increase in the concentration of H₂O will result in a decrease in the yield of NO at equilibrium.

Step 3: (c) Decrease [O₂]:

According to Le Châtelier's principle, decreasing the concentration of a reactant (O₂) will shift the equilibrium in the direction that produces the removed substance. In this case, it would lead to the formation of more NH₃ and less NO and H₂O. Thus, a decrease in the concentration of O₂ will result in a decrease in the yield of NO at equilibrium.

Step 4: (d) Decreasing the volume of the container:

Le Châtelier's principle states that a decrease in the volume of the container will shift the equilibrium in the direction that reduces the number of moles of gas particles. In this reaction, there are 9 moles of gas particles on the left side (4 NH₃ and 5 O₂) and 10 moles of gas particles on the right side (4 NO and 6 H₂O). Decreasing the volume of the container will therefore shift the equilibrium to the left, resulting in a decrease in the yield of NO at equilibrium.

Step 5: (e) Adding a catalyst:

The addition of a catalyst has no effect on the equilibrium position, as it only increases the rate at which the equilibrium is attained. Since the equilibrium position is not affected, there will be no change in the yield of NO.

Step 6: (f) Increasing temperature:

According to Le Châtelier's principle, for an exothermic reaction (ΔH < 0, as in this case), increasing the temperature will shift the equilibrium in the direction that absorbs heat, which is the endothermic or reverse direction. In this reaction, the reverse direction is the formation of NH₃ and O₂. Thus, increasing the temperature will result in a decrease in the yield of NO at equilibrium.

Key Concepts

Le Châtelier's Principle

Le Châtelier's Principle helps us predict how a chemical equilibrium responds to changes in concentration, pressure, and temperature.
This principle states that if a system at equilibrium experiences a change, it will adjust to counteract that change and restore a new equilibrium.

• Increase in reactant concentration: The system shifts to produce more products.
• Increase in product concentration: The system shifts to produce more reactants.
• Changes in pressure or volume (for gases): The system shifts to favor the side with fewer or more gas molecules, depending on the change.

This principle gives us a handy way to predict the effect of various changes on a reaction, such as increasing \([\text{NH}_3]\) which results in more \([\text{NO}]\) production.

Exothermic Reaction

In an exothermic reaction, heat is released during the process, indicated by a negative \(\Delta H\).
For example, in the reaction of ammonia (NH₃) with oxygen (O₂), \(\Delta H = -904.4 \, \text{KJ}\), meaning it's exothermic.

• If the temperature increases, the equilibrium shifts to absorb additional heat, favoring the reverse reaction.
• If the temperature decreases, the reaction produces more heat by favoring the forward reaction.

Understanding the direction of heat flow helps us predict how changing temperature affects equilibrium output, impacting the yield of products like NO.

Catalyst Effect

Catalysts are substances that speed up the rate of a chemical reaction without being consumed.
They achieve this by providing an alternative pathway with a lower activation energy.

• Catalysts increase the rate at which equilibrium is achieved.
• They do not affect the actual position of the equilibrium.

In the given equilibrium scenario, adding a catalyst does not change the amount of NO produced at equilibrium but helps reach equilibrium faster.

Gas Laws

Gas laws describe the behavior of gases in response to changes in pressure, volume, and temperature.
For systems involving gases, like the reaction here, knowing these laws helps us understand equilibrium changes.

• Boyle's Law: Relates pressure and volume, where \( P_1V_1 = P_2V_2 \).
• Charles's Law: Relates volume and temperature, where \( V_1/T_1 = V_2/T_2 \).
• Combined Gas Law: Incorporates both, stating \( P_1V_1/T_1 = P_2V_2/T_2 \).

Decreasing the container volume, per these laws, increases pressure, and shifts equilibrium to the side with fewer moles of gas to minimize pressure changes, decreasing the yield of NO in this case.