Book cover for Thermodynamics: An Engineering Approach

Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

ISBN #9781259822674

9th Edition

2,694 Questions

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Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This chapter focused on the principles of chemical and phase equilibrium, emphasizing that equilibrium is achieved when the Gibbs free energy of a system is minimized (dG=0). It detailed the derivation of the equilibrium constant (KP) for ideal gases, the criteria for phase equilibrium in both single- and multicomponent systems, and the application of the Gibbs phase rule. Additionally, it covered the roles of Henry's and Raoult's laws in determining the solubility of gases in liquids and solids, highlighting the practical importance of these concepts in chemical reactors, combustion systems, and refrigeration cycles.

Learning Objectives

1

Understand the conditions for chemical equilibrium based on the minimization of Gibbs free energy (dG=0).

2

Explain how the equilibrium constant (KP) for ideal-gas mixtures is derived from the standard-state Gibbs function change and its temperature dependence.

3

Describe phase equilibrium in multiphase systems, including the equality of specific Gibbs functions and the application of the Gibbs phase rule.

4

Differentiate between solubility laws (Henry’s law for dilute solutions and Raoult’s law for highly soluble substances) and their relevance in equilibrium systems.

5

Apply equilibrium concepts to predict the compositions in chemical reactors, combustion systems, and refrigeration cycles.

Key Concepts

CONCEPT

DEFINITION

Chemical Equilibrium

The state in which the Gibbs free energy of a reacting system is minimized (dG=0), indicating no net change in the composition of the system over time.

Gibbs Function (G)

A thermodynamic potential that is minimized at equilibrium under constant temperature and pressure conditions.

Equilibrium Constant (KP)

An expression that relates the partial pressures (or concentrations) of reactants and products at equilibrium; for ideal gases, it depends solely on temperature as dictated by the standard-state Gibbs free energy change.

Phase Equilibrium

The condition in a multiphase system where the specific Gibbs free energies of all phases are equal, resulting in no net transfer of matter between phases.

Gibbs Phase Rule

A rule that quantifies the number of degrees of freedom (intensive variables that can be independently varied) in a multicomponent, multiphase system, usually expressed as F = C − P + 2, where F is the degrees of freedom, C is the number of components, and P is the number of phases.

Henry’s Law

A law stating that the solubility of a gas in a liquid is directly proportional to its partial pressure, applicable for dilute solutions.

Raoult’s Law

A law used to describe the vapor pressure of a component in a solution, particularly when the substance is highly soluble, indicating that the partial vapor pressure is proportional to the mole fraction of the component.

Example Problems

Example 1

Why is the criterion for chemical equilibrium expressed in terms of the Gibbs function instead of entropy?

Example 2

Write three different $K_{P}$ relations for reacting idealgas mixtures, and state when each relation should be used.

Example 3

Is a wooden table in chemical equilibrium with the air?

Example 4

A reaction chamber contains a mixture of $\mathrm{CO}_{2}, \mathrm{CO},$ and $\mathrm{O}_{2}$ in equilibrium at a specified temperature and pressure. How will ( $a$ ) increasing the temperature at constant pressure and $(b)$ increasing the pressure at constant temperature affect the number of moles of $\mathrm{CO}_{2}$ ?

Example 5

A reaction chamber contains a mixture of $\mathrm{N}_{2}$ and $\mathrm{N}$ in equilibrium at a specified temperature and pressure. How will ( $a$ ) increasing the temperature at constant pressure and (b) increasing the pressure at constant temperature affect the number of moles of $\mathrm{N}_{2} ?$
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Step-by-Step Explanations

QUESTION

How is the equilibrium constant, KP, for an ideal-gas reaction derived based on Gibbs free energy minimization?

STEP-BY-STEP ANSWER:

Step 1: Recognize that at equilibrium, the system's Gibbs free energy is minimized (dG=0).
Step 2: Express the change in Gibbs free energy in terms of the standard-state Gibbs function change and the partial pressures of reactants and products.
Step 3: Rearrange the resulting expression to isolate the ratio of the partial pressures of products to reactants.
Step 4: Conclude that KP depends solely on temperature, as the standard-state Gibbs free energy change is a function of temperature for ideal gases.
Final Answer: KP is derived by setting dG to zero and relating the partial pressures through the standard-state Gibbs free energy change, yielding a temperature-dependent equilibrium constant expression.

Calculation of KP for Ideal-Gas Mixtures

QUESTION

How does the Gibbs phase rule determine the degrees of freedom in a multiphase, multicomponent system?

STEP-BY-STEP ANSWER:

Step 1: Identify the number of components (C) and the number of phases (P) present in the system.
Step 2: Apply the Gibbs phase rule formula: F = C − P + 2, where F represents the degrees of freedom.
Step 3: Understand that the degrees of freedom represent the number of intensive properties (e.g., temperature, pressure, and composition) that can be independently varied without disturbing equilibrium.
Final Answer: The Gibbs phase rule indicates that in a system with C components and P phases, F = C − P + 2 intensive variables can be independently controlled.

Application of the Gibbs Phase Rule

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Common Mistakes

  • Confusing the minimization of the Gibbs free energy (dG=0) with other thermodynamic conditions, leading to incorrect identification of equilibrium states.
  • Mixing up chemical equilibrium with phase equilibrium, especially in multiphase systems where different criteria apply.
  • Overlooking the dependence of KP solely on temperature for ideal gases and assuming other factors play a role.
  • Incorrectly applying Henry's law or Raoult's law without considering the conditions (dilute vs. highly soluble systems) required for each law.