Fundamentals Of Physical Chemistry Pdf Download

An advanced-level textbook of physical chemistry for the graduate (B.Sc) and postgraduate (M.Sc) students of Indian and foreign universities. This book is a part of four volume series, entitled "A Textbook of Physical Chemistry - Volume I, II, III, IV". ║ Chapter 1: Quantum Mechanics - I ║ Chapter 2: Thermodynamics – I ║Chapter 3: Chemical Dynamics – I ║Chapter 4: Electrochemistry – I: Ion-Ion Interactions ║ Chapter 5: Quantum Mechanics - II ║ Chapter 6: Thermodynamics – II ║Chapter 7: Chemical Dynamics – II ║Chapter 8: Electrochemistry – II: Ion Transport in Solutions ║

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A TEXTBOOK OF PHYSICAL

CHEMISTRY

Volume I

Mandeep Dalal

Publisher:

Dalal Institute, Main Market, Sector 14, Rohtak, Haryana 124001, India

(info@dalalinstitute.com, +91-9802825820)

www.dalalinstitute.com

No part of this book may be reproduced in any written, electronic, recording, or photocopying without written

permission of the publisher or author. The exception would be in the case of brief quotations embodied in the

critical articles or reviews and pages where permission is specifically granted by the publisher or author.

A Textbook of Physical Chemistry – Volume 1 / Mandeep Dalal (First Edition)

First published: 2018, Paperback Identifiers: 9788193872017 (ISBN-13), 8193872010 (ISBN-10)

Disclaimer:

Although every precaution has been taken to verify the accuracy of the information contained herein, the author

and publisher assume no responsibility for any errors or omissions. No liability is assumed for damages that

may result from the use of the information contained within.

Credits:

The dedication image is a derivative work of the famous painting "Innocence" by William-Adolphe

Bouguereau, whereas the image on the front cover is a derivative work of Iain Goodyear's "Atom Tunnel".

Dedicated to my mother "Darshana Devi"

This Page is Intentionally Left Blank

PREFACE

The preface writing has always been a wonderful feeling that cannot be expressed in words as it

relates you to your audience through your work. I conceived the idea of writing a new advanced-level textbook

in physical chemistry during my Ph.D. pursuit when I saw post-graduate chemistry students who were tired in

search of the syllabus topics because of their ill-resourced university or college library. I also decided to write

the textbooks of inorganic and organic chemistry because I think that someone who wants to teach or text one

stream must have the core conceptual understanding of all the three streams of chemical science otherwise one

would not be able to connect and explain the interdisciplinary topics in a comprehensive manner.

Out of the series of three textbooks, the present book, entitled "A Textbook of Physical Chemistry –

Volume 1", is the first installment of "A Textbook of Physical Chemistry", which is a four -volume set in all.

All the students and teachers are advised to read and consult all the four volumes in a subsequent pattern for a

more efficient and thorough understanding of the subject of physical chemistry.

I also celebrate this opportunity for expressing the bottom-hearted gratitude towards the people who

supported me at all stages of my work. First of all, I would like to express my sincere gratitude to my doctoral

supervisors, Prof. S.P. Khatkar and Prof. V.B. Taxak for their continuous support and guidance from day one.

Then I would like to record appreciation to my lovely sister, Jyoti Dalal, for her unconditional love, support

and for being the guiding light when the life threw me in the darkest of corners. I am very much thankful to

my beautiful wife, Anita Sangwan, who always stands shoulder to shoulder with me in my good and bad times.

I especially want to thank my brother Sandeep Dalal for his positive criticism, encouragement, motivation and

truly selfless support. A special thanks to my dearest sister Garima Sheoran for her love, care, and all-time

encouragement. I also wish to thank my entire family, friends, and teachers for providing a loving environment

for me.

Lastly, and most importantly, I wish to thank my mother, Darshana Devi, who bore me, raised me,

supported me, taught me, and loved me.

