Question

How would each of the following changes affect the equilibrium position of the system used to produce methanol from carbon monoxide and hydrogen? $$ \mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+ $$ a. adding \(\mathrm{CO}\) to the system b. cooling the system c. adding a catalyst to the system d. removing \(\mathrm{CH}_{3}\) OH from the system e. decreasing the volume of the system

Short answer

In summary, the effects of the changes on the equilibrium position are as follows: a. Adding CO to the system: Shifts equilibrium to the right, favoring methanol production. b. Cooling the system: Shifts equilibrium to the right, favoring methanol production. c. Adding a catalyst: Has no effect on the equilibrium position. d. Removing CH₃OH: Shifts equilibrium to the right, favoring methanol production. e. Decreasing the volume: Shifts equilibrium to the right, favoring methanol production.

Step-by-step solution

Change a: Adding CO to the system

According to Le Chatelier's principle, adding more CO (carbon monoxide) will shift the equilibrium position to the right, as the system will try to counteract the increase in CO by using up more CO to produce more methanol (CH3OH). Thus, the equilibrium will favor the production of CH3OH.

Change b: Cooling the system

To analyze the effect of cooling the system, we must first determine if the reaction is exothermic or endothermic. In this case, the reaction is exothermic, as it releases heat: CO(g) + 2H2(g) ⇌ CH3OH(g) + heat According to Le Chatelier's principle, if we cool the system, the equilibrium position will shift to favor the exothermic reaction to produce more heat and counteract the cooling. Thus, the equilibrium will shift to the right, favoring the production of methanol.

Change c: Adding a catalyst to the system

A catalyst only speeds up the rate at which equilibrium is achieved but does not change the position of the equilibrium. Therefore, adding a catalyst to the system will have no effect on the equilibrium position.

Change d: Removing CH₃OH from the system

According to Le Chatelier's principle, if we remove CH3OH from the system, the equilibrium position will shift to the right to counteract the decrease in CH3OH. The system will favor the production of more methanol to replace the removed CH3OH.

Change e: Decreasing the volume of the system

When we decrease the volume of the system, the pressure inside the system will increase. According to Le Chatelier's principle, the equilibrium position will shift in the direction that reduces the pressure. In this case, the equilibrium will shift in the direction with fewer moles of gas, which is the right side of the reaction (since 1 mole of CO and 2 moles of H2 react to form 1 mole of CH3OH). Thus, decreasing the volume of the system will shift the equilibrium position to the right, favoring the production of methanol.

Key concepts

Le Chatelier's Principle

Understanding how a chemical system at equilibrium reacts to disturbances is essential for mastering chemical reactions. Le Chatelier's principle is a guiding rule in chemistry that helps predict the behavior of a system when it is subjected to changes. Simply put, this principle states that when a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will respond by altering the equilibrium composition to counteract the change.

For example, if additional CO is added to the methanol production system, the principle predicts that the reaction will shift towards producing more CH3OH to reduce the excess CO. Similarly, removing CH3OH will prompt the system to produce more of it. Such responses occur as the system aims to maintain a state of balance or equilibrium after being disturbed. This concept does not only apply to chemical concentrations but extends to changes in temperature and pressure as well, offering a comprehensive view on how equilibrium systems respond to various types of stress.

Reaction Rates

The speed at which reactions occur, or reaction rates, is another critical aspect of understanding chemical processes. A reaction rate can be affected by several factors such as temperature, concentration of reactants, surface area, and the presence of catalysts. These factors can either accelerate or decelerate the rate at which reactants turn into products.

For example, when a catalyst is added to the methanol production system, it effectively provides an alternative pathway for the reaction with a lower activation energy. However, while catalysts increase the rate at which equilibrium is reached, they do not influence the position of the equilibrium itself. The rates at which the forward and reverse reactions proceed will both be increased equally, thus preserving the balance of the system's equilibrium.

Exothermic and Endothermic Reactions

A clear grasp of the differences between exothermic and endothermic reactions is pivotal for predicting the effect of temperature changes on a system in equilibrium. In exothermic reactions, energy is released into the surrounding environment, often in the form of heat. Conversely, endothermic reactions absorb energy from their surroundings.

Relating to the methanol production example, cooling the system down triggers Le Chatelier's principle. Since the reaction is exothermic, releasing heat, cooling it will cause the equilibrium to shift towards the right to produce more heat. In contrast, if the reaction were endothermic, cooling the system would favor the reverse reaction, as the system would absorb more heat from the surroundings to compensate for the temperature reduction. Understanding the nature of the reaction is crucial to anticipate how temperature fluctuations can alter the equilibrium state of a chemical system.