Problem 63 - Chemistry Matter and Change

Question

Ethylene \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) reacts with hydrogen to form ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right) .\) $$ \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})+ $$ How would you regulate the temperature of this equilibrium in order to accomplish each of the following? a. increase the yield of ethane b. decrease the concentration of ethylene c. increase the amount of hydrogen in the system

Step-by-Step Solution

Answer

To regulate the temperature of this equilibrium: a. Decrease the temperature to increase the yield of ethane. b. Decrease the temperature to decrease the concentration of ethylene. c. Increase the temperature to increase the amount of hydrogen in the system.

Step 1: Identify the reaction's heat type

: First, we need to determine whether the forward reaction is endothermic or exothermic. In this case, the initial statement does not provide this information, so we will assume that the forward reaction is exothermic, which means that heat is released when ethylene reacts with hydrogen to form ethane. Reaction: C₂H₄(g) + H₂(g) → C₂H₆(g) + heat Now that we have identified the heat type of the forward reaction, we can use Le Chatelier's principle to answer each question.

Step 2: Increase the yield of ethane

: According to Le Chatelier's principle, to increase the yield of ethane (C₂H₆), we need to shift the equilibrium to the right (favoring the forward reaction). Since the forward reaction is exothermic, we should decrease the temperature to increase the yield of ethane. Answer to (a): Decrease the temperature to increase the yield of ethane.

Step 3: Decrease the concentration of ethylene

: To decrease the concentration of ethylene (C₂H₄), we again need to shift the equilibrium to the right, favoring the forward reaction. Since the forward reaction is exothermic, we will follow the same process as in (a). Answer to (b): Decrease the temperature to decrease the concentration of ethylene.

Step 4: Increase the amount of hydrogen in the system

: To increase the amount of hydrogen (H₂) in the system, we need to shift the equilibrium to the left, favoring the reverse reaction. Since the forward reaction is exothermic, for this scenario, we need to increase the temperature. Answer to (c): Increase the temperature to increase the amount of hydrogen in the system.

Key Concepts

Le Chatelier's principle

Le Chatelier's principle is an essential concept in chemistry that helps predict how a change in conditions can affect a chemical equilibrium. It states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. Consider a simple equilibrium reaction:

• A + B ⇌ C + D
• If you add more of A or B, the reaction will shift to the right to produce more C and D.
• If you add more of C or D, the reaction will shift to the left to produce more A and B.

Le Chatelier's principle applies not just to concentration changes, but also to pressure, volume, and temperature. For temperature, the effect depends on whether the reaction is exothermic or endothermic. This principle provides a way to control and optimize reactions in industrial and laboratory settings, allowing chemists to increase yields or change compositions by predicting how the equilibrium will respond to changes.

Exothermic reactions

Exothermic reactions are reactions that release heat into their surroundings. These reactions often occur because the energy released from forming the new chemical bonds is greater than the energy required to break the old bonds. In terms of Le Chatelier's principle, an exothermic reaction can be represented as:\[\text{Reactants} \rightarrow \text{Products} + \text{Heat}\]In the context of exothermic reactions, decreasing the temperature favors the formation of products (shifting the equilibrium to the right), because the system will try to compensate by producing more heat. Conversely, increasing the temperature would shift the equilibrium to the left (towards the reactants) as the system attempts to absorb the excess heat. This behavior is crucial in manipulating reactions to obtain a higher yield of desired products, such as ethane in the original exercise.

Effects of temperature on equilibrium

Temperature plays a significant role in chemical equilibria. For exothermic reactions, a temperature decrease typically shifts the equilibrium towards the formation of more products. This is because, at lower temperatures, the equilibrium "attempts" to restore the lost heat by favoring the exothermic direction, which releases heat.

• Decrease in temperature: shifts equilibrium towards products for exothermic reactions.
• Increase in temperature: shifts equilibrium towards reactants for exothermic reactions.

In the case of endothermic reactions, the reverse occurs. Increasing temperature shifts the equilibrium towards the products because the system absorbs the extra heat. For the original exercise, where forming ethane from ethylene is presumed exothermic, a decrease in temperature results in more ethane production, while an increase results in more reactants, like hydrogen. This understanding allows chemists to tailor conditions to control the concentration of specific reactants or products.