Consider The Following Equation In Chemical Equilibrium:$\[ C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ KJ} \\]What Happens To The Amount Of Ethane \[$(C_2H_6)\$\] When The Temperature Of The System Is Increased?A. The

Feb 27, 2025 by ADMIN 233 views

Understanding Chemical Equilibrium: A Case Study of Ethane Formation

Chemical equilibrium is a fundamental concept in chemistry that describes the balance between the forward and reverse reactions of a chemical process. In this article, we will explore the concept of chemical equilibrium using the equation: $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ . This equation represents the formation of ethane ( $C_2H_6$ ) from ethylene ( $C_2H_4$ ) and hydrogen gas ( $H_2$ ). We will examine the effect of temperature on the amount of ethane produced in this reaction.

Chemical Equilibrium: A Balance of Forward and Reverse Reactions

Chemical equilibrium is a state where the rates of the forward and reverse reactions are equal. This means that the concentrations of the reactants and products remain constant over time. The equilibrium constant ( $K$ ) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants. For the equation $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ , the equilibrium constant is given by:

K = \frac{[C_2H_6]}{[C_2H_4][H_2]}

where $[C_2H_6]$ , $[C_2H_4]$ , and $[H_2]$ are the concentrations of ethane, ethylene, and hydrogen gas, respectively.

The Effect of Temperature on Chemical Equilibrium

The temperature of a system can affect the equilibrium constant ( $K$ ) of a chemical reaction. According to Le Chatelier's principle, when the temperature of a system is increased, the equilibrium shifts in the direction that absorbs heat. In the case of the equation $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ , the forward reaction is endothermic, meaning that it absorbs heat. Therefore, when the temperature of the system is increased, the equilibrium will shift in the forward direction, favoring the formation of ethane ( $C_2H_6$ ).

Calculating the Effect of Temperature on the Amount of Ethane

To calculate the effect of temperature on the amount of ethane produced, we can use the van 't Hoff equation:

\ln\left(\frac{K_2}{K_1}\right) = \frac{\Delta H}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

where $K_1$ and $K_2$ are the equilibrium constants at temperatures $T_1$ and $T_2$ , respectively, $\Delta H$ is the enthalpy change of the reaction, and $R$ is the gas constant.

For the equation $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ , the enthalpy change ( $\Delta H$ ) is 137 kJ/mol. Assuming that the equilibrium constant ( $K$ ) is 1 at a temperature of 298 K, we can calculate the equilibrium constant at a temperature of 373 K (100°C) using the van 't Hoff equation:

\ln\left(\frac{K_2}{1}\right) = \frac{137 \text{ kJ/mol}}{8.314 \text{ J/mol K}}\left(\frac{1}{298 \text{ K}} - \frac{1}{373 \text{ K}}\right)

Solving for $K_2$ , we get:

K_2 = 1.35

This means that at a temperature of 373 K (100°C), the equilibrium constant ( $K$ ) is 1.35, indicating that the reaction favors the formation of ethane ( $C_2H_6$ ).

In conclusion, the amount of ethane ( $C_2H_6$ ) produced in the reaction $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ increases with an increase in temperature. This is because the forward reaction is endothermic, and the equilibrium shifts in the forward direction when the temperature is increased. The van 't Hoff equation can be used to calculate the effect of temperature on the equilibrium constant ( $K$ ) of a chemical reaction.

Atkins, P. W., & de Paula, J. (2010). Physical chemistry (9th ed.). Oxford University Press.
Chang, R. (2010). Chemistry: The central science (11th ed.). McGraw-Hill.
Levine, I. N. (2012). Physical chemistry (6th ed.). McGraw-Hill.

