Problem 71 - Chemistry The Science in Context

Question

In which of the following equilibria does an increase in temperature produce a shift toward the formation of more product? a.\(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) \quad \quad \Delta H^{\circ}<0\) b. \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}>0\) c. \(\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \quad \Delta H^{\circ}<0\)

Step-by-Step Solution

Answer

The correct answer is equilibrium b: $\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}>0$. This is because the reaction is endothermic, and according to Le Chatelier's principle, an increase in temperature shifts the equilibrium to the right, favoring product formation.

Step 1: Understand Le Chatelier's principle

Le Chatelier's principle states that if a system at equilibrium is subjected to a change in conditions such as concentration, pressure, or temperature, the position of the equilibrium will shift to counteract the change and restore equilibrium. In the context of temperature changes, the principle can be summarized as follows: - For an endothermic reaction (\(\Delta H^{\circ}>0\)), an increase in temperature will shift the equilibrium to the right, favoring the formation of products. This is because the forward reaction absorbs heat, so an increase in temperature favors the forward reaction. - For an exothermic reaction (\(\Delta H^{\circ}<0\)), an increase in temperature will shift the equilibrium to the left, favoring the formation of reactants. This is because the forward reaction releases heat, so an increase in temperature favors the reverse reaction.

Step 2: Analyze each reaction given in the exercise

We will now apply our understanding of Le Chatelier's principle to each of the chemical equilibria given in the exercise. a. $\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g) \quad \quad \Delta H^{\circ}<0$ This reaction is exothermic because \(\Delta H^{\circ}<0\). Therefore, according to Le Chatelier's principle, an increase in temperature will shift the equilibrium to the left, favoring reactant formation. b. $\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}>0$ This reaction is endothermic because \(\Delta H^{\circ}>0\). Therefore, according to Le Chatelier's principle, an increase in temperature will shift the equilibrium to the right, favoring product formation. c. $\mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+\mathrm{H}_{2}(g) \quad \Delta H^{\circ}<0$ This reaction is exothermic because \(\Delta H^{\circ}<0\). Therefore, according to Le Chatelier's principle, an increase in temperature will shift the equilibrium to the left, favoring reactant formation.

Step 3: Identify which equilibrium fulfills the given condition

We are asked to find the equilibrium in which an increase in temperature leads to the formation of more product. From our analysis in Step 2, we can conclude that: - For equilibrium a, an increase in temperature leads to the formation of more reactants. - For equilibrium b, an increase in temperature leads to the formation of more products. - For equilibrium c, an increase in temperature leads to the formation of more reactants. So, the correct answer is equilibrium b: \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3 \mathrm{H}_{2}(g) \quad \Delta H^{\circ}>0\)

Key Concepts

Chemical Equilibrium

Chemical equilibrium occurs in a process where the rate of the forward reaction equals the rate of the reverse reaction. In this state, the concentration of reactants and products remains constant over time. This doesn't mean that the reactants and products are equal in concentration, rather that their rates have balanced each other out. This dynamic balance can be affected by changes in conditions like temperature, pressure, and concentration. To illustrate, let's consider a scenario: imagine a seesaw. At equilibrium, this seesaw is perfectly balanced. A child jumping onto one side (a change such as a temperature increase) will throw the balance off. The system will react, through Le Chatelier's Principle, to regain that balance. That's essentially what happens in chemical equilibria when external conditions are altered.

Endothermic Reactions

Endothermic reactions are processes where the system absorbs heat from its surroundings. These reactions require energy to proceed, with heat serving as one of the reactants. In chemical terms, this means that the enthalpy change (\(\Delta H^{\circ} > 0 \)) is positive.Consider the equation: \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2}\mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3\mathrm{H}_{2}(g) \). Here, \(\Delta H^{\circ} > 0\), indicating an endothermic reaction. When temperature increases in such systems, they favor the direction that absorbs heat, namely the forward direction, forming more products. This principle helps chemists manipulate conditions to optimize product yields in industrial processes.

Temperature Effect on Equilibrium

The temperature has a significant effect on the state of equilibrium in a chemical system. According to Le Chatelier's Principle, if you change the temperature of a system, the equilibrium will shift to counteract this change.

• In exothermic reactions (\(\Delta H^{\circ} < 0 \)), where heat is released, increasing the temperature causes the equilibrium to shift towards reactants, as the system tries to absorb the extra heat by favoring the endothermic reverse reaction.
• In endothermic reactions (\(\Delta H^{\circ} > 0 \)), where heat is absorbed, increasing the temperature results in the system shifting towards products, as it benefits the endothermic forward reaction that absorbs heat.

For a reaction like \(\mathrm{CH}_{4}(g)+\mathrm{H}_{2}\mathrm{O}(g) \rightleftharpoons \mathrm{CO}(g)+3\mathrm{H}_{2}(g) \), an increase in temperature will cause the equilibrium to favor product formation since it’s endothermic. Understanding these effects allows chemists to control reactions more effectively, enhancing efficiency and yield.