Partial Pressures at Equilibrium

Oct 13, 2025 by talynt.org 65 views

Introduction

In chemistry, understanding the equilibrium constant ( $K_p$ ) is crucial for predicting the behavior of chemical reactions. The equilibrium constant is a measure of the ratio of the concentrations of the products to the reactants at equilibrium. In this article, we will explore how to calculate $K_p$ for a given reaction using the partial pressures of the reactants and products.

The Reaction

The reaction we will be focusing on is:

2 \, \text{NO}(g) + \text{Cl}_2(g) \rightleftharpoons 2 \, \text{NOCl}(g)

This reaction involves the formation of nitrosyl chloride (NOCl) from nitrogen monoxide (NO) and chlorine gas (Cl $_2$ ).

Calculating $K_p$

To calculate $K_p$ , we need to know the partial pressures of the reactants and products at equilibrium. The partial pressure of a gas is the pressure it would exert if it were the only gas present in the container.

In this case, we are given the initial partial pressure of NOCl as 3.60 atm and the partial pressure of NOCl at equilibrium as 0.160 atm. We can use this information to calculate the partial pressures of the reactants and products at equilibrium.

Partial Pressures at Equilibrium

Let's start by calculating the partial pressures of the reactants and products at equilibrium.

The partial pressure of NOCl at equilibrium is given as 0.160 atm. Since the reaction involves the formation of 2 moles of NOCl from 2 moles of NO and 1 mole of Cl $_2$ , the partial pressures of NO and Cl $_2$ will decrease by a factor of 2.

Therefore, the partial pressure of NO at equilibrium is:

P_{\text{NO}} = \frac{P_{\text{NOCl}}}{2} = \frac{0.160 \, \text{atm}}{2} = 0.080 \, \text{atm}

Similarly, the partial pressure of Cl $_2$ at equilibrium is:

P_{\text{Cl}_2} = \frac{P_{\text{NOCl}}}{2} = \frac{0.160 \, \text{atm}}{2} = 0.080 \, \text{atm}

Calculating $K_p$

Now that we have the partial pressures of the reactants and products at equilibrium, we can calculate $K_p$ using the following equation:

K_p = \frac{P_{\text{NOCl}}^2}{P_{\text{NO}}^2 P_{\text{Cl}_2}}

Substituting the values we calculated earlier, we get:

K_p = \frac{(0.160 \, \text{atm})^2}{(0.080 \, \text{atm})^2 (0.080 \, \text{atm})}

Simplifying the expression, we get:

K_p = \frac{0.0256 \, \text{atm}^2}{0.000512 \, \text{atm}^3}

K_p = 49.8 \, \text{atm}^{-1}

Conclusion

In this article, we calculated the equilibrium constant ( $K_p$ ) for the reaction of NOCl using the partial pressures of the reactants and products at equilibrium. We found that $K_p$ is equal to 49.8 atm $^{-1}$ . This value can be used to predict the behavior of the reaction under different conditions.

Discussion

The calculation of $K_p$ is an important step in understanding the behavior of chemical reactions. By knowing the equilibrium constant, we can predict the concentrations of the reactants and products at equilibrium, which is essential for designing and optimizing chemical reactions.

In this case, the reaction of NOCl is an example of a reversible reaction, where the forward and reverse reactions occur simultaneously. The equilibrium constant ( $K_p$ ) is a measure of the ratio of the rates of the forward and reverse reactions.

The value of $K_p$ we calculated is a measure of the favorability of the reaction. A high value of $K_p$ indicates that the reaction is favorable, while a low value indicates that the reaction is unfavorable.

References

Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
Levine, I. N. (2009). Physical chemistry. McGraw-Hill.
Moore, J. W., & Stanitski, C. L. (2012). Chemistry: The Central Science. Prentice Hall.

Q: What is the significance of $K_p$ in chemistry?

A: $K_p$ is a measure of the equilibrium constant for a chemical reaction, which indicates the ratio of the concentrations of the products to the reactants at equilibrium. It is a crucial concept in chemistry, as it helps predict the behavior of chemical reactions and the concentrations of reactants and products at equilibrium.

Q: What is the difference between $K_p$ and $K_c$ ?

A: $K_p$ and $K_c$ are both equilibrium constants, but they are expressed in different units. $K_p$ is expressed in terms of partial pressures, while $K_c$ is expressed in terms of concentrations. The relationship between $K_p$ and $K_c$ is given by the equation:

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

where $R$ 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 $K_p$ for a reaction?

A: To calculate $K_p$ , you need to know the partial pressures of the reactants and products at equilibrium. You can use the following equation:

K_p = \frac{P_{\text{products}}}{P_{\text{reactants}}}

where $P_{\text{products}}$ is the partial pressure of the products and $P_{\text{reactants}}$ is the partial pressure of the reactants.

Q: What is the relationship between $K_p$ and the equilibrium constant $K_c$ ?

A: The relationship between $K_p$ and $K_c$ is given by the equation:

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

where $R$ 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 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 in a reaction, you need to count the number of moles of gas on the reactant side and the product side of the equation. The difference between these two values is the change in the number of moles of gas in the reaction.

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

A: The equilibrium constant $K_p$ is a crucial concept in many real-world applications, including:

Chemical engineering: $K_p$ is used to design and optimize chemical reactors.
Environmental science: $K_p$ is used to predict the behavior of pollutants in the environment.
Biotechnology: $K_p$ is used to design and optimize bioreactors.

Q: How do I calculate the equilibrium constant $K_p$ for a reaction involving gases?

