Pharmaceutical
Physical Chemistry
Theory and Practices

S K Bhasin

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Copyright © 2012 by Dorling Kindersley (India) Pvt. Ltd
Licensees of Pearson Education in South Asia
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Dedicated to
All Those Who
Toiled in Shaping Me

into What I Am Today

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Contents

Preface

xxi

About the Author

xxii

1. Behaviour of Gases
1.1 Introduction 2
1.2 Gas Laws 2
1.2.1 Boyle’s Law 2
1.2.2 Charles Law 3
1.2.3 Avogadro’s Law 4

1.2.4 The Combined Gas Law Equation or the Gas Equation 4
1.2.5 Graham’s Law of Diffusion 6
1.2.6 Dalton’s Law of Partial Pressure 6
1.3 Kinetic Theory of Gases 6
1.3.1 Postulates (Assumptions) of Kinetic Theory 6
1.4 Derivation of Kinetic Gas Equation 7
1.5 Derivation of Gas Laws from Kinetic Equation 9
1.5.1 Some Useful Deductions from Kinetic Theory of Gases 12
1.6 Ideal and Real Gases 17
1.6.1 Ideal Gases 17
1.6.2 Real Gas 17
1.7 Deviations of Real Gases from Gas Laws 18
1.7.1 Deviations from Boyle’s Law 18
1.8 Causes of the Derivations from Ideal Behaviour 20
1.9 van der Waals’ Equation (Reduced Equation of State)
(Equation of State for Real Gases) 20
1.9.1 Units of van der Waals’ Constants 23
1.9.2 Significance of van der Waals’ Constant 24
1.10 Explanation of Behaviour of Real Gases on the Basis of
van der Waals’ Equation 24
1.11 Isotherms of Carbon Dioxide—Critical Phenomenon 28
1.12 Principle of Continuity of States 30
1.13 Critical Constants 31
1.13.1 Relations Between van der Waals’ Constants and Critical Constants
3
1.13.2 Derivation of PcVc = RTc from van der Waals’ Equation 33
8

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1.13.3 Calculation of van der Waals’ Constants in terms of Tc and Pc
1.14 Law of Corresponding States 34
1.14.1 Significance of Law of Corresponding States 35
1.15 Limitations of van der Waals’ Equation 36

34

Revision Questions 36
Multiple Choice Questions

39

Answers 42

2. The Liquid State
2.1
2.2
2.3
2.4

2.5


2.6

2.7

2.8
2.9

Introduction 44
General Characteristics of Liquids 44
Classification of Physical Properties of Liquids 46
Surface Tension 46
2.4.1 Some Important Results 47
2.4.2 Effect of Temperature on Surface Tension 48
2.4.3 Measurement of Surface Tension 48
2.4.4 Surface Tension in Everyday Life 51
2.4.5 Surface Tension and Chemical Constitution (Parachor)
Viscosity 57
2.5.1 Coefficient of Viscosity 58
2.5.2 Measurement of Viscosity 59
2.5.3 Effect of Temperature on Viscosity 60
2.5.4 Factors Affecting Viscosity 61
2.5.5 Viscosity and Chemical Constitution 62
Refractive Index 64
2.6.1 Measurement of Refractive Index 65
2.6.2 Refractive Index and Chemical Constitution 66
Optical Activity 69
2.7.1 Optical Activity 70
2.7.2 Specific Rotation 70
2.7.3 Optical Activity and Chemical Constitution 71

Polarity of Bonds 74
2.8.1 Polar Character of Covalent Bond 75
Dipole Moment 75
2.9.1 Unit of Dipole Moment 75
2.9.2 Dipole Moment and Molecular Structure 76
2.9.3 Application of Dipole Moments 76

