Problem 75 - Chemistry The Molecular Science

Question

Consider the system $$ \begin{aligned} 4 \mathrm{NH}_{3}(\mathrm{~g})+3 \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{~N}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \\ \Delta_{\mathrm{r}} H^{\circ} &=-1530.4 \mathrm{~kJ} / \mathrm{mol} \end{aligned} $$ (a) How will the amount of ammonia at equilibrium be affected by (i) removing \(\mathrm{O}_{2}(\mathrm{~g})\) without changing the total gas volume? (ii) adding \(\mathrm{N}_{2}(\mathrm{~g})\) without changing the total gas volume? (iii) adding water without changing the total gas volume? (iv) expanding the container? (v) increasing the temperature? (b) Which of these changes (i to v) increases the value of \(K ?\) Which decreases it?

Step-by-Step Solution

Answer

Removing \(\mathrm{O}_2\), adding \(\mathrm{N}_2\), adding water, or expanding increases \(\mathrm{NH}_3\); increasing temperature decreases. Only temperature change affects \(K\), decreasing it.

Step 1: Understand the Reaction

The given system is a chemical equilibrium involving the reaction of ammonia (\(\mathrm{NH}_3\)) with oxygen (\(\mathrm{O}_2\)) to produce nitrogen (\(\mathrm{N}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). The reaction is exothermic, as indicated by the negative \(\Delta_{\mathrm{r}} H^{\circ}\).

Step 2: Analyze Effect of Removing \(\mathrm{O}_2\)

Removing \(\mathrm{O}_2\) shifts the equilibrium towards the side with \(\mathrm{O}_2\) to replace the removed substance. This results in increased ammonia at equilibrium, as more reactants (including \(4 \mathrm{NH}_3\)) will be needed to produce \(\mathrm{O}_2\).

Step 3: Analyze Effect of Adding \(\mathrm{N}_2\)

Adding \(\mathrm{N}_2\) shifts the equilibrium towards the production of more reactants (Le Chatelier's Principle), leading to an increase in ammonia at equilibrium, as the system adjusts to consume the added \(\mathrm{N}_2\).

Step 4: Analyze Effect of Adding Water

Adding water, which is a product in this reaction, would shift the equilibrium towards the reactants to balance the change, leading to an increase in ammonia at equilibrium.

Step 5: Analyze Effect of Expanding the Container

Expanding the container decreases the pressure of the system. The equilibrium will shift towards the side with more moles of gas to counteract this change, which is the reactants' side. This increases ammonia at equilibrium.

Step 6: Analyze Effect of Increasing Temperature

Increasing the temperature shifts the equilibrium towards the endothermic side (reactant side, since the reaction is exothermic) to absorb the added heat, resulting in increased ammonia at equilibrium.

Step 7: Determine Effect on Equilibrium Constant \(K\)

(i) Removing \(\mathrm{O}_2\), (ii) Adding \(\mathrm{N}_2\), (iii) Adding water, and (iv) Expanding the container does not change \(K\) as they involve concentration and pressure changes without temperature change. (v) Increasing temperature decreases \(K\) because the reaction is exothermic.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that describes how a system at equilibrium responds to external changes. This principle helps us predict the movement of equilibrium when there are changes in concentration, pressure, or temperature.

When you remove \(O_2\) from the system, the equilibrium shifts toward the side that will produce more of it. This means the system moves towards the reactants (the left side). Similarly, adding \(N_2\) or water, which are products, pushes the equilibrium toward the reactants, effectively increasing the amount of ammonia (\(NH_3\)).

This principle also explains why expanding the container affects equilibrium. Increasing the volume decreases the pressure, and the equilibrium compensates by shifting towards the side of the reaction with more gas molecules—here, the reactants side. This shift results in more ammonia being present.

Overall, Le Chatelier's Principle provides a powerful tool for chemists to predict the direction of equilibrium shifts under various conditions.

Exothermic Reactions

Exothermic reactions are chemical reactions that release energy in the form of heat. The reaction provided in the exercise, which involves ammonia and oxygen producing nitrogen and water, has a negative \(\Delta_{\mathrm{r}} H^{\circ}\), indicating it's exothermic.

In any exothermic reaction, heat is one of the products. This means if you increase the temperature, the system will counteract this change by shifting the equilibrium toward the reactants. This is because the system wants to absorb the extra heat, effectively balancing the temperature change.

Understanding whether a reaction is exothermic is crucial for predicting how temperature changes affect the system. In our example, increasing temperature leads to a shift towards more ammonia production, as the equilibrium adjusts to reduce the effects of added heat. This aspect demonstrates how energy levels and heat affect chemical reactions and equilibrium.

Equilibrium Constant

The equilibrium constant, symbolized by \(K\), is a value that expresses the ratio of the concentrations of products to reactants at equilibrium in a chemical reaction.

It is important to note that \(K\) only changes with temperature. This means changes involving concentration or pressure, such as the removal of \(O_2\), the addition of \(N_2\), or water, and expanding the container (volume change), do not affect \(K\).

However, since the reaction is exothermic, increasing the temperature decreases the value of \(K\). This decrease happens because the equilibrium shifts towards the reactants, reducing the proportion of products in comparison to reactants, thereby lowering the equilibrium constant.

Understanding this concept helps predict how different factors influence the equilibrium state of a chemical system.