Problem 12 - Chemistry The Molecular Science

Question

Consider the gas-phase reaction of \(\mathrm{N}_{2}+\mathrm{O}_{2}\) to give \(2 \mathrm{NO}\) and the reverse reaction of 2 NO to give \(\mathbf{N}_{2}+\mathrm{O}_{2},\) discussed in Section 12-2e. An equilibrium mixture of \(\mathrm{NO}\), \(\mathrm{N}_{2}\), and \(\mathrm{O}_{2}\) at \(5000 . \mathrm{K}\) that contains equal concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) has a concentration of NO about half as great. Make qualitatively correct plots of the concentrations of reactants and products versus time for these two processes, showing the initial state and the final dynamic equilibrium state. Assume a temperature of \(5000 . \mathrm{K}\). Don't do any calculations-just sketch how you think the plots should look.

Step-by-Step Solution

Answer

Concentrations of reactants decrease, and NO increases until equilibrium is reached.

Step 1: Understand the Chemical Reaction

The reaction is \( \mathrm{N}_2 + \mathrm{O}_2 \rightarrow 2 \mathrm{NO} \) and its reverse \( 2 \mathrm{NO} \rightarrow \mathrm{N}_2 + \mathrm{O}_2 \). At equilibrium, \( [\mathrm{N}_2] = [\mathrm{O}_2] \) and \( [\mathrm{NO}] = \frac{1}{2} [\mathrm{N}_2] = \frac{1}{2} [\mathrm{O}_2] \). This tells us the direction of the concentration change that should occur over time.

Step 2: Sketch Reactant Concentrations Over Time

Begin with the initial concentrations of \( \mathrm{N}_2 \) and \( \mathrm{O}_2 \). As the reaction progresses, both will decrease as they are converted to \( \mathrm{NO} \). Show a decreasing trend in the graph until equilibrium where both maintain constant concentrations.

Step 3: Sketch Product Concentration Over Time

Initially, \( [\mathrm{NO}] \) might be zero or much lower than \( [\mathrm{N}_2] \) and \( [\mathrm{O}_2] \). As the reaction progresses, \( [\mathrm{NO}] \) will increase. Sketch an increasing curve reaching equilibrium at \( \frac{1}{2} [\mathrm{N}_2] \). Then maintain this constant level.

Step 4: Indicate Equilibrium on the Graph

Mark the point where the concentrations of \( \mathrm{N}_2 \), \( \mathrm{O}_2 \), and \( \mathrm{NO} \) become constant. This is when forward and reverse reactions occur at the same rate. The graph will show horizontal lines for all species at equilibrium levels.

Step 5: Reflect on the Graph

Check that the concentration lines meet the equilibrium condition: \( [\mathrm{NO}] = \frac{1}{2} [\mathrm{N}_2] = \frac{1}{2} [\mathrm{O}_2] \). The concentrations should reflect that initially, reactants are consumed to form products until equilibrium is reached.

Key Concepts

Gas-phase Reactions

Gas-phase reactions involve reactants transitioning in a gaseous state. These reactions are characterized by the molecules moving freely in space and colliding with one another. In the given example of the reaction between nitrogen (\(\mathrm{N}_2\)) and oxygen (\(\mathrm{O}_2\)) to form nitric oxide (\(\mathrm{NO}\)), this is a direct combination reaction that occurs in a gas phase. Gas-phase reactions can be influenced by several factors, including:

• Temperature: Higher temperatures generally increase reaction rates, as there are more energetic collisions.
• Pressure: Adjusting the pressure can shift the equilibrium according to Le Chatelier's principle.
• Volume: Changes in volume can also affect the equilibrium state by changing the concentration of gases.

Understanding these factors is crucial for anticipating how reactant and product concentrations will change over time. At equilibrium, the system's gaseous state allows for the dynamic interconversion of the species, keeping concentrations stable.

Reaction Kinetics

Reaction kinetics involves studying the rate at which chemical reactions occur and understanding the factors that affect these rates. In the context of the nitrogen-oxygen reaction to form nitric oxide, you need to grasp how quickly the reaction progresses towards equilibrium. Key principles include:

• Collision Theory: For a reaction to occur, reactant molecules must collide with sufficient energy and proper orientation.
• Activation Energy: This is the minimum energy required for a reaction to proceed. Lowering activation energy, such as by using a catalyst, can speed up the reaction.
• Reaction Rate: This is the change in concentration of reactants or products per unit time. It varies depending on conditions like temperature, concentration, and presence of catalysts.

In our exercise, visualizing these kinetics helps predict how nitrogen and oxygen concentrations decrease, while nitric oxide increases as the system approaches equilibrium.

Dynamic Equilibrium

Dynamic equilibrium in a chemical reaction is reached when the rate of the forward reaction equals the rate of the reverse reaction. At this point, there is no net change in the concentrations of the reactants and products. The exercise highlights this state by showing that although individual molecules continue to react, the overall concentrations remain constant.Dynamic equilibrium in a gas-phase reaction can be explained with the following points:

• Reversibility: Both forward and backward reactions occur simultaneously in a closed system.
• Constant Concentrations: Once equilibrium is achieved, the concentrations of \(\mathrm{N}_2\), \(\mathrm{O}_2\), and \(\mathrm{NO}\) will not change over time.
• Le Chatelier's Principle: If an external change such as pressure or temperature is applied, the equilibrium will shift to counteract the change and re-establish equilibrium.

Such an understanding is essential for constructing accurate concentration vs. time graphs, demonstrating how a reaction reaches and maintains equilibrium under given conditions.