Question

For the equilibrium \(\mathrm{N}_{2} \mathrm{O}_{4}+57 \mathrm{~kJ} \rightleftarrows 2 \mathrm{NO}_{2}\) list four stresses that serve to increase the amount of \(\mathrm{NO}_{2}\).

Short answer

Increase temperature, decrease pressure, remove \( \text{NO}_2 \), add \( \text{N}_2\text{O}_4 \).

Step-by-step solution

Understand the Equilibrium Reaction

The given equilibrium reaction is \( \text{N}_2\text{O}_4 + 57 \text{ kJ} \rightleftharpoons 2 \text{NO}_2 \). This means that \( \text{N}_2\text{O}_4 \) decomposes into \( \text{NO}_2 \) while absorbing 57 kJ of energy. It is important to note that this is an endothermic reaction.

Le Chatelier's Principle

Le Chatelier's Principle states that if an external stress is applied to a system at equilibrium, the system adjusts in such a way as to counteract the stress and establish a new equilibrium. We will apply this principle to find stresses that shift the equilibrium towards \( \text{NO}_2 \).

Increase Temperature

Since the reaction is endothermic, increasing the temperature will favor the formation of \( \text{NO}_2 \). According to Le Chatelier's Principle, the system will shift to absorb the added heat.

Decrease Pressure

In the given reaction, one mole of \( \text{N}_2\text{O}_4 \) produces two moles of \( \text{NO}_2 \). By decreasing the pressure, the equilibrium will shift towards the side with more moles of gas, which is the right side, thereby increasing \( \text{NO}_2 \).

Remove \( \text{NO}_2 \) from the System

By continuously removing \( \text{NO}_2 \) from the system, the equilibrium will shift to the right to produce more \( \text{NO}_2 \) to replace what was removed.

Add \( \text{N}_2\text{O}_4 \) to the System

Adding more \( \text{N}_2\text{O}_4 \) to the system will shift the equilibrium to the right, resulting in more \( \text{NO}_2 \) being formed, trying to use up the excess reactant.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemical equilibrium. It helps predict how a system in equilibrium responds to external changes or stresses. When a system at equilibrium experiences a change in concentration, temperature, or pressure, it adjusts itself to minimize that change and re-establish equilibrium.
For example, if a reactant is added to the system, the equilibrium will shift to consume the excess reactant, producing more product in the process. Similarly, if a product is removed, the system will shift to produce more of that product.

• **Stress Addition**: The system counteracts any added stress by shifting equilibrium in the direction that decreases the effect of the change.
• **Direction of Shift**: Depending on the nature of the external change, equilibrium may shift to the right (towards products) or to the left (towards reactants).

Understanding this principle is essential to predict outcomes in dynamic equilibrium systems, such as the formation of \(\text{NO}_2\) from \(\text{N}_2\text{O}_4\).

Endothermic Reactions

Endothermic reactions are processes where energy is absorbed from the surroundings. This absorption is typically in the form of heat. In the chemical reaction \(\text{N}_2\text{O}_4 + 57\text{ kJ} \rightleftharpoons 2 \text{NO}_2\), energy is absorbed during the conversion of \(\text{N}_2\text{O}_4\) into \(\text{NO}_2\).

• **Heat as a Reactant**: For endothermic reactions, temperature and heat can be considered as additional reactants. Increasing the temperature increases the system's heat, shifting the equilibrium towards the products.
• **Effect on \(\Delta H\)**: In these reactions, the enthalpy change (\(\Delta H\)) is positive, indicating energy input rather than release.

The understanding of endothermic reactions helps in identifying conditions under which more \(\text{NO}_2\) can be formed by leveraging temperature changes.

Pressure Effects on Equilibrium

The effect of pressure on equilibrium depends on the number of moles of gas present on the reactant and product sides of the equation. Le Chatelier's Principle helps us understand how varying pressure influences the reaction: In this equilibrium between \(\text{N}_2\text{O}_4\) and \(\text{NO}_2\):

• **Unequal Molar Quantity**: There are fewer moles of gas on the left side (1 mole of \(\text{N}_2\text{O}_4\)) compared to the right side (2 moles of \(\text{NO}_2\)).
• **Pressure Decrease**: Reducing the system’s pressure favors the shift toward the side with more moles of gas, thus producing more \(\text{NO}_2\).
• **Practical Application**: Industrially, pressure adjustments become crucial in maximizing the yields of desired products by focusing on gas phase reactions.

Hence, manipulating pressure is a strategic tool in steering the chemical equilibrium to favor a specific product.

Temperature Effects on Equilibrium

Temperature changes significantly impact chemical equilibria, especially in endothermic and exothermic reactions. According to Le Chatelier's Principle, adding heat to an endothermic reaction like \(\text{N}_2\text{O}_4 + 57 \text{kJ} \rightleftharpoons 2 \text{NO}_2\) will drive the equilibrium towards product formation because heat acts as a reactant.

• **Temperature Increase**: For endothermic reactions, increasing the temperature supplies additional energy, which shifts the equilibrium to favor the product side.
• **Dynamic Changes**: The equilibrium constant, \(K\), itself can change with temperature changes, reflecting the new balance point.
• **Economic Considerations**: In industrial settings, understanding how temperature shifts equilibrium is crucial for designing energy-efficient processes.

Temperature adjustments are not just scientific interest but hold practical implications in maximizing yields and optimizing reaction conditions.