Problem 61 - General Chemistry: Principles and Modern Applications

Question

If the volume of an equilibrium mixture of \(\mathrm{N}_{2}(\mathrm{g}), \mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{NH}_{3}(\mathrm{g})\) is reduced by doubling the pressure, will \(P_{\mathrm{N}_{2}}\) have increased, decreased, or remained the same when equilibrium is re established? Explain. $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{g})$$

Step-by-Step Solution

Answer

When the volume of the equilibrium mixture is reduced (or pressure is increased), the partial pressure of Nitrogen, \(P_{N2}\), will decrease when equilibrium is reestablished to counteract the change in pressure according to Le Chatelier's Principle.

Step 1: Identify the Reaction

The chemical reaction in the exercise is: \[ N_{2(g)} + 3 H_{2(g)} \rightleftharpoons 2 NH_{3(g)} \]. It properly indicates the states of the compounds, the reversibility of the reaction as depicted by the double arrow, and the stoichiometry of the compounds involved.

Step 2: Understand the Change in Pressure

Decreasing the volume (or increasing the pressure) on the equilibrium mixture shifts the equilibrium position to counteract the change according to Le Chatelier’s Principle. The system will favor the side of the reaction with fewer gas molecules to reduce the pressure.

Step 3: Identify the Effect on Nitrogen

In the reaction equation, there are 4 molecules of gas on the left (1 nitrogen and 3 hydrogens) and 2 molecules of gas on the right (2 ammonias) per the reaction stoichiometry. The equilibrium will shift to the right side (towards the production of ammonia) to reduce the total number of gas molecules and thereby reduce the pressure. As a result, the amount of Nitrogen (N2) will decrease. Hence, \(P_{\mathrm{N}_{2}}\) (the partial pressure of N2) will decrease.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a crucial concept in understanding how reactions behave under different conditions. It happens when the forward and reverse reactions in a chemical system occur at the same rate, so the concentrations of reactants and products remain constant over time. This doesn't mean the reactions stop, just that their activities balance each other out.

The equilibrium state is denoted by a double arrow (\(\rightleftharpoons\)) in a chemical equation. This balance is influenced by factors like temperature, concentration, and pressure. Maintaining equilibrium is essential because it allows for prediction and control of reaction behavior in various industrial and biological processes.

Understanding equilibrium helps in predicting how changes affect a reaction, which is where Le Chatelier's Principle comes into play. This principle helps identify how a system at equilibrium responds to external changes like pressure or volume, making chemical equilibrium a dynamic and flexible concept.

Reaction Stoichiometry

Reaction stoichiometry refers to the relationship between the quantities of reactants and products in a chemical reaction. It's crucial for understanding how changes in conditions affect chemical equilibrium.

In the reaction \( \mathrm{N}_2(\mathrm{g}) + 3 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{g}) \), stoichiometry comes into play to determine how reactants and products are consumed and generated. Here, one mole of nitrogen reacts with three moles of hydrogen to produce two moles of ammonia.

Understanding stoichiometry helps in calculating the shifts in equilibrium due to changes in conditions. It allows chemists to predict how much of each substance is involved and to what extent the equilibrium will shift according to the changes imposed by Le Chatelier's Principle.

Gas Pressure Effects

Gas pressure effects are essential to understanding reactions involving gases. According to Le Chatelier's Principle, an increase in pressure due to volume reduction will cause the equilibrium to shift toward the side with fewer gas molecules.

In this reaction: \( \mathrm{N}_2(\mathrm{g}) + 3 \mathrm{H}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NH}_3(\mathrm{g}) \), there are four molecules of gas on the reactant side and two on the product side. Thus, a pressure increase will push the equilibrium toward the formation of ammonia, which has fewer gas molecules compared to the reactant side.

This results in a decrease in the partial pressure of nitrogen gas (\(P_{\mathrm{N}_2}\)) as more ammonia is produced. By understanding gas pressure effects, it's possible to manipulate the outcome of reactions, making them an important aspect of chemical engineering and industrial processes.