For a more detailed discussion of chemical equilibrium, see Atkins and de Paula (2010).
For a more detailed discussion of the van 't Hoff equation, see Chang (2010).
For a more detailed discussion of the effect of temperature on chemical equilibrium, see Levine (2012).
Q&A: Understanding Chemical Equilibrium and the Effect of Temperature

Chemical equilibrium is a fundamental concept in chemistry that describes the balance between the forward and reverse reactions of a chemical process. In our previous article, we explored the concept of chemical equilibrium using the equation: $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ . We examined the effect of temperature on the amount of ethane ( $C_2H_6$ ) produced in this reaction. In this article, we will answer some frequently asked questions about chemical equilibrium and the effect of temperature.

Q: What is chemical equilibrium?

A: Chemical equilibrium is a state where the rates of the forward and reverse reactions are equal. This means that the concentrations of the reactants and products remain constant over time.

Q: What is the equilibrium constant ( $K$ )?

A: The equilibrium constant ( $K$ ) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants. For the equation $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ , the equilibrium constant ( $K$ ) is given by:

K = \frac{[C_2H_6]}{[C_2H_4][H_2]}

Q: How does temperature affect chemical equilibrium?

A: According to Le Chatelier's principle, when the temperature of a system is increased, the equilibrium shifts in the direction that absorbs heat. In the case of the equation $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ , the forward reaction is endothermic, meaning that it absorbs heat. Therefore, when the temperature of the system is increased, the equilibrium will shift in the forward direction, favoring the formation of ethane ( $C_2H_6$ ).

Q: Can you give an example of how to calculate the effect of temperature on the equilibrium constant ( $K$ )?

A: Yes, we can use the van 't Hoff equation to calculate the effect of temperature on the equilibrium constant ( $K$ ). For the equation $C_2H_4(g) + H_2(g) \Leftrightarrow C_2H_6(g) + 137 \text{ kJ}$ , the enthalpy change ( $\Delta H$ ) is 137 kJ/mol. Assuming that the equilibrium constant ( $K$ ) is 1 at a temperature of 298 K, we can calculate the equilibrium constant at a temperature of 373 K (100°C) using the van 't Hoff equation:

\ln\left(\frac{K_2}{1}\right) = \frac{137 \text{ kJ/mol}}{8.314 \text{ J/mol K}}\left(\frac{1}{298 \text{ K}} - \frac{1}{373 \text{ K}}\right)

Solving for $K_2$ , we get:

K_2 = 1.35

This means that at a temperature of 373 K (100°C), the equilibrium constant ( $K$ ) is 1.35, indicating that the reaction favors the formation of ethane ( $C_2H_6$ ).

Q: What are some common applications of chemical equilibrium?

A: Chemical equilibrium has many practical applications in fields such as chemistry, biology, and engineering. Some examples include:

Catalysis: Chemical equilibrium is used to design catalysts that can speed up chemical reactions.
Biotechnology: Chemical equilibrium is used to understand the behavior of enzymes and other biomolecules.
Environmental science: Chemical equilibrium is used to understand the behavior of pollutants in the environment.
Materials science: Chemical equilibrium is used to design new materials with specific properties.

Q: What are some common mistakes to avoid when working with chemical equilibrium?

A: Some common mistakes to avoid when working with chemical equilibrium include:

Not considering the temperature dependence of the equilibrium constant ( $K$ ): Temperature can have a significant effect on the equilibrium constant ( $K$ ), so it's essential to consider this when designing experiments or modeling chemical reactions.
Not accounting for the presence of catalysts: Catalysts can significantly affect the equilibrium constant ( $K$ ), so it's essential to account for their presence when designing experiments or modeling chemical reactions.
Not considering the effects of pressure: Pressure can also have a significant effect on the equilibrium constant ( $K$ ), so it's essential to consider this when designing experiments or modeling chemical reactions.

In conclusion, chemical equilibrium is a fundamental concept in chemistry that describes the balance between the forward and reverse reactions of a chemical process. The equilibrium constant ( $K$ ) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants. Temperature can have a significant effect on the equilibrium constant ( $K$ ), and it's essential to consider this when designing experiments or modeling chemical reactions. By understanding chemical equilibrium, we can design new materials, understand the behavior of biomolecules, and develop new technologies.