### Summary

**Physical Chemistry for Engineering and Applied Sciences** is the product of over 30 years of teaching first-year Physical Chemistry as part of the Faculty of Applied Science and Engineering at the University of Toronto. Designed to be as rigorous as compatible with a first-year student’s ability to understand, the text presents detailed step-by-step derivations of the equations that permit the student to follow the underlying logic and, of equal importance, to appreciate any simplifying assumptions made or mathematical tricks employed.

In addition to the 600 exercises and end-of-chapter problems, the text is rich in worked non-trivial examples, many of which are designed to be inspiring and thought-provoking. Step-by-step derivation of all equations enables the student to smoothly follow the derivation by sight, and can be understood relatively easily by students with moderate skills and backgrounds in mathematics.

Clear and accessible, **Physical Chemistry for Engineering and Applied Sciences **includes:

- The answers to all of the 112 worked examples, 99 exercises following many of the worked examples, and 496 end-of-chapter problems
- Topics not normally seen in introductory physical chemistry textbooks (ionic reaction rates, activities and activity coefficients) or not regularly explained in much detail (electrochemistry, chemical kinetics), with an eye on industrial applications
- Special appendices that provide detailed explanations of basic integration and natural logarithms for students lacking a background in integral calculus
- An in-depth chapter on electrochemistry, in which activities and activity coefficients are used extensively, as required for accurate calculations

### Table of Contents

**THINGS YOU SHOULD KNOW BUT PROBABLY FORGOT **

Basic Definitions

SI Units

Dalton’s Atomic Theory

Stoichiometry

Equivalent Weight

Amount of Substance: the Mole

Avogadro’s Hypothesis

Conservation of Mass

Conservation of Charge

Atomic Mass Scales

**STATES OF MATTER AND THE PROPERTIES OF GASES **

The Three States of Matter

Pressure

Archimedes’ Principle

Temperature

**THE IDEAL GAS **

The Ideal Gas Equation of State

Molar Volumes

Combined Gas Equation

Dalton’s Law of Partial Pressures

Mole Fractions

Partial Volumes

**THE KINETIC THEORY OF GASES **

Postulates

Simplified Derivation of the Ideal Gas Law

The Meaning of Pressure

The Meaning of Temperature

Diffusion and Effusion

The Speeds of Gas Molecules

Effect of Pressure on Speed

Distribution of Molecular Speeds

The Maxwell-Boltzmann Distribution as an Energy Distribution

Fraction of Molecules Having *E* > *E'*

Concluding Remarks

**REAL GASES **

Real Gases

Isotherms for Real Gases

Equations of State for Real Gases

The Virial Equation

The Van der Waals Equation

Liquefaction of Gases

**THERMODYNAMICS (I) **

Thermodynamics

Definitions Used In Thermodynamics

Work

*PV*-Work

Maximum Work Obtainable from the Isothermal Expansion of an Ideal Gas

Reversible Processes

**THERMODYNAMICS (II) **

Internal Energy (*U*) and the First Law of Thermodynamics

State Functions

Work and Heat Are Not State Functions

*Q* and *W* Have Algebraic Signs

Another Look At *PV*-Work

Chemical Reaction in a Constant Volume System

The Heat Capacity of a Single Phase System

*ΔU* for the Isothermal Expansion of an Ideal Gas

The Internal Energy of a Monatomic Ideal Gas

**THERMODYNAMICS (III) **

Enthalpy (*H*)

Constant Pressure Processes

Thermochemistry

*ΔH* for Fusion (Melting) and Freezing

*ΔH* for Vaporization and Condensation

*ΔH* for Sublimation

Ionization Enthalpies

Electron Affinities

Bond Enthalpies

**THERMODYNAMICS (IV) **

The Standard State for Chemical Reactions

Hess’s Law of Constant Heat Summation

Standard Enthalpies of Formation

Variation of *ΔH* with Temperature at Constant Pressure

**THERMODYNAMICS (V) **

Spontaneous Processes

Entropy (*S*)

*ΔS* for the Isothermal Expansion of an Ideal Gas

*ΔS* for a Constant Pressure Heating or Cooling Process

*ΔS* for a Constant Volume Heating or Cooling Process

*ΔS* for a Reversible Phase Change

Whenever a Real Process Takes Place *ΔS*_{univ} Increases

Trouton’s Rule

**THERMODYNAMICS (VI) **

Absolute Entropies and the Third Law of Thermodynamics

Dealing With Phase Transitions

Entropy Changes for Chemical Reactions

**THERMODYNAMICS (VII) **

Gibbs Free Energy (*G*)

