Textbook of

Physical Chemistry Volume I

Textbook of

Physical Chemistry Volume I

N.K. Vishnoi Professor, Department of Basic Sciences N.I.I.T. University Neemrana (Rajasthan)

& R.J. Shukla Ex. Head Deptt. of Chemistry, Kamla Nehru Institute of Physical & Social Sciences, Sultanpur (U.P.)

Ane Books Pvt. Ltd. New Delhi ♦ Chennai

Textbook of Physical Chemistry Vol. I N.K. Vishnoi & R.J. Shukla © Authors First Edition : 2010 Reprint : 2014, 2020

Published by Ane Books Pvt. Ltd. 4821, Parwana Bhawan, 1st Floor, 24 Ansari Road, Darya Ganj, New Delhi - 110 002, India Tel.: +91(011) 23276843-44, Fax: +91(011) 23276863 e-mail: [email protected], Website: www.anebooks.com

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ISBN : 978-81-9083-226-7 All rights reserved. No part of this book may be reproduced in any form including photocopying, microfilms, photoprints, storage in any retrieval system, transmission in any permanent or temporary form, without the prior written consent of the publisher.

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Preface Physical chemistry is the branch of chemistry that deals with the principles of physics underlying chemical interactions and transformation of material in order to correlate the quantitative as well as a qualitative aspect of matter energy interactions. A course in physical chemistry forms an essential part of the curriculum of not only science students but also of students in various branches of engineering and technology. It therefore becomes important to define the scope of the book on physical chemistry. Presently we have chosen the model syllabus suggested by panel of experts appointed by the university grants commission in the quest for uniformity of syllabi in the Indian universities. As per the U.G.C. course structure, the entire study material of physical chemistry at graduate level has been divided into three units with each unit including the course material expected to be studied in each of the three years of a B.Sc. course. Volume one of the present book of physical chemistry deals with unit I of the above course which includes states of the matter–gaseous, liquid, solid and colloidal state and chemical kinetics along with catalysis. Any course in physical chemistry incorporates a large number of definitions and concepts which need to be explained to the students through application of these in the from of solved exercises as well as numerical problems. Therefore in order to develop the understanding of the basic principles and fundamentals of the subject we have introduced solved example which are interspersed throughout the text. To sustain the interest of the student in the text a number of examples have been incorporated in the text. This is followed by objective, short answer and subjective questions. It has been our attempt to ensure the incorporation of essentials of the subject without compromising on the accuracy of the concepts. Unified treatment of the subject and explanation of facts at molecular level are the highlights of the present text. In addition to the above there is an introductory unit which includes chapters on ‘Mathematics for Chemists’ and ‘Computer for Chemists’ as required in the U.G.C. model syllabus. We sincerely hope that the present effort with help the students in acquiring a better understanding of the subject.

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Textbook of Physical Chemistry-Vol. I

We wish to thank earlier authors of the subject, teachers and students who have all contributed in shaping our thoughts while writing the present text. Thanks are due to our Publisher M/S Ane Books Pvt. Ltd. for bringing out the books in an excellent form and to Dr. S.N. Pandey for encouraging us to write the present text. Constructive criticism and suggestions for the improvement of the text are Welcome. N.K. Vishnoi R.J. Shukla

Contents

Preface

(v)

UNIT-I 1. Mathematical Concepts (Pages 3-25) 1.1 Logarithm 1.1.1 Definition of Logarithm 1.1.2 Some Important Laws of Logarithm 1.1.3 Common Logarithm 1.1.4 Characteristic and Mantissa of Logarithm 1.2 Antilogarithm 1.3 Curve Sketching 1.3.1 Introduction 1.3.2 Tracing of Cartesian Curves 1.3.3 Tracing of Polar-Curves 1.3.4 Tracing of Parametric Equations 1.4 Linear graphs and calculation of slope 1.5 Differentiation of Functions 1.5.1 Differential Coefficient of a Function 1.5.2 Differential Coefficient of xn 1.5.3 Differential Coefficient of ex 1.5.4 Differential Coefficient of Some Other Functions 1.5.5 Differential Coefficient of a Product of Two Functions 1.5.6 Differential Coefficient of a Quotient of Two Functions 1.5.7 Partial Differentiation 1.6 Maxima and Minima

3 3 4 4 4 5 5 5 6 8 10 11 13 13 13 14 14 15 15 16 17

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Textbook of Physical Chemistry-Vol. I