Mandeep Dalal

This Page is Intentionally Left Blank

Table of Contents

CHAPTER 1 ................................................................................................................................................ 11

Quantum Mechanics – I ........................................................................................................................ 11

Postulates of Quantum Mechanics .................................................................................................. 11

Derivation of Schrodinger Wave Equation...................................................................................... 16

Max-Born Interpretation of Wave Functions .................................................................................. 21

The Heisenberg's Uncertainty Principle .......................................................................................... 24

Quantum Mechanical Operators and Their Commutation Relations ............................................... 29

Hermitian Operators – Elementary Ideas, Quantum Mechanical Operator for Linear Momentum,

Angular Momentum and Energy as Hermitian Operator ................................................................. 52

The Average Value of the Square of Hermitian Operators ............................................................. 62

Commuting Operators and Uncertainty Principle (x & p ; E & t ) .................................................... 63

Schrodinger Wave Equation for a Particle in One Dimensional Box .............................................. 65

Evaluation of Average Position, Average Momentum and Determination of Uncertainty in Position

and Momentum and Hence Heisenberg's Uncertainty Principle..................................................... 70

Pictorial Representation of the Wave Equation of a Particle in One Dimensional Box and Its

Influence on the Kinetic Energy of the Particle in Each Successive Quantum Level ..................... 75

Lowest Energy of the Particle ......................................................................................................... 80

Problems .......................................................................................................................................... 82

Bibliography .................................................................................................................................... 83

CHAPTER 2 ................................................................................................................................................ 84

Thermodynamics – I .............................................................................................................................. 84

Brief Resume of First and Second Law of Thermodynamics .......................................................... 84

Entropy Changes in Reversible and Irreversible Processes ............................................................. 87

Variation of Entropy with Temperature, Pressure and Volume ...................................................... 92

Entropy Concept as a Measure of Unavailable Energy and Criteria for the Spontaneity of Reaction

...........................................................................................................................................................94

Free Energy, Enthalpy Functions and Their Significance, Criteria for Spontaneity of a Process ... 98

Partial Molar Quantities (Free Energy, Volume, Heat Concept) ................................................... 104

Gibb's-Duhem Equation ................................................................................................................ 108

Problems ........................................................................................................................................ 111

Bibliography .................................................................................................................................. 112

CHAPTER 3 .............................................................................................................................................. 113

Chemical Dynamics – I ........................................................................................................................ 113

Effect of Temperature on Reaction Rates ...................................................................................... 113

Rate Law for Opposing Reactions of Ist Order and IInd Order..................................................... 119

Rate Law for Consecutive & Parallel Reactions of Ist Order Reactions ....................................... 127

Collision Theory of Reaction Rates and Its Limitations ............................................................... 135

Steric Factor ................................................................................................................................... 141

Activated Complex Theory ........................................................................................................... 143

Ionic Reactions: Single and Double Sphere Models ..................................................................... 147

Influence of Solvent and Ionic Strength ........................................................................................ 152

The Comparison of Collision and Activated Complex Theory ..................................................... 157

Problems ........................................................................................................................................ 158

Bibliography .................................................................................................................................. 159

CHAPTER 4 .............................................................................................................................................. 160

Electrochemistry – I: Ion-Ion Interactions ..................................................................................... 160

The Debye-Huckel Theory of Ion-Ion Interactions ....................................................................... 160

Potential and Excess Charge Density as a Function of Distance from the Central Ion ................. 168

Debye-Huckel Reciprocal Length ................................................................................................. 173

Ionic Cloud and Its Contribution to the Total Potential ................................................................ 176

Debye-Huckel Limiting Law of Activity Coefficients and Its Limitations ................................... 178

Ion-Size Effect on Potential ........................................................................................................... 185

Ion-Size Parameter and the Theoretical Mean - Activity Coefficient in the Case of Ionic Clouds with

Finite-Sized Ions ............................................................................................................................ 187

Debye-Huckel-Onsager Treatment for Aqueous Solutions and Its Limitations ............................ 190

Debye-Huckel-Onsager Theory for Non-Aqueous Solutions ........................................................ 195

The Solvent Effect on the Mobility at Infinite Dilution ................................................................ 196

Equivalent Conductivity (Λ) vs Concentration C 1/2 as a Function of the Solvent ......................... 198

Effect of Ion Association Upon Conductivity (Debye-Huckel-Bjerrum Equation) ...................... 200

Problems ........................................................................................................................................ 209

Bibliography .................................................................................................................................. 210

CHAPTER 5 .............................................................................................................................................. 211

Quantum Mechanics – II .................................................................................................................... 211

Schrodinger Wave Equation for a Particle in a Three Dimensional Box ...................................... 211

