The Equilibrium Constant

Summary

This video explains how to relate the equilibrium constant to mole fractions for a gas-phase reaction where A reacts to form 2B. It covers the derivation of Gibbs free energy change, using stoichiometric coefficients and formation energies at standard conditions. The script explores how the equilibrium constant is derived using fugacity and mole fractions, and it emphasizes the role of pressure in shifting equilibrium for gas-phase reactions. The video provides insights into how pressure changes affect the equilibrium conversion, with key takeaways on dimensionless equilibrium constants and the behavior of ideal gases.

Takeaways

• 😀 The video covers a simple gas phase reaction where A reacts to form 2B molecules in the gas phase.
• 😀 The equilibrium constant can be related to mole fractions in the reaction.
• 😀 To calculate the equilibrium constant, the Gibbs free energy change must be determined.
• 😀 Gibbs free energy of formation values are provided for 298K and standard conditions (1 bar pressure for gases).
• 😀 The formula for the Gibbs free energy change involves stoichiometric coefficients and the Gibbs free energy of formation for each component.
• 😀 The equilibrium constant is dimensionless, which allows us to take the logarithm of the Gibbs free energy expression.
• 😀 The relationship between Gibbs free energy change and the equilibrium constant can be written using fugacity ratios of the components.
• 😀 Fugacity in the mixture is given by the mole fraction times the pressure, and the standard state fugacity is set at 1 bar.
• 😀 For an ideal gas, the fugacity of a component in the mixture is its mole fraction multiplied by the pressure.
• 😀 When considering changes in pressure, increasing pressure causes the reaction to shift left, meaning the mole fraction of B decreases.
• 😀 Pressure changes can significantly affect the equilibrium conversion, especially in gas phase reactions, due to the nature of phase changes.

Q & A

What is the focus of the screencast?

The screencast focuses on understanding the relationship between the equilibrium constant and mole fractions for a simple gas-phase reaction, and how to calculate the Gibbs free energy change to determine the equilibrium constant.

What are the standard conditions for calculating Gibbs free energy in this context?

Standard conditions for calculating Gibbs free energy in this context refer to a pressure of 1 bar and a temperature of 298 K (25°C). The substance is assumed to be an ideal gas.

How is the Gibbs free energy change (ΔG) calculated for the reaction?

The Gibbs free energy change (ΔG) is calculated by summing the stoichiometric coefficients multiplied by the Gibbs free energy of formation for each component at standard conditions (298 K, 1 bar).

What role does the equilibrium constant play in this reaction?

The equilibrium constant relates the Gibbs free energy change to the mole fractions of the reactants and products at equilibrium. It is dimensionless, which allows us to take its logarithm.

Why is the equilibrium constant considered dimensionless?

The equilibrium constant is dimensionless because it represents a ratio of fugacities, and fugacities are expressed in terms of pressure, making them dimensionless when normalized by the standard state pressure (1 bar).

What is fugacity, and how is it used in the calculation of the equilibrium constant?

Fugacity is a measure of the effective pressure exerted by a component in a mixture. It is used in the calculation of the equilibrium constant to express the ratio of the fugacity of each component in the mixture to that of the pure component at standard conditions.

How does pressure affect the equilibrium of a gas-phase reaction?

Pressure influences the equilibrium of a gas-phase reaction by shifting the reaction in the direction that compensates for the change in pressure. Increasing the pressure typically shifts the equilibrium towards the side with fewer moles of gas, which in this case means the reaction shifts to the left.

What happens to the mole fraction of B when the pressure is increased?

When the pressure is increased, the mole fraction of B decreases, which means the reaction shifts to the left, resulting in more reactant A and less product B.

What does the equation involving fugacities and mole fractions represent?

The equation involving fugacities and mole fractions represents the equilibrium constant in terms of the activities of the components, raised to their respective stoichiometric coefficients. It describes how the equilibrium concentrations are related to the physical properties of the gases in the system.

How does the reaction shift when the system is at standard conditions (1 bar, 298 K)?

At standard conditions (1 bar, 298 K), the fugacities are normalized, making it easier to calculate the equilibrium constant. The system behaves ideally, and the equilibrium constant is determined by the ratio of fugacities or mole fractions, allowing for a predictable behavior based on pressure and temperature changes.