Problem 68 - Chemistry: The Central Science in SI Units, Global Edition

Question

Explain, using Le Châtelier's principle, why the equilibrium constant for the formation of \(\mathrm{NO}\) from \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) increases with increasing temperature, whereas the equilibrium constant for the formation of \(\mathrm{NO}_{2}\) from \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) decreases with increasing temperature.

Step-by-Step Solution

Answer

In summary, the equilibrium constant for the formation of NO from N2 and O2 increases with temperature because it is an endothermic reaction (ΔH > 0), and increasing temperature favors the formation of products. On the other hand, the equilibrium constant for the formation of NO2 from NO and O2 decreases with temperature because it is an exothermic reaction (ΔH < 0), and increasing temperature favors the formation of reactants. This behavior can be explained using Le Châtelier's principle, as endothermic reactions shift towards products with increasing temperature, while exothermic reactions shift towards reactants with increasing temperature.

Step 1: Identify the reactions

First, let's write down the balanced chemical equations for the formation of NO from N2 and O2, and the formation of NO2 from NO and O2: 1. Formation of NO: \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) 2. Formation of NO2: \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) Now that we know the reactions, we can analyze them using Le Châtelier's principle.

Step 2: Understanding Le Châtelier's principle

Le Châtelier's principle states that if a system at equilibrium experiences a change in temperature, pressure, or concentration, the system will adjust to counteract the change and restore equilibrium. In the current exercise, the focus is on the change in temperature. The key point to keep in mind is that an increase in temperature favors the endothermic reaction, while a decrease in temperature favors the exothermic reaction.

Step 3: Determine enthalpy changes

The formation of NO from N2 and O2 is an endothermic process, meaning it absorbs heat from the surroundings: \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) , ΔH > 0 (Endothermic) The formation of NO2 from NO and O2 is an exothermic process, meaning it releases heat to the surroundings: \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) , ΔH < 0 (Exothermic) Now we will use this information and Le Châtelier's principle to explain why the equilibrium constant for these reactions changes as the temperature increases.

Step 4: Explain the behavior of equilibrium constants with increasing temperature

When the temperature increases: 1. For the endothermic reaction (formation of NO), the equilibrium will shift towards the products to counteract the increased temperature. Therefore, the equilibrium constant will increase: \(N_2(g) + O_2(g) \rightleftharpoons 2NO(g)\) , Kc increases as temperature increases. 2. For the exothermic reaction (formation of NO2), the equilibrium will shift towards the reactants to counteract the increased temperature. Therefore, the equilibrium constant will decrease: \(2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)\) , Kc decreases as temperature increases. These changes in equilibrium constants with temperature can be explained using Le Châtelier's principle: An endothermic reaction will shift towards products with increasing temperature, while an exothermic reaction will shift towards reactants with increasing temperature.

Key Concepts

Equilibrium Constant

The equilibrium constant, often symbolized as \( K_c \) for reactions in solution or \( K_p \) for reactions involving gases, is a measure of the position of equilibrium in a chemical reaction. It reflects the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their respective stoichiometric coefficients.
Here’s why it's important:

• A large equilibrium constant (\( K_c >> 1 \)) means the reaction heavily favors the formation of products.
• A small equilibrium constant (\( K_c << 1 \)) indicates a reaction that favors the reactants at equilibrium.

The value of \( K_c \) is specific to a given reaction at a specific temperature. It indicates which way the reaction will shift to maintain equilibrium when subjected to changes, such as pressure or concentration. With changes in temperature, however, \( K_c \) itself changes because the relative energies of reactants and products change with temperature.Understanding the equilibrium constant can guide us on the concentration balance at equilibrium, making it a crucial concept in predicting how a reaction behaves under different conditions.

Endothermic Reaction

An endothermic reaction is a fascinating process where the system absorbs heat from its surroundings. This means that the enthalpy change, \( \Delta H \), is positive. In thermodynamic terms, endothermic reactions need an input of energy to proceed.
Consider this:

• These reactions increase in yield with increasing temperature because they need external energy to overcome energy barriers.
• An example of this is the formation of NO from \( N_2 \) and \( O_2 \): \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \). Here, adding heat pushes the equilibrium towards the production of more NO.

Le Châtelier's principle helps us understand that if you increase the temperature for an endothermic reaction, the system shifts towards the products to counteract this change. This is why the equilibrium constant increases with temperature for such reactions, as seen in the formation of NO.

Exothermic Reaction

An exothermic reaction releases energy, typically in the form of heat, to its surroundings. As a result, the enthalpy change \( \Delta H \) for these reactions is negative, signifying that the products are at a lower energy level than the reactants.
Key points to note:

• Exothermic reactions produce heat, meaning they are often spontaneous and more favorable at lower temperatures.
• One typical example is the formation of \( NO_2 \) from \( NO \) and \( O_2 \): \( 2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g) \). This reaction releases heat, thus naturally proceeding towards formation of \( NO_2 \) without extra energy input.

According to Le Châtelier's principle, increasing the temperature of an exothermic reaction causes the system to shift towards reactants, countering the added heat. Hence, the equilibrium constant decreases because a higher temperature promotes a shift backwards, making it less favorable for product formation.