The Concept of Degeneracy Among Energy Levels for a Particle in Three Dimensional Box .... 215

Schrodinger Wave Equation for a Linear Harmonic Oscillator & Its Solution by Polynomial Method

.........................................................................................................................................................217

Zero Point Energy of a Particle Possessing Harmonic Motion and Its Consequence ................... 229

Schrodinger Wave Equation for Three Dimensional Rigid Rotator .............................................. 231

Energy of Rigid Rotator ................................................................................................................ 241

Space Quantization ........................................................................................................................ 243

Schrodinger Wave Equation for Hydrogen Atom: Separation of Variable in Polar Spherical

Coordinates and Its Solution ......................................................................................................... 247

Principal, Azimuthal and Magnetic Quantum Numbers and the Magnitude of Their Values ....... 268

Probability Distribution Function .................................................................................................. 276

Radial Distribution Function ......................................................................................................... 278

Shape of Atomic Orbitals (s , p & d) .............................................................................................. 281

Problems ........................................................................................................................................ 287

Bibliography .................................................................................................................................. 288

CHAPTER 6 .............................................................................................................................................. 289

Thermodynamics – II ........................................................................................................................... 289

Clausius-Clapeyron Equation ........................................................................................................ 289

Law of Mass Action and Its Thermodynamic Derivation ............................................................. 293

Third Law of Thermodynamics (Nernst Heat Theorem, Determination of Absolute Entropy,

Unattainability of Absolute Zero) And Its Limitation ................................................................... 296

Phase Diagram for Two Completely Miscible Components Systems ........................................... 304

Eutectic Systems (Calculation of Eutectic Point) .......................................................................... 311

Systems Forming Solid Compounds Ax By with Congruent and Incongruent Melting Points ....... 321

Phase Diagram and Thermodynamic Treatment of Solid Solutions.............................................. 332

Problems ........................................................................................................................................ 342

Bibliography .................................................................................................................................. 343

CHAPTER 7 .............................................................................................................................................. 344

Chemical Dynamics – II ...................................................................................................................... 344

Chain Reactions: Hydrogen-Bromine Reaction, Pyrolysis of Acetaldehyde, Decomposition of

Ethane ............................................................................................................................................ 344

Photochemical Reactions (Hydrogen-Bromine & Hydrogen-Chlorine Reactions) ....................... 352

General Treatment of Chain Reactions (Ortho-Para Hydrogen Conversion and Hydrogen-Bromine

Reactions) ....................................................................................................................................... 358

Apparent Activation Energy of Chain Reactions .......................................................................... 362

Chain Length ................................................................................................................................. 364

Rice-Herzfeld Mechanism of Organic Molecules Decomposition (Acetaldehyde) ...................... 366

Branching Chain Reactions and Explosions (H2 -O2 Reaction) ..................................................... 368

Kinetics of (One Intermediate) Enzymatic Reaction: Michaelis-Menten Treatment .................... 371

Evaluation of Michaelis's Constant for Enzyme-Substrate Binding by Lineweaver-Burk Plot and

Eadie-Hofstee Methods ................................................................................................................. 375

Competitive and Non-Competitive Inhibition ............................................................................... 378

Problems ........................................................................................................................................ 388

Bibliography .................................................................................................................................. 389

CHAPTER 8 .............................................................................................................................................. 390

Electrochemistry – II: Ion Transport in Solutions ....................................................................... 390

Ionic Movement Under the Influence of an Electric Field ............................................................ 390

Mobility of Ions ............................................................................................................................. 393

Ionic Drift Velocity and Its Relation with Current Density .......................................................... 394

Einstein Relation Between the Absolute Mobility and Diffusion Coefficient .............................. 398

The Stokes-Einstein Relation ........................................................................................................ 401

The Nernst-Einstein Equation ....................................................................................................... 403

Walden's Rule ............................................................................................................................... 404

The Rate-Process Approach to Ionic Migration ............................................................................ 406

The Rate-Process Equation for Equivalent Conductivity .............................................................. 410

Total Driving Force for Ionic Transport: Nernst-Planck Flux Equation ....................................... 412

Ionic Drift and Diffusion Potential ................................................................................................ 416

The Onsager Phenomenological Equations ................................................................................... 418

The Basic Equation for the Diffusion ............................................................................................ 419

