Question

For which of the following reaction is product formation favoured by low pressure and low temperature? (a) \(\mathrm{CO}_{2}(g)+\mathrm{C}(s) \rightleftharpoons 2 \mathrm{CO}(g) ; \quad \Delta H^{\circ}=172.5 \mathrm{~kJ}\) (b) \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}\) \(\Delta H^{\circ}=-21.7 \mathrm{~kJ}\) (c) \(2 \mathrm{O}_{3}(g) \rightleftharpoons 3 \mathrm{O}_{2}(g)\) \(\Delta H^{\circ}=-285 \mathrm{~kJ}\) (d) \(\mathrm{H}_{2}(g)+\mathrm{F}_{2}(g) \rightleftharpoons 2 \mathrm{HF}(g)\) \(\Delta H^{\circ}=-541 \mathrm{~kJ}\)

Short answer

Product formation for reaction (b) is favored by low pressure and low temperature.

Step-by-step solution

Evaluate Pressure Dependency

To determine how pressure affects the reaction, compare the number of moles of gas on both sides of the reaction. A reaction that produces fewer moles of gas is favored by high pressure, while a reaction that produces more moles of gas is favored by low pressure.

Evaluate Temperature Dependency Based on the Enthalpy Change

The temperature dependency of a reaction is based on the sign of the enthalpy change \(\Delta H^\circ\). A reaction with a negative \(\Delta H^\circ\) (exothermic) is favored at lower temperatures, while a reaction with a positive \(\Delta H^\circ\) (endothermic) is favored at higher temperatures.

Apply Principles to Each Reaction

Analyze each reaction based on the principles from the previous steps. (a) Since this reaction produces more gaseous products than reactants, it is favored by low pressure. Given that \(\Delta H^\circ\) is positive, the reaction is endothermic and so is favored at higher temperatures. (b) There are fewer moles of gas on the product side, so higher pressure would favor it; the reaction is exothermic (\(\Delta H^\circ < 0\)), so lower temperatures would favor product formation. For (c), the reaction is exothermic and results in a lower number of gas molecules, so it's favored by higher pressure and lower temperature. (d) Neither pressure nor temperature affects the shift in equilibrium as the number of gas molecules remains the same, and being exothermic implies it is favored at lower temperatures.

Identify the Correct Reaction

Considering both pressure and temperature, the reaction that is favored by both low pressure and low temperature is option (b), as it proceeds with a decrease in the number of gas molecules (higher pressure favors reactants) and is exothermic, thus favored by a decrease in temperature.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that explains how a change in conditions can shift the position of a chemical equilibrium. According to the principle, if a system at equilibrium experiences a change in pressure, temperature, or concentration of components, the equilibrium will adjust to counteract the change and restore a new balance.

For example, increasing the pressure on a reaction involving gases will shift the equilibrium toward the side with fewer gas molecules. This is because the system seeks to reduce the pressure, and by favoring the formation of fewer gas particles, the pressure exerted by the gases decreases. Conversely, decreasing the pressure favors the side with more gas molecules. Temperature changes affect equilibrium depending on whether the reaction is endothermic or exothermic. An increase in temperature will shift the equilibrium of an endothermic reaction (which absorbs heat) to the right, producing more products, while an exothermic reaction (which releases heat) will be favored at lower temperatures.

When applying Le Chatelier's Principle, it's also important to consider that not all changes will have a significant impact on the equilibrium. For example, changes in the concentration of solids or liquids typically do not affect the gas or aqueous equilibria because their concentrations are not part of the equilibrium constant expression.

Enthalpy Change

Understanding Enthalpy Change

Enthalpy change, represented as \( \Delta H \), is a measure of the heat change during a reaction at constant pressure. It's a critical factor in determining how temperature affects a chemical reaction's equilibrium.

A positive \( \Delta H \), or endothermic reaction, means that the system absorbs heat. In this scenario, increasing temperature supplies more heat to the system, which shifts the equilibrium toward the product side, favoring the formation of products. On the other hand, a negative \( \Delta H \), indicative of an exothermic reaction, means that the system releases heat. Lower temperatures are then favored for product formation, as the system seeks to generate heat by shifting the equilibrium toward the product side.

Applying to Reactions

By analyzing the \( \Delta H \), students can predict which way the reaction will shift when subjected to temperature changes. This understanding can aid in controlling reactions, for example in industrial synthesis, where the desired product can be maximized by manipulating the temperature based on the reaction's enthalpy change.

Pressure and Temperature Effects on Reaction

Pressure and temperature are two physical factors that can significantly influence the position of chemical equilibrium. Their effects are interconnected, and understanding their relationship is essential to predicting how a reaction will shift when subjected to changes.

Pressure Effects

The effect of pressure on a reaction is more straightforward to conceptualize for reactions involving gases. An increase in pressure will favor the reaction that produces fewer gas molecules, as this reduces the total pressure. Conversely, a decrease in pressure will favor the reaction that produces more gas molecules. This is directly linked to Le Chatelier's Principle, which states that the system will adjust to counteract the applied change.

Temperature Effects

The temperature effects on reaction are dictated by the enthalpy change. Exothermic reactions (with a negative \( \Delta H \) value) will be favored at lower temperatures because excess heat is released during the reaction. In contrast, endothermic reactions (with a positive \( \Delta H \) value) require heat input and are thus favored at higher temperatures.

It's essential for students to consider both factors when analyzing a reaction, as combining the effects of pressure and temperature can lead to a more nuanced understanding of how the reaction will proceed under various conditions. For instance, lowering both temperature and pressure for a reaction that creates more products in the form of gases, and is endothermic, will not necessarily favor the formation of more products; the lower temperature may favor the reactants, while the lower pressure may favor the products. Only by studying both aspects in relation to the specific reaction can students accurately predict the favored direction of the reaction's shift.