Consider The Following Equilibrium:${ N_2 O_4(g) \leftrightarrow 2 NO_2(g) \quad K_{eq}=5.85 \times 10^{-3} }$Which Statement About This System Is True?□ If The Equilibrium Concentration Of { NO_2 $}$ Is [$ 1.78 \times

by ADMIN 220 views

In chemistry, equilibrium constants and concentrations play a crucial role in understanding the behavior of chemical reactions. The equilibrium constant, denoted by K, is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. In this article, we will explore the concept of equilibrium constants and concentrations, and use the given equilibrium reaction to illustrate the relationship between these two important concepts.

The Equilibrium Reaction

The given equilibrium reaction is:

N2O4(g)↔2NO2(g)Keq=5.85×10−3{ N_2 O_4(g) \leftrightarrow 2 NO_2(g) \quad K_{eq}=5.85 \times 10^{-3} }

This reaction involves the dissociation of nitrogen tetroxide (N2O4) into two molecules of nitrogen dioxide (NO2). The equilibrium constant (Keq) for this reaction is given as 5.85 × 10^−3.

Understanding Equilibrium Constants

The equilibrium constant (Keq) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. Mathematically, it can be expressed as:

Keq=[NO2]2[N2O4]{ K_{eq} = \frac{[NO_2]^2}{[N_2O_4]} }

where [NO2] and [N2O4] are the concentrations of nitrogen dioxide and nitrogen tetroxide, respectively.

Calculating Concentrations

Given the equilibrium constant (Keq) and the concentration of one of the reactants or products, we can calculate the concentration of the other reactant or product. Let's use the given equilibrium reaction to illustrate this concept.

Statement 1: If the equilibrium concentration of NO2 is 1.78 × 10^−2 M, what is the equilibrium concentration of N2O4?

To solve this problem, we can use the equilibrium constant expression:

Keq=[NO2]2[N2O4]{ K_{eq} = \frac{[NO_2]^2}{[N_2O_4]} }

Rearranging this expression to solve for [N2O4], we get:

[N2O4]=[NO2]2Keq{ [N_2O_4] = \frac{[NO_2]^2}{K_{eq}} }

Substituting the given values, we get:

[N2O4]=(1.78×10−2)25.85×10−3{ [N_2O_4] = \frac{(1.78 \times 10^{-2})^2}{5.85 \times 10^{-3}} }

Simplifying this expression, we get:

[N2O4]=5.43×10−2M{ [N_2O_4] = 5.43 \times 10^{-2} M }

Therefore, the equilibrium concentration of N2O4 is 5.43 × 10^−2 M.

Statement 2: If the equilibrium concentration of N2O4 is 1.78 × 10^−2 M, what is the equilibrium concentration of NO2?

To solve this problem, we can use the equilibrium constant expression:

Keq=[NO2]2[N2O4]{ K_{eq} = \frac{[NO_2]^2}{[N_2O_4]} }

Rearranging this expression to solve for [NO2], we get:

[NO2]=Keq×[N2O4]{ [NO_2] = \sqrt{K_{eq} \times [N_2O_4]} }

Substituting the given values, we get:

[NO2]=(5.85×10−3)×(1.78×10−2){ [NO_2] = \sqrt{(5.85 \times 10^{-3}) \times (1.78 \times 10^{-2})} }

Simplifying this expression, we get:

[NO2]=1.78×10−2M{ [NO_2] = 1.78 \times 10^{-2} M }

Therefore, the equilibrium concentration of NO2 is 1.78 × 10^−2 M.

Conclusion

In conclusion, the equilibrium constant (Keq) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. By using the equilibrium constant expression, we can calculate the concentration of one reactant or product given the concentration of the other reactant or product. In this article, we used the given equilibrium reaction to illustrate the relationship between equilibrium constants and concentrations.

