Problem 26 - Chemistry and Chemical Reactivity

Question

\(K_{\mathrm{p}}\) for the following reaction is 0.16 at \(25^{\circ} \mathrm{C}\) $$ 2 \mathrm{NOBr}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\mathrm{g}) $$ The enthalpy change for the reaction at standard conditions is \(+16.3 \mathrm{kJ} / \mathrm{mol}\) -rxn. Predict the effect of the following changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of the following changes is made. (a) adding more \(\mathrm{Br}_{2}(\mathrm{g})\) (b) removing some \(\mathrm{NOBr}(\mathrm{g})\) (c) decreasing the temperature (d) increasing the container volume

Step-by-Step Solution

Answer

(a) Equilibrium shifts left; (b) Equilibrium shifts left; (c) Equilibrium shifts left; (d) Equilibrium shifts right.

Step 1: Analyze the effect of adding more Br2(g)

According to Le Chatelier’s Principle, if a component is added to a reaction at equilibrium, the system will shift in the direction that consumes the added component. Here, adding more \( \mathrm{Br}_2(\mathrm{g}) \) will drive the reaction to the left, favoring the formation of \( \mathrm{NOBr}(\mathrm{g}) \) to consume the excess \( \mathrm{Br}_2(\mathrm{g}) \).

Step 2: Analyze the effect of removing some NOBr(g)

According to Le Chatelier’s Principle, if a component is removed from a reaction at equilibrium, the system will shift in the direction that forms more of the removed component. Here, removing \( \mathrm{NOBr}(\mathrm{g}) \) will drive the reaction to the left, as the system tries to restore the lost \( \mathrm{NOBr}(\mathrm{g}) \) by consuming \( \mathrm{NO}(\mathrm{g}) \) and \( \mathrm{Br}_2(\mathrm{g}) \) to produce \( \mathrm{NOBr}(\mathrm{g}) \).

Step 3: Analyze the effect of decreasing the temperature

The reaction is endothermic (\( \Delta H = +16.3 \mathrm{kJ/mol} \)). According to Le Chatelier’s Principle, decreasing the temperature will shift the equilibrium towards the exothermic direction, which is to the left in this case, where more \( \mathrm{NOBr}(\mathrm{g}) \) is produced, releasing energy.

Step 4: Analyze the effect of increasing the container volume

Increasing the volume of the container decreases the pressure of the system. Le Chatelier’s Principle states the equilibrium will shift toward the side with more moles of gas to reestablish the pressure. In this reaction, the forward direction produces 3 moles of gas (2 NO + 1 Br2) compared to the 2 moles of NOBr. Thus, the equilibrium will shift to the right.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps predict how a chemical equilibrium will respond to various changes. When a system at equilibrium experiences a change in concentration, pressure, or temperature, the system will adjust in a way to counteract this change. It acts as a balancing act to maintain equilibrium.

For example:

• If a reactant or product is added, the equilibrium will shift to consume the added substance.
• Conversely, if a component is removed, the equilibrium will shift to produce more of the missing component.
• Changes in pressure and volume will shift the equilibrium depending on the number of moles of gases involved.
• Temperature changes will shift the equilibrium towards endothermic or exothermic directions depending on the heat absorbed or released.

Understanding this principle is crucial for predicting how a system reacts to external changes and is essential for processes like chemical synthesis and industrial reactions.

Endothermic Reactions

Endothermic reactions are processes that absorb energy from their surroundings in the form of heat. In these reactions, the enthalpy change (delta H) is positive since energy is taken in. This can influence the direction in which a reaction equilibrium shifts.

In the exercise, the reaction has an enthalpy change of \(+16.3 \; \mathrm{kJ/mol}\), indicating that it is endothermic:

• Heat can be considered a reactant when dealing with endothermic reactions.
• If the temperature is increased, the equilibrium will shift to the right (forward direction) as it tries to absorb more heat.
• If the temperature decreases, the equilibrium shifts to the left (reverse direction) because, since less heat is available, the system compensates by producing more heat.

This characteristic of endothermic reactions is important in adjusting conditions during chemical processes to ensure optimal product formation.

Equilibrium Shifts

Equilibrium shifts occur when a change is introduced to a system that is already at equilibrium causing it to move to a new equilibrium position. The shift direction can be predicted using Le Chatelier’s Principle.

Equilibrium can shift:

• To the right: Adequate conditions lead to increased formation of products.
• To the left: Conditions favor the formation of reactants.

When considering the given reaction, several factors can cause shifts:

• Adding more \(\mathrm{Br}_2(\mathrm{g})\) shifts the equilibrium left as the system compensates for the excess \(\mathrm{Br}_2(\mathrm{g})\) by forming more \(\mathrm{NOBr}(\mathrm{g})\).
• Removing \(\mathrm{NOBr}(\mathrm{g})\) also shifts it left to increase concentration through production.
• Decreasing temperature naturally favors exothermic (backward) reactions.
• Increasing the container's volume shifts equilibrium to the right, as more moles of gas can be accommodated in lower pressures.

Understanding these shifts is essential for predicting outcomes in chemical reactions, particularly in controlled industrial processes or laboratory settings.

Reaction Quotient

The reaction quotient, often denoted as \(Q\), is a key indicator in determining the direction in which a reaction needs to shift to reach equilibrium. It is calculated using the same equation as the equilibrium constant (\(K_\text{p}\)), except it uses the initial concentrations or pressures rather than equilibrium values.

The direction of the shift depends on the comparison between \(Q\) and \(K_\text{p}\):

• If \(Q < K_\text{p}\), the reaction will proceed to the right, favoring the formation of products.
• If \(Q > K_\text{p}\), the reaction will shift left, favoring reactants, as the system tends to reach equilibrium.
• If \(Q = K_\text{p}\), the system is already at equilibrium, and no shift is observed.

For the given exercise, understanding \(Q\) helps deduce whether additional changes in concentration or pressure will move the system towards or away from equilibrium.