At $ 100^{\circ} C\$} , { K_c = 0.078$}$ For The Reaction ${ SO_2Cl_2(g) \rightleftharpoons SO_2(g) + Cl_2(g) }$In An Equilibrium Mixture Of The Three Gases, The Concentrations Of { SO_2Cl_2$ $ And

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Introduction

In chemistry, the equilibrium constant expression is a mathematical representation of the equilibrium between reactants and products in a chemical reaction. It is denoted by the symbol Kc and is used to determine the concentrations of reactants and products at equilibrium. In this article, we will explore the concept of equilibrium constant expression and concentration calculations using the given reaction: SO2Cl2(g) ⇌ SO2(g) + Cl2(g).

Understanding the Equilibrium Constant Expression

The equilibrium constant expression for the given reaction is:

Kc = [SO2] [Cl2] / [SO2Cl2]

where [SO2], [Cl2], and [SO2Cl2] are the concentrations of SO2, Cl2, and SO2Cl2, respectively.

Given Values

We are given the following values:

  • Temperature (T) = 100°C
  • Equilibrium constant (Kc) = 0.078

Step 1: Convert Temperature to Kelvin

To use the given values in the equilibrium constant expression, we need to convert the temperature from Celsius to Kelvin.

T (K) = T (°C) + 273.15 = 100 + 273.15 = 373.15 K

Step 2: Write the Equilibrium Constant Expression

Now that we have the temperature in Kelvin, we can write the equilibrium constant expression:

Kc = [SO2] [Cl2] / [SO2Cl2]

Step 3: Determine the Concentration of SO2Cl2

Let's assume that the initial concentration of SO2Cl2 is x M. At equilibrium, the concentration of SO2Cl2 will be (x - y) M, where y is the amount of SO2Cl2 that has dissociated into SO2 and Cl2.

Step 4: Determine the Concentration of SO2 and Cl2

The concentration of SO2 will be y M, and the concentration of Cl2 will also be y M.

Step 5: Substitute the Concentrations into the Equilibrium Constant Expression

Now that we have the concentrations of SO2, Cl2, and SO2Cl2, we can substitute them into the equilibrium constant expression:

Kc = (y) (y) / (x - y)

Step 6: Simplify the Expression

We can simplify the expression by canceling out the y terms:

Kc = y^2 / (x - y)

Step 7: Substitute the Given Value of Kc

We are given the value of Kc as 0.078. We can substitute this value into the expression:

0.078 = y^2 / (x - y)

Step 8: Solve for y

To solve for y, we can rearrange the equation:

y^2 = 0.078 (x - y)

y^2 = 0.078x - 0.078y

y^2 + 0.078y = 0.078x

y (y + 0.078) = 0.078x

y = 0.078x / (y + 0.078)

Step 9: Solve for x

To solve for x, we can substitute the value of y into the equation:

x = y / (0.078 - y)

Step 10: Calculate the Concentration of SO2Cl2

Now that we have the value of x, we can calculate the concentration of SO2Cl2:

[SO2Cl2] = x M

Conclusion

In this article, we have explored the concept of equilibrium constant expression and concentration calculations using the given reaction: SO2Cl2(g) ⇌ SO2(g) + Cl2(g). We have used the given values of temperature and equilibrium constant to determine the concentrations of SO2, Cl2, and SO2Cl2. The final answer is the concentration of SO2Cl2, which is x M.

References

  • Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Chemistry. McGraw-Hill.

Appendix

The following is a list of equations and formulas used in this article:

  • Kc = [SO2] [Cl2] / [SO2Cl2]
  • T (K) = T (°C) + 273.15
  • y^2 = 0.078 (x - y)
  • y^2 + 0.078y = 0.078x
  • y (y + 0.078) = 0.078x
  • y = 0.078x / (y + 0.078)
  • x = y / (0.078 - y)
  • [SO2Cl2] = x M
    Equilibrium Constant Expression and Concentration Calculations: A Q&A Guide ====================================================================

Introduction

In our previous article, we explored the concept of equilibrium constant expression and concentration calculations using the given reaction: SO2Cl2(g) ⇌ SO2(g) + Cl2(g). In this article, we will answer some frequently asked questions related to equilibrium constant expression and concentration calculations.

Q: What is the equilibrium constant expression?

A: The equilibrium constant expression is a mathematical representation of the equilibrium between reactants and products in a chemical reaction. It is denoted by the symbol Kc and is used to determine the concentrations of reactants and products at equilibrium.

Q: How do I calculate the equilibrium constant expression?

A: To calculate the equilibrium constant expression, you need to know the concentrations of the reactants and products at equilibrium. You can use the following formula:

Kc = [SO2] [Cl2] / [SO2Cl2]

where [SO2], [Cl2], and [SO2Cl2] are the concentrations of SO2, Cl2, and SO2Cl2, respectively.

Q: What is the significance of the equilibrium constant expression?

A: The equilibrium constant expression is significant because it allows us to predict the concentrations of reactants and products at equilibrium. It also helps us to understand the direction of the reaction and the extent to which it occurs.

Q: How do I determine the concentration of a reactant or product?

A: To determine the concentration of a reactant or product, you need to know the initial concentration of the reactant or product and the amount of it that has reacted or formed. You can use the following formula:

[Reactant or Product] = Initial Concentration - Amount Reacted or Formed

Q: What is the difference between Kc and Kp?

A: Kc and Kp are two different types of equilibrium constants. Kc is the equilibrium constant expression in terms of concentrations, while Kp is the equilibrium constant expression in terms of partial pressures.

Q: How do I convert between Kc and Kp?

A: To convert between Kc and Kp, you need to know the temperature and the gas constant (R). You can use the following formula:

Kp = Kc (RT)^Δn

where Δn is the change in the number of moles of gas.

Q: What is the significance of the equilibrium constant expression in real-world applications?

A: The equilibrium constant expression is significant in real-world applications because it allows us to predict the concentrations of reactants and products at equilibrium. This is important in many fields, such as chemistry, biology, and engineering.

Q: How do I use the equilibrium constant expression in problem-solving?

A: To use the equilibrium constant expression in problem-solving, you need to follow these steps:

  1. Write the equilibrium constant expression for the reaction.
  2. Determine the concentrations of the reactants and products at equilibrium.
  3. Substitute the concentrations into the equilibrium constant expression.
  4. Solve for the equilibrium constant.

Conclusion

In this article, we have answered some frequently asked questions related to equilibrium constant expression and concentration calculations. We hope that this article has been helpful in understanding the concept of equilibrium constant expression and concentration calculations.

References

  • Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
  • Chang, R. (2010). Chemistry. McGraw-Hill.

Appendix

The following is a list of equations and formulas used in this article:

  • Kc = [SO2] [Cl2] / [SO2Cl2]
  • Kp = Kc (RT)^Δn
  • [Reactant or Product] = Initial Concentration - Amount Reacted or Formed
  • Δn = Number of moles of gas reacted or formed

Glossary

The following is a list of terms used in this article:

  • Equilibrium constant expression: A mathematical representation of the equilibrium between reactants and products in a chemical reaction.
  • Kc: The equilibrium constant expression in terms of concentrations.
  • Kp: The equilibrium constant expression in terms of partial pressures.
  • Δn: The change in the number of moles of gas.
  • RT: The product of the gas constant (R) and the temperature (T).