Key Takeaways

  • The equilibrium constant (Keq) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.
  • By using the equilibrium constant expression, we can calculate the concentration of one reactant or product given the concentration of the other reactant or product.
  • The equilibrium constant expression can be used to solve problems involving equilibrium concentrations.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Physical chemistry for the life sciences. Cambridge University Press.
  • Levine, I. N. (2012). Physical chemistry. McGraw-Hill Education.
    Q&A: Equilibrium Constants and Concentrations =====================================================

In the previous article, we explored the concept of equilibrium constants and concentrations, and used the given equilibrium reaction to illustrate the relationship between these two important concepts. In this article, we will answer some frequently asked questions about equilibrium constants and concentrations.

Q: What is the equilibrium constant (Keq)?

A: The equilibrium constant (Keq) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. It is a numerical value that describes the extent to which a reaction proceeds.

Q: How is the equilibrium constant (Keq) calculated?

A: The equilibrium constant (Keq) is calculated using the concentrations of the reactants and products at equilibrium. The formula for calculating Keq is:

Keq=[NO2]2[N2O4]{ K_{eq} = \frac{[NO_2]^2}{[N_2O_4]} }

where [NO2] and [N2O4] are the concentrations of nitrogen dioxide and nitrogen tetroxide, respectively.

Q: What is the relationship between the equilibrium constant (Keq) and the concentrations of the reactants and products?

A: The equilibrium constant (Keq) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. A large value of Keq indicates that the reaction proceeds to the right, resulting in a high concentration of products. A small value of Keq indicates that the reaction proceeds to the left, resulting in a low concentration of products.

Q: How can the equilibrium constant (Keq) be used to solve problems involving equilibrium concentrations?

A: The equilibrium constant (Keq) can be used to solve problems involving equilibrium concentrations by rearranging the equilibrium constant expression to solve for the concentration of one reactant or product given the concentration of the other reactant or product.

Q: What is the significance of the equilibrium constant (Keq) in chemistry?

A: The equilibrium constant (Keq) is a fundamental concept in chemistry that describes the behavior of chemical reactions. It is used to predict the direction of a reaction, the extent to which a reaction proceeds, and the concentrations of the reactants and products at equilibrium.

Q: Can the equilibrium constant (Keq) be used to predict the direction of a reaction?

A: Yes, the equilibrium constant (Keq) can be used to predict the direction of a reaction. If Keq is greater than 1, the reaction proceeds to the right, resulting in a high concentration of products. If Keq is less than 1, the reaction proceeds to the left, resulting in a low concentration of products.

Q: Can the equilibrium constant (Keq) be used to calculate the concentration of one reactant or product given the concentration of the other reactant or product?

A: Yes, the equilibrium constant (Keq) can be used to calculate the concentration of one reactant or product given the concentration of the other reactant or product. By rearranging the equilibrium constant expression, we can solve for the concentration of one reactant or product given the concentration of the other reactant or product.

Q: What are some common applications of the equilibrium constant (Keq) in chemistry?

A: The equilibrium constant (Keq) has many applications in chemistry, including:

  • Predicting the direction of a reaction
  • Calculating the concentrations of reactants and products at equilibrium
  • Determining the extent to which a reaction proceeds
  • Understanding the behavior of chemical reactions

Conclusion

In conclusion, the equilibrium constant (Keq) is a fundamental concept in chemistry that describes the behavior of chemical reactions. It is used to predict the direction of a reaction, the extent to which a reaction proceeds, and the concentrations of the reactants and products at equilibrium. By understanding the equilibrium constant (Keq), we can gain a deeper understanding of chemical reactions and their behavior.

Key Takeaways

  • The equilibrium constant (Keq) is a measure of the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium.
  • The equilibrium constant (Keq) can be used to predict the direction of a reaction, the extent to which a reaction proceeds, and the concentrations of the reactants and products at equilibrium.
  • The equilibrium constant (Keq) can be used to calculate the concentration of one reactant or product given the concentration of the other reactant or product.

References

  • Atkins, P. W., & De Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Physical chemistry for the life sciences. Cambridge University Press.
  • Levine, I. N. (2012). Physical chemistry. McGraw-Hill Education.