Question

Oxygen can be converted into ozone by the action of lightning or electric sparks: $$ 3 \mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{O}_{3}(g) $$ For this reaction, \(\Delta H=+285 \mathrm{~kJ} / \mathrm{mol}\) and \(K=2.68 \times 10^{-29}\) at \(298 \mathrm{~K}\) (a) Is the reaction exothermic or endothermic? (b) Are the reactants or the products favored at equilibrium? (c) Explain the effect on the equilibrium of (1) Increasing pressure by decreasing volume (2) Increasing the concentration of \(\mathrm{O}_{2}(g)\) (3) Increasing the concentration of \(\mathrm{O}_{3}(g)\) (4) Adding a catalyst (5) Increasing the temperature

Short answer

(a) Endothermic. (b) Reactants favored. (c) (1) Shift to products, (2) Shift to products, (3) Shift to reactants, (4) No shift, (5) Shift to products.

Step-by-step solution

Identifying Reaction Type

The given reaction has a positive \( \Delta H = +285 \, \text{kJ/mol} \), which indicates the reaction is endothermic, meaning it absorbs heat from the surroundings.

Determining Equilibrium Position

The equilibrium constant \( K = 2.68 \times 10^{-29} \) is very small, suggesting that at equilibrium, the concentration of reactants \( \mathrm{O}_2(g) \) is favored over products \( \mathrm{O}_3(g) \).

Effect of Increasing Pressure by Decreasing Volume

At increased pressure, the reaction will shift towards the side with fewer gas molecules. The reaction \( 3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{O}_{3}(g) \) involves a reduction in gas molecules, so the equilibrium would shift towards products to reduce pressure.

Effect of Increasing \( \mathrm{O}_2(g) \) Concentration

Increasing the concentration of \( \mathrm{O}_{2}(g) \) will cause the equilibrium to shift towards the products \( \mathrm{O}_{3}(g) \) to partially counteract the change using Le Chatelier's principle.

Effect of Increasing \( \mathrm{O}_3(g) \) Concentration

Increasing the concentration of \( \mathrm{O}_{3}(g) \) will shift the equilibrium towards the reactants \( \mathrm{O}_2(g) \) in order to reduce the concentration of \( \mathrm{O}_3(g) \) again according to Le Chatelier's principle.

Effect of Adding a Catalyst

Adding a catalyst will speed up both the forward and reverse reactions equally but does not change the equilibrium position; it only helps the system reach equilibrium faster.

Effect of Increasing Temperature

Since the reaction is endothermic, increasing the temperature provides more energy, causing the equilibrium to shift towards the products \( \mathrm{O}_3(g) \) as it absorbs heat.

Key concepts

Endothermic Reactions

Endothermic reactions are processes where energy is absorbed from the surroundings in the form of heat. A key feature of these reactions is a positive enthalpy change (\( \Delta H > 0 \)). The absorption of heat means the system gains energy, which becomes stored in the chemical bonds of the products.
In the reaction converting oxygen (\( \mathrm{O}_2 \)) to ozone (\( \mathrm{O}_3 \)), \( \Delta H = +285 \, \text{kJ/mol} \) clearly tells us it's endothermic. Because of this, the reaction benefits from added heat, making it more favorable. Increasing temperature can often make endothermic reactions proceed more readily.
Understanding the nature of endothermic reactions helps determine how they respond to environmental changes, such as temperature shifts, which is crucial when analyzing chemical equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle provides insight into how a system at equilibrium reacts to changes. It states that if a system is subjected to a change (like pressure, temperature, or concentration), it will adjust to partially counteract that change and re-establish equilibrium.
Consider our reaction:

• Increasing the concentration of \( \mathrm{O}_2(g) \) will shift the equilibrium towards the products \( \mathrm{O}_3(g) \), as the system attempts to counter the addition of reactants by forming more product.
• Conversely, adding more \( \mathrm{O}_3(g) \) will cause a shift towards \( \mathrm{O}_2(g) \), as the system works to lower the concentration of excess product.
• Increasing temperature benefits endothermic reactions, resulting in a shift towards \( \mathrm{O}_3(g) \) since it absorbs more heat.
• Raising pressure by lowering volume drives the equilibrium toward fewer gas molecules. Here, the reaction to form \( \mathrm{O}_3(g) \) results in a decrease from 3 to 2 molecules, thus moving the equilibrium to the right (products).

These shifts follow Le Chatelier’s Principle in their quest to restore equilibrium.

Equilibrium Constant

The equilibrium constant (\( K \)) quantifies the position of equilibrium in a reversible reaction. It is derived from the concentrations of products and reactants at equilibrium. For the conversion of \( \mathrm{O}_2 \) to \( \mathrm{O}_3 \), we have a very small \( K = 2.68 \times 10^{-29} \).
This tiny value indicates that, under standard conditions, the equilibrium strongly favors the reactants (\( \mathrm{O}_2 \)), not the products (\( \mathrm{O}_3 \)). In other words, much more oxygen remains unreacted compared to the amount of ozone formed.
The equilibrium constant is fixed for a given reaction at a particular temperature, meaning any shift in equilibrium conditions does not change \( K \) itself, but rather alters the ratio of the products to reactants until the new equilibrium is established.

Catalysts Effect on Equilibrium

Catalysts are substances that alter the speed of a reaction without being consumed. Importantly, they provide a pathway for the reaction with a lower activation energy, speeding up the attainment of equilibrium. They do not change the position of equilibrium itself.
In the conversion of \( \mathrm{O}_2 \) to \( \mathrm{O}_3 \), adding a catalyst would make both the forward and reverse reactions proceed faster. However, the catalyst does not preferentially shift the equilibrium towards reactants or products.
The primary function of a catalyst is to reduce the time it takes for a chemical system to reach equilibrium. This means while the equilibrium position (like \( K \)) remains unchanged, the overall process becomes more efficient. Understanding this concept is key in industrial and laboratory settings where speed and efficiency are often as important as yield.