Question

The reaction to prepare methanol from carbon monoxide and hydrogen $$\mathrm{CO}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{3} \mathrm{OH}(g)$$ is exothermic. If you wanted to use this reaction to produce methanol commercially, would high or low temperatures favor a maximum yield? Explain.

Short answer

A low temperature would favor a maximum yield of methanol in this exothermic reaction, as it would shift the equilibrium towards the products according to Le Chatelier's principle. This is because lowering the temperature causes the reaction to produce more heat, favoring the formation of methanol.

Step-by-step solution

Identify the type of reaction and write the equilibrium expression

The given reaction is: \[ \mathrm{CO}(g)+\mathrm{H}_{2}(g) \leftrightharpoons \mathrm{CH}_{3}\mathrm{OH}(g) \] This reaction is exothermic, which means it releases heat energy. The equilibrium constant expression for this reaction would be: \[ K_c = \frac{[\mathrm{CH}_3\mathrm{OH}]}{[\mathrm{CO}][\mathrm{H}_2]} \]

Apply Le Chatelier's principle

According to Le Chatelier's principle, if we increase the temperature of an exothermic reaction, the reaction will shift towards the reactants to oppose the change (i.e., consume the added heat by moving towards the endothermic direction). On the other hand, if we decrease the temperature, the reaction shifts towards the products to counteract the change (i.e., produce more heat by moving towards the exothermic direction).

Determine the effect of temperature on yield

Since we want to maximize the yield of methanol (\(\mathrm{CH}_{3}\mathrm{OH}\)), we need the reaction to favor the formation of products. Based on Le Chatelier's principle, lowering the temperature would favor the formation of methanol, as the reaction would shift towards the products to produce more heat in response to the decrease in temperature. Therefore, a low temperature would favor a maximum yield of methanol in this exothermic reaction.

Key concepts

Le Chatelier's Principle

Le Chatelier's Principle is a fundamental concept in chemistry that helps us understand how a reaction at equilibrium responds to changes in conditions. When you change the temperature, pressure, or concentration in a chemical reaction, the system will adjust to counteract that change and re-establish equilibrium.

For example, if the concentration of reactants is increased, the equilibrium will shift to the right, favoring the formation of products. Similarly, if the temperature in an exothermic reaction is increased, the equilibrium will shift to the left, favoring reactants.

• Increase in concentration of reactants: shifts to products
• Increase in temperature for exothermic reactions: shifts to reactants
• Decrease in temperature for exothermic reactions: shifts to products

Understanding this principle helps in designing chemical processes to maximize yield and efficiency.

Exothermic Reaction

An exothermic reaction is one that releases energy to the surroundings, usually in the form of heat. In the given reaction between carbon monoxide and hydrogen to form methanol, heat is released, indicating it is exothermic.

It’s helpful to remember that exothermic reactions cool their surroundings as they lose energy. Industrially, this type of reaction can be influenced by temperature changes based on Le Chatelier’s Principle. Lowering the temperature can typically drive the reaction forward, producing more product as the system tries to generate more heat to balance the loss.

• Releases heat
• Favored by low temperature
• Shifts equilibrium to the right when temperature is decreased

Equilibrium Constant

The equilibrium constant, denoted as \(K_c\), is a crucial factor that indicates the ratio of concentrations of products to reactants at equilibrium. It's specific to a particular reaction at a given temperature.

For the methanol synthesis reaction, the expression for \(K_c\) is: \[ K_c = \frac{[\mathrm{CH}_3\mathrm{OH}]}{[\mathrm{CO}][\mathrm{H}_2]} \]

A larger value of \(K_c\) suggests that the reaction favors products at equilibrium, while a smaller \(K_c\) indicates a preference for reactants. Understanding \(K_c\) helps in predicting how the reaction will adjust to changes in conditions, especially when employing Le Chatelier’s principle.

Reaction Yield

Reaction yield refers to the quantity of product formed in a chemical reaction. In industrial processes, maximizing yield is essential for economic efficiency.

For the exothermic reaction of methanol production, the yield can be maximized by lowering the temperature, as suggested by Le Chatelier’s Principle. This shifts the equilibrium towards the product side, increasing methanol formation.

• High yield favored by low temperatures in exothermic processes
• Increased pressure may also enhance yield by shifting equilibrium

By optimizing these conditions, industries can achieve higher production rates and better resource utilization.