Problem 80 - Chemistry The Molecular Science

Question

For each of these chemical reactions, predict whether the equilibrium constant at \(25^{\circ} \mathrm{C}\) is greater than 1 or less than \(1,\) or state that insufficient information is available. Also indicate whether each reaction is product-favored or reactant-favored. (a) \(2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g}) \quad \Delta_{\mathrm{r}} H^{\circ}=-115 \mathrm{~kJ} / \mathrm{mol}\) (b) \(2 \mathrm{O}_{3}(\mathrm{~g}) \rightleftharpoons 3 \mathrm{O}_{2}(\mathrm{~g})\) \(\Delta_{\mathrm{r}} H^{\circ}=-285 \mathrm{~kJ} / \mathrm{mol}\) (c) \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NCl}_{3}(\mathrm{~g})\) \(\Delta_{1} H^{\circ}=460 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

(a) \( K > 1 \), product-favored; (b) \( K > 1 \), product-favored; (c) \( K < 1 \), reactant-favored.

Step 1: Analyze Reaction (a)

The reaction given is \( 2 \text{NO} (g) + \text{O}_2 (g) \rightleftharpoons 2 \text{NO}_2 (g) \) with \( \Delta_r H^\circ = -115 \text{ kJ/mol} \). This negative enthalpy change suggests the reaction is exothermic, which typically implies that products (NO\(_2\)) are favored at lower temperatures. Therefore, the equilibrium constant \( K \) is expected to be greater than 1 at \(25^{\circ}C\), making the reaction product-favored.

Step 2: Analyze Reaction (b)

The reaction given is \( 2 \text{O}_3 (g) \rightleftharpoons 3 \text{O}_2 (g) \) with \( \Delta_r H^\circ = -285 \text{ kJ/mol} \). This is also an exothermic reaction. Products (O\(_2\)) are likely favored, which suggests the equilibrium constant \( K \) is greater than 1 at \(25^{\circ}C\), indicating the reaction is product-favored.

Step 3: Analyze Reaction (c)

The reaction given is \( \text{N}_2 (g) + 3 \text{Cl}_2 (g) \rightleftharpoons 2 \text{NCl}_3 (g) \) with \( \Delta_r H^\circ = 460 \text{ kJ/mol} \). This positive enthalpy change suggests the reaction is endothermic and typically does not favor product formation at lower temperatures. Hence, the equilibrium constant \( K \) is expected to be less than 1 at \(25^{\circ}C\), making the reaction reactant-favored.

Key Concepts

Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a crucial value in chemistry that provides insight into the balance of chemical reactions at equilibrium. This constant is derived from the concentrations of the reactants and products when the forward and reverse reactions occur at the same rate, meaning no net change in concentrations over time.
\[ K = \frac{[\text{products}]}{[\text{reactants}]} \]
where the concentrations are raised to the power of their respective coefficients in the balanced chemical equation.

• When \( K > 1 \), the products are favored, indicating that at equilibrium, the concentration of products is higher than that of reactants.
• If \( K < 1 \), the reactants are favored, meaning the equilibrium mixture contains more reactants.

Understanding the value of \( K \) helps predict the direction of the reaction under given conditions, such as temperature and pressure.

Exothermic Reactions

Exothermic reactions are processes that release energy in the form of heat to the surroundings. This characteristic is indicated by a negative enthalpy change (\( \Delta_r H^\circ < 0 \)).
For example, in reactions (a) and (b) from the original exercise, the negative \( \Delta_r H^\circ \) values suggest they are exothermic.
Key features of exothermic reactions include:

• Energy is released as heat, increasing the temperature of the surroundings.
• Products are generally more stable than reactants since they reside in a lower energy state.
• They tend to have an equilibrium constant \( K > 1 \) at lower temperatures, meaning products are favored when less heat is applied.

Understanding exothermic reactions is essential when predicting the effects of temperature changes on equilibrium, as these reactions tend to shift towards reactants when temperature increases.

Endothermic Reactions

Endothermic reactions require energy input to proceed, absorbing heat from the surroundings. This process is characterized by a positive enthalpy change (\( \Delta_r H^\circ > 0 \)). In the case of reaction (c) from the exercise, the positive enthalpy indicates an endothermic process.
Important points about endothermic reactions include:

• Energy is absorbed, making the surroundings cooler.
• Reactants are typically more stable than products since products are in a higher energy state.
• These reactions often show an equilibrium constant \( K < 1 \) at lower temperatures, indicating they favor reactants.

In endothermic processes, an increase in temperature can lead to increased product formation by shifting the equilibrium position rightwards. This behavior makes a precise understanding of endothermic reactions vital for controlling chemical processes, especially in industrial applications.