A: To calculate the equilibrium constant $K_p$ for a reaction involving gases, you need to know the partial pressures of the reactants and products at equilibrium. You can use the following equation:

K_p = \frac{P_{\text{products}}}{P_{\text{reactants}}}

where $P_{\text{products}}$ is the partial pressure of the products and $P_{\text{reactants}}$ is the partial pressure of the reactants.

Q: What is the relationship between the equilibrium constant $K_p$ and the reaction quotient $Q_p$ ?

A: The reaction quotient $Q_p$ is a measure of the ratio of the concentrations of the products to the reactants at a given point in a reaction. The relationship between $K_p$ and $Q_p$ is given by the equation:

Q_p = \frac{P_{\text{products}}}{P_{\text{reactants}}}

where $P_{\text{products}}$ is the partial pressure of the products and $P_{\text{reactants}}$ is the partial pressure of the reactants.

Q: How do I determine the equilibrium constant $K_p$ for a reaction involving gases?

A: To determine the equilibrium constant $K_p$ for a reaction involving gases, you need to know the partial pressures of the reactants and products at equilibrium. You can use the following equation:

K_p = \frac{P_{\text{products}}}{P_{\text{reactants}}}

where $P_{\text{products}}$ is the partial pressure of the products and $P_{\text{reactants}}$ is the partial pressure of the reactants.

Q: What is the significance of the equilibrium constant $K_p$ in the context of chemical equilibrium?

A: The equilibrium constant $K_p$ is a measure of the ratio of the concentrations of the products to the reactants at equilibrium. It is a crucial concept in the context of chemical equilibrium, as it helps predict the behavior of chemical reactions and the concentrations of reactants and products at equilibrium.

Q: How do I calculate the equilibrium constant $K_p$ for a reaction involving gases using the van 't Hoff equation?

A: To calculate the equilibrium constant $K_p$ for a reaction involving gases using the van 't Hoff equation, you need to know the partial pressures of the reactants and products at equilibrium. You can use the following equation:

\ln K_p = \frac{\Delta H^{\circ}}{RT}

where $\Delta H^{\circ}$ is the standard enthalpy change, $R$ is the gas constant, and $T$ is the temperature in Kelvin.

Q: What is the relationship between the equilibrium constant $K_p$ and the standard enthalpy change $\Delta H^{\circ}$ ?

A: The relationship between the equilibrium constant $K_p$ and the standard enthalpy change $\Delta H^{\circ}$ is given by the van 't Hoff equation:

\ln K_p = \frac{\Delta H^{\circ}}{RT}

where $R$ is the gas constant and $T$ is the temperature in Kelvin.

Q: How do I determine the standard enthalpy change $\Delta H^{\circ}$ for a reaction?

A: To determine the standard enthalpy change $\Delta H^{\circ}$ for a reaction, you need to know the enthalpy change for the reaction at standard conditions. You can use the following equation:

\Delta H^{\circ} = \sum \Delta H_f^{\circ}(\text{products}) - \sum \Delta H_f^{\circ}(\text{reactants})

where $\Delta H_f^{\circ}$ is the standard enthalpy of formation.

Q: What is the significance of the standard enthalpy change $\Delta H^{\circ}$ in the context of chemical equilibrium?

A: The standard enthalpy change $\Delta H^{\circ}$ is a measure of the energy change for a reaction at standard conditions. It is a crucial concept in the context of chemical equilibrium, as it helps predict the behavior of chemical reactions and the concentrations of reactants and products at equilibrium.

Q: How do I calculate the equilibrium constant $K_p$ for a reaction involving gases using the Gibbs free energy equation?

A: To calculate the equilibrium constant $K_p$ for a reaction involving gases using the Gibbs free energy equation, you need to know the partial pressures of the reactants and products at equilibrium. You can use the following equation:

\Delta G^{\circ} = -RT \ln K_p

where $\Delta G^{\circ}$ is the standard Gibbs free energy change, $R$ is the gas constant, and $T$ is the temperature in Kelvin.

Q: What is the relationship between the equilibrium constant $K_p$ and the standard Gibbs free energy change $\Delta G^{\circ}$ ?

A: The relationship between the equilibrium constant $K_p$ and the standard Gibbs free energy change $\Delta G^{\circ}$ is given by the Gibbs free energy equation:

\Delta G^{\circ} = -RT \ln K_p

where $R$ is the gas constant and $T$ is the temperature in Kelvin.

Q: How do I determine the standard Gibbs free energy change $\Delta G^{\circ}$ for a reaction?

A: To determine the standard Gibbs free energy change $\Delta G^{\circ}$ for a reaction, you need to know the Gibbs free energy change for the reaction at standard conditions. You can use the following equation:

\Delta G^{\circ} = \sum \Delta G_f^{\circ}(\text{products}) - \sum \Delta G_f^{\circ}(\text{reactants})

where $\Delta G_f^{\circ}$ is the standard Gibbs free energy of formation.

Q: What is the significance of the standard Gibbs free energy change $\Delta G^{\circ}$ in the context of chemical equilibrium?

A: The standard Gibbs free energy change $\Delta G^{\circ}$ is a measure of the energy change for a reaction at standard conditions. It is a crucial concept in the context of chemical equilibrium, as it helps predict the behavior of chemical reactions and the concentrations of reactants and products at equilibrium.

Q: How do I calculate the equilibrium constant $K_p$ for a reaction involving gases using the Nernst equation?

A: To calculate the equilibrium constant $K_p$ for a reaction involving gases using the Nernst equation, you need to know the partial pressures of the reactants and products at equilibrium. You can use the following equation:

E = E^{\circ