Planck-Henderson Equation for the Diffusion Potential ............................................................... 422

Problems ........................................................................................................................................ 425

Bibliography .................................................................................................................................. 426

INDEX ......................................................................................................................................................... 427

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INDEX

Absolute-rate theory ........................................ 143

Activated complex theory................................ 143

Activation energy of chain reactions ............... 362

Arrhenius equation .......................................... 116

Basic equation for the diffusion ....................... 419

Branching chain reactions ............................... 368

Calculation of eutectic point ............................ 311

Chain length .................................................... 364

Chain reactions ................................................ 344

Decomposition of ethane ............................. 350

Hydrogen-bromine reaction ......................... 346

Pyrolysis of acetaldehyde ............................ 348

Clausius-Clapeyron equation ........................... 289

Applications ................................................ 292

Derivation .................................................... 289

Collision Theory of reaction rates .................... 135

Bimolecular reactions .................................. 135

Unimolecular reactions ................................ 139

Comparison of collision and activated complex

theory ........................................................... 157

Competitive and non-competitive inhibition .... 378

Consecutive reactions ...................................... 127

Debye-Huckel limiting law of activity coefficients

..................................................................... 178

Debye-Huckel reciprocal length ...................... 173

Debye-Huckel theory of ion-ion interactions ... 160

Debye-Huckel-Bjerrum equation ..................... 200

Debye-Huckel-Onsager equation ..................... 190

Aqueous solutions ........................................ 190

Non-aqueous solutions ................................ . 195

Degeneracy among energy levels for a particle in

three dimensional box .................................. 215

Double sphere model ....................................... 147

428 A Textbook of Physical Chemistry – Volume I

Effect of ion association upon conductivity..... 200

Effect of temperature on reaction rates ............ 113

Eigen function ................................................... 15

Eigen value ........................................................ 15

Einstein relation between the absolute mobility

and diffusion coefficient .............................. 398

Energy time uncertainty .................................... 28

Enthalpy ............................................................ 98

Enthalpy of activation ..................................... 144

Entropy .............................................................. 87

Equivalent conductivity (Λ) vs concentration . 198

Eutectic systems .............................................. 311

Lead-Silver system (Pb-Ag) ........................ 318

Potassium iodide-water system (KI-H2 O).... 320

Eutectic Systems

Bismuth-cadmium system (Bi-Cd) .............. 317

Excess charge density ...................................... 168

Experimental methods for the determination of

phase diagram of two-component systems .. 308

Cooling curve method ................................. 308

Thaw-melt method ....................................... 310

Explosions ....................................................... 368

First law of thermodynamics.............................. 84

Gibbs-Duhem equation .................................... 108

Hamiltonian operator ......................................... 14

Heat content ....................................................... 98

Heisenberg's uncertainty principle .................... 24

Hermitian operators ........................................... 52

Hydrogen atom ................................................ 247

Separation of variables ................................. 249

Solution of r-equation .................................. 258

Solution of θ-equation .................................. 253

Solution of ϕ-equation ................................. 250

Influence of the solvent on reaction rate .......... 152

Ion transport in solutions ................................. 390

Ionic cloud ....................................................... 176

Ionic drift ......................................................... 394

INDEX 429

Ionic drift and diffusion potential .................... 416

Ionic movement under the influence of an electric

field ............................................................. 390

Ionic reactions ................................................. 147

Double sphere model ................................... 147

Single-sphere model .................................... 149

Ionic strength ................................................... 154

Ion-Ion interactions ......................................... 160

Ion -size effect on potential .............................. 185

Ion-size parameter ........................................... 187

Law of mass action .......................................... 293

Limitations of collision theory ........................ 141

Limitations of Debye-Huckel limiting law ...... 184

Lowest energy of the particle ............................ 80

Magnetic quantum number .............................. 273

Max-Born interpretation of wave functions

One-dimensional system ............................... 22

Three-dimensional system ............................. 23

Two-dimensional system ............................... 22

Max-Born interpretation of wave functions ....... 21

Maxwell's distribution of energies ................... 115

Michaelis-Menten equation.............................. 371

Mobility of ions ............................................... 393

Nernst-Einstein equation .................................. 403

Nernst-Planck flux equation............................. 412

Onsager phenomenological equations .............. 418

Operator evaluation............................................ 36

Operators ........................................................... 29

