The Relationship Between Kc and Kp

Oct 13, 2025 by recoveryshake.com 125 views

Equilibrium Constants: Understanding the Relationship Between Kc and Kp

In chemistry, equilibrium constants play a crucial role in understanding the behavior of chemical reactions. Two types of equilibrium constants are commonly used: Kc (concentration equilibrium constant) and Kp (partial pressure equilibrium constant). While Kc is expressed in terms of concentrations, Kp is expressed in terms of partial pressures. In this article, we will explore the relationship between Kc and Kp, and how to convert between the two.

The Relationship Between Kc and Kp

The relationship between Kc and Kp is given by the equation:

K_p = K_c(RT)^{\Delta n}

where:

$K_p$ is the partial pressure equilibrium constant
$K_c$ is the concentration equilibrium constant
$R$ is the gas constant (1.987 cal/mol·K or 8.314 J/mol·K)
$T$ is the temperature in Kelvin
$\Delta n$ is the change in the number of moles of gas in the reaction

Calculating Kp from Kc

To calculate Kp from Kc, we need to know the value of Kc, the temperature, and the gas constant. We are given the following values:

$K_c = 82$
$T = 200.0 \, K$
$R = 0.0821 \, L \cdot atm / mol \cdot K$

We can now plug these values into the equation:

K_p = K_c(RT)^{\Delta n}

Determining the Change in the Number of Moles of Gas

To determine the change in the number of moles of gas, we need to examine the balanced equation:

2 \, NO_2(g) \rightleftharpoons N_2O_4(g)

In this reaction, 2 moles of NO2 are converted to 1 mole of N2O4. Therefore, the change in the number of moles of gas is:

\Delta n = 1 - 2 = -1

Calculating Kp

Now that we have the value of $\Delta n$ , we can calculate Kp:

K_p = K_c(RT)^{\Delta n}

K_p = 82(0.0821 \cdot 200.0)^{-1}

K_p = 82(16.42)^{-1}

K_p = 82 \cdot 0.0613

K_p = 5.04

In this article, we explored the relationship between Kc and Kp, and how to convert between the two. We used the equation $K_p = K_c(RT)^{\Delta n}$ to calculate Kp from Kc, and determined the change in the number of moles of gas in the reaction. We then calculated Kp using the given values of Kc, T, and R. The result is a value of Kp = 5.04.

Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
Chang, R. (2010). Chemistry: The Central Science. McGraw-Hill.
Levine, I. N. (2012). Physical chemistry. McGraw-Hill.

For a more detailed discussion of equilibrium constants, see Atkins and de Paula (2010).
For a more detailed discussion of the relationship between Kc and Kp, see Chang (2010).
For a more detailed discussion of the calculation of Kp, see Levine (2012).
Equilibrium Constants: Understanding the Relationship Between Kc and Kp - Q&A

In our previous article, we explored the relationship between Kc and Kp, and how to convert between the two. We used the equation $K_p = K_c(RT)^{\Delta n}$ to calculate Kp from Kc, and determined the change in the number of moles of gas in the reaction. In this article, we will answer some frequently asked questions about equilibrium constants and provide additional examples to help you understand the concept.

Q: What is the difference between Kc and Kp?

A: Kc is the concentration equilibrium constant, which is expressed in terms of concentrations. Kp is the partial pressure equilibrium constant, which is expressed in terms of partial pressures.

Q: How do I determine the change in the number of moles of gas in a reaction?

A: To determine the change in the number of moles of gas, you need to examine the balanced equation and count the number of moles of gas on both sides of the equation. The change in the number of moles of gas is the difference between the number of moles of gas on the product side and the number of moles of gas on the reactant side.

Q: What is the relationship between Kc and Kp?

A: The relationship between Kc and Kp is given by the equation $K_p = K_c(RT)^{\Delta n}$ , where $K_p$ is the partial pressure equilibrium constant, $K_c$ is the concentration equilibrium constant, $R$ is the gas constant, $T$ is the temperature in Kelvin, and $\Delta n$ is the change in the number of moles of gas in the reaction.

Q: How do I calculate Kp from Kc?

A: To calculate Kp from Kc, you need to know the value of Kc, the temperature, and the gas constant. You can then use the equation $K_p = K_c(RT)^{\Delta n}$ to calculate Kp.

Q: What is the significance of the gas constant (R) in the equation?

A: The gas constant (R) is a fundamental constant that relates the pressure and volume of a gas to its temperature. In the equation $K_p = K_c(RT)^{\Delta n}$ , R is used to convert the concentration equilibrium constant (Kc) to the partial pressure equilibrium constant (Kp).

Q: Can I use the equation $K_p = K_c(RT)^{\Delta n}$ to calculate Kp from Kc for any reaction?

A: No, the equation $K_p = K_c(RT)^{\Delta n}$ can only be used to calculate Kp from Kc for reactions that involve gases. If the reaction does not involve gases, you cannot use this equation to calculate Kp from Kc.

Q: What are some common mistakes to avoid when calculating Kp from Kc?

A: Some common mistakes to avoid when calculating Kp from Kc include:

Failing to determine the change in the number of moles of gas in the reaction
Using the wrong value of the gas constant (R)
Using the wrong temperature in Kelvin
Failing to convert the concentration equilibrium constant (Kc) to the partial pressure equilibrium constant (Kp)

In this article, we answered some frequently asked questions about equilibrium constants and provided additional examples to help you understand the concept. We also discussed some common mistakes to avoid when calculating Kp from Kc. By following the equation $K_p = K_c(RT)^{\Delta n}$ and avoiding common mistakes, you can accurately calculate Kp from Kc for reactions that involve gases.

Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
Chang, R. (2010). Chemistry: The Central Science. McGraw-Hill.
Levine, I. N. (2012). Physical chemistry. McGraw-Hill.

For a more detailed discussion of equilibrium constants, see Atkins and de Paula (2010).
For a more detailed discussion of the relationship between Kc and Kp, see Chang (2010).
For a more detailed discussion of the calculation of Kp, see Levine (2012).