1.7 Reciprocity Relations 1.8 Integration of a Function 1.8.1 Integration of Some Useful Functions 1.9 Permutation and Combination 1.9.1 Factorials 1.9.2 Permutation 1.9.3 Combination 1.10 Probability 1.10.1 Random Experiments and Sample Space 1.11 Event ■ Objective Type Questions ■ Short Answer Type Questions ■ Subjective Questions

18 18 19 20 20 20 20 21 21 21 23 24 25

2. Computers for Chemists (Pages 27-38) 2.1 Introduction to Computers 2.2 Types of Computers 2.2.1 Minicomputers 2.2.2 Mainframe Computers 2.2.3 Super Computers 2.2.4 Micro Computers – Personal Computers — IBM PC 2.3 Components of a computer 2.4 Computer Hardware—Input-Devices 2.5 Computer Hardware-output devices 2.6 Computer Hardware-Storage Devices : Hard-Disk 2.7 Binary Numbers and Computer Arithmetic 2.7.1 Binary Number System 2.8 Introduction to Computer Language 2.8.1 Computer Languages 2.8.2 High Level Languages 2.9 Programming 2.9.1 Develop an Algorithm 2.9.2 Flow Chart 2.9.3 Programming in Basic Language 2.10 Laptop Computer 2.11 Internet ■ Objective Type Questions ■ Short Answer Type Questions ■ Subjective Questions

27 27 27 27 28 28 28 28 29 29 29 29 31 31 32 32 32 32 32 34 35 35 36 37

Contents

ix

UNIT-II 1. Gaseous State (Pages 41-70) 1.1 Introduction 1.1.1 Postulates of the Kinetic Theory of Gases 1.1.2 Pressure of an Ideal Gas 1.2 Gas Constant (R) 1.2.1 Deviation from Ideal Behaviour of Gases: 1.2.2 Causes of Deviation of Real Gases from Ideal Behaviour 1.3 The Van der Waals equation of State 1.3.1 Behaviour of Real Gases and van der Waals Equation 1.4 Critical Phenomenon: PV Isotherms of Real Gases 1.5 Continuity of States 1.6 Isotherms based on Van der Waals Equation 1.7 Relationship between critical constants and Van der Waals Constants 1.7.1 Determination of Critical Constants, Measurement of Tc and Pc 1.7.2 Measurement of Critical Volume (Vc) 1.8 The Law of Corresponding States 1.9 Molecular Velocities : Root-Mean Square, Average and Most Probable Velocities 1.9.1 Most Probable Velocity (Cm.p.) 1.9.2 Average Velocity () 1.9.3 Root Mean Square Velocity (Cr.m.s.) 1.10 Maxwell’s Distribution of Molecular Velocities 1.11 Collision Number, Mean Free-Path and Collision Diameter 1.11.1 Collision Number 1.12 ■ ■ ■

1.11.2 Mean Free-Path (l) Liquefaction of Gases (Based on Joule-Thomson Effect) 1.12.1 Linde’s Method (Application of Joule-Thomson Effect) Objective Type Questions Short Answer Type Questions Subjective Questions

41 41 42 46 50 51 51 54 55 56 57 58 59 60 61 62 62 62 62 62 64 65 66 66 67 67 69 69

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Textbook of Physical Chemistry-Vol. I

2. Liquid State (Pages 71-84) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10

■ ■ ■

Introduction Intermolecular Forces Structure of Liquids Difference between solids, liquids and gases Liquid Crystals Difference between liquid crystal, solid and liquid 2.6.1 Phases of Matter Namely Liquid Crystal, Solid and Liquid Classification of Liquid Crystals Structure of Nematic and Cholesteric Phases Thermography Seven Segment Cell 2.10.1 Seven-Segment Display Layout 2.10.2 Schematic Diagram Objective Type Questions Short Answer Type Questions Subjective Questions

71 71 74 75 76 77 78 79 79 79 80 81 81 82 83 83

3. Solid State (Pages 85-104) 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10.

Introduction Types of Crystalline Solids Space Lattice (or Crystal Lattice) and Unit Cell Polymorphism and Isomorphism Number of atoms/molecules/ions per unit cell Crystallography X-ray Diffraction by Crystals and Bragg’s Law Determination of Crystal Structure Experimentally Calculations involving unit cell dimensions Structure of Crystals 3.10.1 Structure of Rock Salt (NaCl) Crystal 3.10.2 Structure of Potassium Chloride (KCl) Crystal 3.10.3 Structure of Caesium Chloride (CsCl) Crystal 3.11 Imperfection in crystals 3.11.1 Schottky Defect

85 85 87 89 90 90 92 94 96 98 98 99 99 99 100

Contents

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3.11.2 Frenkel Defect 3.11.3 Impurity Defects: Semiconductors ■ Objective Type Questions ■ Short Answer Type Questions ■ Subjective Questions