Algebra of operators ...................................... 30

Operator commutation ................................... 39

Opposing reactions .......................................... 119

First order by first order ............................... 119

First order by second order .......................... 122

Second order by first order........................... 123

second order by second order ....................... 125

Orbital angular momentum quantum number .. 271

Ortho-Para hydrogen conversion ..................... 358

430 A Textbook of Physical Chemistry – Volume I

Parallel reactions ............................................. 132

Partial molar quantities .................................... 104

Particle in one dimensional box......................... 65

Average momentum ...................................... 71

Average momentum-squared ......................... 72

Average position ........................................... 70

Average position-squared .............................. 71

Heisenberg's uncertainty ................................ 73

Non-quantization of energy ........................... 78

Probability density ......................................... 79

Quantization of energy .................................. 77

Zero point energy .......................................... 80

Particle in the three-dimensional box .............. 211

Phase diagram ................................................. 304

Eutectic systems .......................................... 306

Solid solutions ............................................. 308

Systems with congruent and incongruent

melting points .......................................... 306

Photochemical reactions .................................. 352

Planck-Henderson equation ............................. 422

Position momentum uncertainty ........................ 25

Postulates of quantum mechanics ...................... 11

1st .................................................................. 11

2nd ................................................................. 12

3rd .................................................................. 14

4th .................................................................. 15

5th .................................................................. 15

Principal quantum number ............................... 268

Probability distribution function ...................... 276

Quantum numbers ............................................ 268

Azimuthal quantum number ......................... 271

Magnetic quantum number .......................... 273

Principal quantum number ........................... 268

Radial distribution function ............................. 278

Rate-Process approach to ionic migration ........ 406

Rate-Process equation for equivalent conductivity

..................................................................... 410

Resultant operator .............................................. 37

Rice-Herzfeld mechanism ................................ 366

INDEX 431

Rigid rotator .................................................... 231

Classical treatment ...................................... 241

Eigenfunctions ............................................. 240

Quantum mechanical treatment ................... 242

Schrodinger wave equation ............................... 16

Harmonic oscillator ..................................... 217

Hydrogen atom ............................................ 247

Particle in 1-D box ........................................ 65

Particle in 3-D box ...................................... 211

Rigid rotator ................................................ 231

Second law of thermodynamics ......................... 86

Shape of atomic orbitals .................................. 281

d-orbital ....................................................... 284

p-orbital ....................................................... 282

s-orbital ....................................................... 281

Side reactions .................................................. 132

Simple harmonic oscillator .............................. 217

Classical treatment ...................................... 217

Eigenfunctions ............................................. 224

Eigenvalues ................................................. 226

Quantum mechanical treatment .................... 219

Zero point energy ......................................... 229

Single sphere model ......................................... 149

Solid solutions ................................................. 332

Ascending solid solutions ............................ 336

Maximum-type solid solutions ..................... 340

Space quantization ........................................... 243

Spontaneity of reaction ...................................... 97

Steric factor...................................................... 141

Stokes-Einstein relation ................................... 401

Systems forming solid compounds with congruent

and incongruent melting points .................... 321

Ferric chloride system (FeCl3 -H2 O) ............. 325

Magnesium-zinc system (Mg-Zn) ................ 323

Sodium chloride-water system (NaCl-H2 O) . 329

Sodium sulphate-water system (Na2 SO4 -H2O)

................................................................. 331

Theory of absolute reaction rates ..................... 143

Third Law of thermodynamics ......................... 296

Determination of absolute entropy ............... 299

432 A Textbook of Physical Chemistry – Volume I

Limitations .................................................. 303

Nernst-heat theorem .................................... 296

Unattainability of absolute zero ................... 302

Transition state theory ..................................... 143

Unavailable energy ............................................ 94

Uncertainty principle ......................................... 63

Van't Hoff ........................................................ 116

Walden's rule ................................................... 404

ResearchGate has not been able to resolve any citations for this publication.

141 Limitations of Debye-Huckel limiting law

................... . Theory

Limitations of collision theory........................ 141 Limitations of Debye-Huckel limiting law...... 184

123 second order by second order

...................... . First Order

Second order by first order........................... 123 second order by second order....................... 125

Source: https://www.researchgate.net/publication/337797765_A_Textbook_of_Physical_Chemistry_-_Volume_1

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