Question

The dimerization of \(\mathrm{NO}_{2}\) to form \(\mathrm{N}_{2} \mathrm{O}_{4}\) is an exothermic equilibrium reaction described in this section. Which substance does the equilibrium favor at high temperatures?

Short answer

The equilibrium favors \(NO_2\) at high temperatures.

Step-by-step solution

Understand the Reaction

The dimerization of nitrogen dioxide \(NO_2\) to form \(N_2O_4\) can be represented by the chemical equation: \(2NO_2 ightleftharpoons N_2O_4\). This is an exothermic reaction, meaning that it releases heat when moving from reactants \(NO_2\) to products \(N_2O_4\).

Consider Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to partially counteract the effect of the disturbance. In the case of an exothermic reaction, increasing the temperature adds heat to the system.

Predict the Effect of Temperature Increase

According to Le Chatelier's Principle, increasing the temperature of an exothermic reaction will shift the equilibrium position to counteract the added heat. Therefore, the system will favor the endothermic direction, which in this case is the reverse reaction: \(N_2O_4\) decomposing back to \(2NO_2\).

Equilibrium at High Temperature

At high temperatures, the equilibrium will favor \(NO_2\) rather than \(N_2O_4\), as the reaction shifts left to absorb additional heat in the endothermic direction.

Key concepts

Equilibrium reactions

In chemical systems, equilibrium reactions are fascinating because they involve a dynamic balance between reactants and products. For the dimerization of nitrogen dioxide (\(2NO_2 \rightleftharpoons N_2O_4\)), the concept of chemical equilibrium plays a significant role. At this stage, both the forward reaction (which forms \(N_2O_4\)) and the reverse reaction (which breaks it down into \(NO_2\)) occur at equal rates. This results in a stable concentration of reactants and products over time.

• Equilibrium does not mean reactions stop; instead, they happen simultaneously and continuously.
• The position of equilibrium in an exothermic reaction like this one influences how much \(NO_2\) or \(N_2O_4\) is present at any time.

Understanding this equilibrium is crucial because changes in conditions, such as temperature, can shift the balance toward one side or the other. This is where deeper concepts like Le Chatelier's Principle come into play, helping predict how the system might respond to external changes.

Le Chatelier's Principle

Le Chatelier's Principle is a cornerstone of understanding how equilibrium reactions respond to changes. It essentially states that if a system at equilibrium experiences a change in concentration, temperature, or pressure, the system will adjust to partially counteract that change. For our reaction, \(2NO_2 \rightleftharpoons N_2O_4\), when we alter the conditions, this principle helps us predict the direction of the shift.

• If the concentration of \(NO_2\) increases, the equilibrium will shift to produce more \(N_2O_4\).
• Adding heat to an exothermic reaction disturbs the balance, as the system minimizes the effect by favoring the endothermic reverse reaction.

So, under higher temperatures, there's a noticeable shift to favor the decomposition of \(N_2O_4\) back to \(NO_2\), as the system works to absorb excess heat. This principle provides an intuitive way to predict and understand equilibrium shifts.

Exothermic reactions

Exothermic reactions are those that release energy, usually in the form of heat. In the case of dimerization of \(NO_2\) to \(N_2O_4\), this process releases heat energy into the surroundings. The general equation \(2NO_2 \rightleftharpoons N_2O_4 + ext{heat}\) explains why it's classified as exothermic.

• When these reactions proceed in the forward direction, they give off energy, making the surroundings warmer.
• Having energy as one of the products means the reaction's equilibrium is sensitive to temperature changes.

Understanding that an exothermic reaction releases heat helps clarify why increasing temperature causes the equilibrium to shift towards the reactants, as highlighted by Le Chatelier's Principle. It compensates for the excess thermal energy by decomposing the product back into reactants.

Temperature effects on equilibrium

Temperature effects on equilibrium reactions are intriguing, particularly because of their impact on the direction of the reaction. In exothermic reactions like \(2NO_2 \rightleftharpoons N_2O_4\), temperature changes lead to significant shifts.Increasing temperature in such a reaction introduces additional heat. According to Le Chatelier’s Principle, this prompts the equilibrium to move in the endothermic direction to counterbalance the change.

• For the reaction involving \(NO_2\) and \(N_2O_4\), the endothermic reaction is the breakdown of \(N_2O_4\) back to \(NO_2\).
• This means that higher temperatures will favor the decomposition of \(N_2O_4\), increasing the concentration of \(NO_2\).

As a result, understanding how temperature modifies the equilibrium position provides a practical approach for controlling the yield of reactions, like the production of nitrogen dioxide and its dimer.