Problem 80 - Chemistry: An Atoms-Focused Approach

Question

In which of the following hypothetical cquilibria docs the product yield decrease with increasing temperature? a. \(2 \mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z} \quad \Delta H>0\) b. \(2 X+Y \rightleftharpoons Z \quad \Delta H=0\) c. \(2 \mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z} \quad \Delta H<0\)

Step-by-Step Solution

Answer

Answer: Case c, where the reaction is \(2 \mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z} \quad \Delta H<0\), has a lower product yield as temperature increases.

Step 1: Understanding Le Chatelier's principle and the effect of temperature on equilibrium

Le Chatelier's principle states that when a system in equilibrium is subjected to external stress, the system will adjust itself to partially counteract the stress and achieve a new equilibrium. One of the external factors that can affect equilibrium is temperature. For a given reaction at equilibrium, if the temperature is increased, the reaction will shift to either the endothermic or exothermic side to "consume" the extra heat energy.

Step 2: Analyzing case a (\(\Delta H > 0\))

In this case, the enthalpy change of the reaction is positive, which means the reaction is endothermic. When temperature increases, the equilibrium will shift towards the endothermic side (product side) to consume the extra heat. As a result, the product yield will increase with increasing temperature. So, case a does not fit the given condition.

Step 3: Analyzing case b (\(\Delta H = 0\))

In this case, the enthalpy change of the reaction is zero, which means the reaction is neither endothermic nor exothermic. When temperature increases, there will be no shift in the equilibrium position, as there is no heat to be absorbed or released. Therefore, the product yield remains the same with increasing temperature. So, case b does not fit the given condition as well.

Step 4: Analyzing case c (\(\Delta H < 0\))

In this case, the enthalpy change of the reaction is negative, which means the reaction is exothermic. When temperature increases, the equilibrium will shift towards the endothermic side (reactant side) to consume the extra heat. As a result, the product yield will decrease with increasing temperature. So, case c fits the given condition.

Step 5: Conclusion

For the given hypothetical equilibria, the product yield decreases with increasing temperature in case c (\(2 \mathrm{X}+\mathrm{Y} \rightleftharpoons \mathrm{Z} \quad \Delta H<0\)).

Key Concepts

Equilibrium

Equilibrium refers to the state where the forward and reverse reactions occur at the same rate, resulting in no net change in the concentration of reactants and products. This balanced state can be disrupted by external factors such as temperature, pressure, and concentration. When a change occurs, the system adjusts itself to minimize the effect, a concept known as Le Chatelier's Principle.
For example, if a reaction at equilibrium is exposed to a change in temperature, the system will respond by shifting the position of equilibrium to counteract this change. This shift might favor the formation of either the reactants or the products, depending on whether the reaction absorbs or releases heat.

Endothermic Reaction

An endothermic reaction is a process where heat is absorbed from the surroundings. This results in a positive enthalpy change (\(\Delta H > 0\)), indicating that the system takes in energy.
When the temperature increases in an endothermic reaction, the equilibrium shifts towards the side that absorbs heat, usually the products. This shift happens because the system attempts to reduce the excess heat by favoring the reaction that "consumes" heat.

• An example could be if \(2 \text{X} + \text{Y} \rightarrow \text{Z}\) is endothermic, more \(\text{Z}\) will form at higher temperatures.

This is why, for an endothermic reaction, increasing temperature typically increases the yield of products.

Exothermic Reaction

An exothermic reaction releases heat into the surroundings, characterized by a negative enthalpy change (\(\Delta H < 0\)). These reactions are often perceived as "giving off" energy.
When temperature rises, an exothermic reaction undergoes a shift in equilibrium towards the side that absorbs heat, which is usually the reactant side. This counteracts the added heat, resulting in decreased product yields at higher temperatures.

• For instance, if \(2 \text{X} + \text{Y} \rightarrow \text{Z}\) is exothermic, an increase in temperature would lead to more reactants being favored.

Thus, exothermic reactions generally produce less product when the temperature is increased.

Enthalpy Change

Enthalpy change (\(\Delta H\)) represents the heat absorbed or released in a reaction. It is a crucial factor in determining how a reaction responds to temperature changes.
Positive enthalpy change indicates endothermic reactions, where heat is absorbed, while a negative value represents exothermic reactions, where heat is released.

• If \(\Delta H > 0\), the system needs energy and shifts towards products with added heat.
• If \(\Delta H < 0\), the system releases energy and shifts towards reactants when heated.

Understanding the enthalpy change helps predict the shift in equilibrium positions when temperature changes, aligning with Le Chatelier's Principle.