100 101 102 103 104

4. Colloidal State (Pages 105-120) 4.1 Introduction 4.2 Classification of Colloids 4.3 Preparation of Colloidal Sols 4.3.1 Dispersion Methods 4.3.2 Condensation Methods 4.4 Purification of Colloidal Sols 4.5 Properties of Colloidal Sols 4.6 Origin of Charge on Colloidal Sols 4.7 Coagulation of Colloids 4.8 Protection of Colloidal Sols 4.9 Emulsions 4.9.1 Emulsifiers 4.10 Gels 4.10.1 Properties of Gels 4.11 Micelle formation 4.12 Applications of Colloids ■ Objective Type Questions ■ Short Answer Type Questions ■ Subjective Questions

105 106 106 106 107 107 108 110 112 113 113 114 114 115 116 116 118 119 119

5. Chemical Kinetics and Catalysis (Pages 121-174) 5.1 5.2 5.3 5.4 5.5 5.6

Introduction Rate of Chemical Reaction Factors Influencing the Rate of Reaction Concentration Dependence of Reaction Rate Molecularity and Order of Reaction Mathematical Characteristics of Simple Reactions

121 121 123 124 125 126

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5.7

5.8

5.9

5.10

5.11 5.12

5.13

■ ■ ■

5.6.1 Zero Order Reactions 5.6.2 First Order Reactions 5.6.3 Pseudo Unimolecular Reactions : Pseudo Order Reactions 5.6.4 Second Order Reactions 5.6.5 Third Order Reaction Radioactive Decay as a First Order Phenomenon 5.7.1 Radio-Dating 5.7.2 Mineral Dating 5.7.3 Fossil Dating or Carbon Dating Determination of Order of Reaction 5.8.1 Differential Method 5.8.2 Integration Method 5.8.3 Half-Life Method 5.8.4 Isolation Method Experimental Methods of Chemical Kinetics 5.9.1 Conductometric Titration 5.9.2 Potentiometric Measurements 5.9.3 Optical Methods : (a) Optical Rotation Method 5.9.4 Spectrophotometric Method Theories of Chemical Kinetics 5.10.1 Effect of Temperature on Rate of Reaction 5.10.2 Equilibrium Constant and Rate Constants 5.10.3 Activation Energy (Ea) 5.10.4 Simple Collision Theory Based on Hard Sphere Model 5.10.5 Transition State Theory (Equilibrium Hypothesis) 5.10.6 Thermodynamic Treatment of Transition State Theory Complex Reactions Catalysis 5.12.1 Characteristics of Catalyzed Reactions 5.12.2 Classification of Catalysis Miscellaneous Examples 5.13.1 Monsanto Process for the Production of Acetic acid 5.13.2 Ziegler-Natta Catalyst 5.13.3 Hoechst-Wacker Process 5.13.4 Heck Reaction Objective Type Questions Short Answer Type Questions Subjective Questions

126 128 131 132 136 137 139 139 140 141 141 141 142 142 143 143 144 145 146 148 148 150 150 151 153 154 155 156 157 158 168 168 168 169 169 170 172 172

UNIT-I CHAPTER 1

MATHEMATICAL CONCEPTS

3-25

CHAPTER 2

COMPUTERS FOR CHEMISTS

27-38

1 Mathematical Concepts Most of the present studies undertaken in chemistry, particularly physical chemistry, require some basic understanding of simple modern mathematical operations and tools. For example, study of chemical kinetics and quantum chemistry requires a knowledge of differential and integral calculus. Use of logarithm and curve sketching is also a necessity in chemistry. It is, therefore, necessary that these topics of mathematics are introduced to a learner of physical chemistry.

1.1 LOGARITHM 1.1.1 Definition of Logarithm Consider an exponential relation, say, ax = y (1.1) where, ‘x’ is any rational number and ‘a’ is a positive real number (but not 1). Here, logarithm of ‘y’ to the base of ‘a’ is x which is expressed as: loga y = x (1.2) ■ Example: The expression 102 = 100 may be written as log10 100 = 2, which implies that logarithm of 100 to the base 10 is equal to 2. Important Points to Remember (i) The logarithm of 1 to any base is zero, i.e., log0 1 = 0 (ii) The logarithm of any number to the same base is always 1. Thus, log3 3 = 1 and log100 100 = 1 1 = – 1. 10 Writing the given expression in the form an = y, we have

Problem 1. Find the value of x in the expression logx Solution:

1 = 10– 1 10 x = 10

x– 1 = Þ