Gibbs Free Energy Changes, "Other" Work, and Spontaneity

Evaluation of *ΔG*_{T,P}

*ΔG°* for a Chemical Reaction

Thermodynamic Stability

**CHEMICAL EQUILIBRIUM (I) **

Equilibrium Constants

The Reaction Quotient (*Q*) and Relative Activities (*a*_{i})

Formulation of Equilibrium Constants

Molar Free Energies

*ΔG*_{R} for Chemical Reactions

**CHEMICAL EQUILIBRIUM (II) **

Calculations Using Thermodynamic Equilibrium Constants

Effect of Catalyst on *K*

Effect of Temperature on *K*

Effect of Pressure on K

**PHASE EQUILIBRIUM (I) **

Phase Change and Gibbs Free Energy

Phase Diagram for a Single Pure Substance

The Phase Rule

**PHASE EQUILIBRIUM (II) **

Phase Diagram for CO_{2}

Phase Diagram for Water

The Clapeyron Equation

Phase Diagram for Carbon

Phase Diagram for Helium

The Clausius-Clapeyron Equation

**MIXTURES **

Expressions for Concentration

Partial Molar Volumes

The Chemical Potential (*μ*)

The Chemical Potential of a Component in an Ideal Gas Mixture

More About Activities

Ideal Liquid Solutions of Volatile Solutes: Raoult’s Law

Ideal Liquid Solutions of Non-Volatile Solutes

Ideal Liquid Solutions of Two Volatile Liquids

Real (Non-Ideal) Solutions

Chemical Potential and Solvent Activity

Ideal Dilute Solutions of Volatile Solutes: Henry’s Law

The Solubility of Gases

Distillation

The Lever Rule

Liquid-Liquid Phase Diagrams

Liquid-Solid Phase Diagrams

Compound Formation

**COLLIGATIVE PROPERTIES **

Colligative Properties

Vapor Pressure Depression

Boiling Point Elevation and Freezing Point Depression

Osmotic Pressure

**IONIC EQUILIBRIUM **

Ionic Equilibrium

Activities of Dissolved Species in Solution

Activities and Activity Coefficients of Electrolytes in Solution

Acids and Bases: The Brønsted–Lowry Concept

The Self-Dissociation of Water

Neutral Solutions

**ACID AND BASE DISSOCIATION **

Acid Dissociation Constants, *K*_{a}

Dissociation of a Weak Acid

Polyprotic Acid Calculation: Charge and Mass Balances

Simplified Approach

**BASES AND THEIR SALTS **

Weak Bases: *B* or *BOH*

The Salt of a Weak Acid: Hydrolysis

The Rigorous Method

The Salt of a Weak Base

Acid-Base Titrations

**BUFFER SOLUTIONS **

Buffer Solutions

Buffer of a Weak Acid and its Salt: *HA + NaA*

Rigorous Derivation: *HA/NaA* Buffer

Buffer of a Weak Base and Its Salt: *BOH + BCl*

Rigorous Expression for *BOH/BCl* Buffer

Acid-Base Indicators: *HIn*

**SOLUBILITY EQUILIBRIA **

Solubility Equilibria

Relationship Between *K*_{SP} and Solubility for Different Salt Types

Activity Effects and Solubility

The Common Ion Effect

Salting In

Selective Precipitation

**OXIDATION–REDUCTION REACTIONS **

Oxidation–Reduction (Redox) Reactions

Rules for Assignment of Oxidation Numbers

Steps for Balancing Redox Reactions

**ELECTROCHEMISTRY **

Half-Reactions, Electrodes, and Electrochemical Cells

Electrical Work

Types of Cells

Liquid Junctions and Salt Bridges

Equilibrium Voltages

The Nernst Equation

Single Electrode Potentials

Calculation of Equilibrium Cell Voltages from Half-Cell Potentials

Equilibrium Constants from Cell Voltages

Thermodynamic Functions from Cell Voltages

Concentration Cells

**CHEMICAL REACTION KINETICS **

Rates of Reactions: Chemical Kinetics

Concentration Profiles

Expression of Reaction Rates

Differential Rate Laws

First Order Reactions

Half-Lives

Second Order Reactions

Zeroth Order Reactions

Experimental Determination of *k*, *m*, and *n*

Reaction Mechanisms

The Rate-Determining Step

Reaction Rates and Equilibrium

Reaction Intermediates

Effect of Temperature

Rates of Ionic Reactions

**APPENDICES **

Properties of the Elements

Thermodynamic Data for Selected Gases and Vapors

Thermodynamic Data for Selected Liquids

Thermodynamic Data for Selected Solids

Thermodynamic Data for Selected Aqueous Ions

Analytical Solution of a Cubic Equation

The Newton-Raphson Method

Understanding Basic Integration

Understanding Logarithms, Exponentials, and the Integral of *1/x*

Standard Reduction Potentials

Answers to Exercises

Answers to Problems