43

52

Revision Questions 80
Multiple Choice Questions

81

Answers 83

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Contents | vii

3. Solution

85

3.1 Introduction 86

3.2 Modes of Expressing Concentration of Solutions 87
3.3 Raoult’s Law 89
3.3.1 For a Solution of Volatile Liquids 89
3.3.2 For a Solution of Non-volatile Solute 90
3.4 Ideal Solution 90
3.4.1 Non-ideal Solution 91
3.4.2 Solutions Showing Positive Deviations 91
3.4.3 Solutions Showing Negative Deviations 91
3.4.4 Factors Responsible for Deviations 92
3.4.5 Distinction Between Ideal and Non-ideal Solutions 93
3.4.6 Difference Between Solutions of Positive and Negative Deviations 93
3.5 Colligative Properties of Dilute Solution 95
3.6 Lowering of Vapour Pressure 95
3.6.1 Determination of Molecular Masses of Non-volatile Solute 96
3.7 Elevation in Boiling Point 99
3.7.1 Expression for the Elevation in Boiling Point 99
3.7.2 Calculation of Molecular Masses 101
3.8 Depression of Freezing Point 102
3.8.1 Expression for the Depression in Freezing Point 103
3.8.2 Calculation of Molecular Masses 104
3.9 Osmotic Pressure 105
3.9.1 Difference Between Osmosis and Diffusion 105
3.9.2 Osmotic Pressure 105
3.9.3 Determination of Osmotic Pressure Berkley and Hertley’s Method 106
3.9.4 Osmotic Pressure is a Colligative Property 107
3.9.5 Isotonic Solutions 107
3.9.6 Calculation of Molecular Masses from Osmotic Pressure 108
3.10 Abnormal Molecular Masses 112
3.10.1 Modified Equation for Colligative Properties in Case of
Abnormal Molecular Masses 114

Revision Question 115
Multiple Choice Questions

117

Answers 118

4. Thermodynamics

119

4.1 Introduction 119
4.1.1 Objective of Thermodynamics 120
4.1.2 Limitation of Thermodynamics 120

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4.2 Some Common Thermodynamics Terms 121
4.2.1 Thermodynamic Equilibrium 122
4.2.2 Thermodynamic Processes 122
4.2.3 Reversible and Irreversible Processes 123
4.2.4 Thermodynamic Properties 124
4.3 Zeroth Law of Thermodynamics 126
4.3.1 Absolute Scale of Temperature 126
4.4 Work, Heat and Energy Changes 127

4.4.1 Work 127
4.4.2 Heat 129
4.4.3 Equivalence Between Mechanical Work and Heat 130
4.4.4 Internal Energy 130
4.5 First Law of Thermodynamics 131
4.5.1 Mathematical Formulation of First Law of Thermodynamics 132
4.5.2 Some Special Forms of First Law of Thermodynamics 132
4.5.3 Limitations of the First Law of Thermodynamics 133
4.6 The Heat Content or Enthalpy of a System 135
4.7 Heat Capacities at Constant Pressure and at Constant Volume 136
4.7.1 Heat Capacity at Constant Volume 137
4.7.2 Heat Capacity at Constant Pressure 137
4.7.3 Relationship Between Cp and Cv 138
4.8 Joule-Thomson Effect 138
4.9 Reversible-Isothermal Expansion of an Ideal Gas 140
4.9.1 Maximum Work 141
4.10 Second Law of Thermodynamics 142
4.10.1 Spontaneous Processes and Reactions (Basis of Second Law) 143
4.10.2 Spontaneous Reactions 143
4.11 Entropy 145
4.11.1 Mathematical Explanation of Entropy 145
4.11.2 Entropy Change in Chemical Reaction 147
4.11.3 Units of Entropy 147
4.11.4 Physical Significance of Entropy 147
4.11.5 Entropy Change Accompanying Change of Phase 147
4.11.6 Entropy Changes in Reversible Processes 148
4.11.7 Entropy Changes in Irreversible Processes 149
4.11.8 Entropy as Criterion of Spontaneity 150
4.11.9 Entropy Changes for an Ideal Gas 150
Revision Questions 154

Multiple Choice Questions

156

Answers 157

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Contents | ix

5. Adsorption and Catalysis

159

5.1
5.2
5.3
5.4
5.5

Adsorption 160
Types of Adsorption 161
Factors Affecting Adsorption of Gases on Solids 162
Adsorption Isobar (Effect of Temperature on Adsorption) 163
Adsorption Isotherm (Effect of Pressure) 163
5.5.1 Explanation of Type I Isotherm 164
5.5.2 Freundlich Adsorption Isotherm 164

5.5.3 The Langmuir Adsorption Isotherm 165
5.5.4 Verification 166
5.5.5 Explanation of Type II and III Isotherms 167
5.5.6 Explanation of Type IV and V Isotherms 167
5.6 Theory of Adsorption 168
5.7 Gibbs’ Adsorption Equation 169
5.8 Applications of Gibbs’ Adsorption Equation 173
5.9 Equation for Multi-Layer Adsorption (B.E.T. Equation) 176
5.9.1 Determination of Surface Area of the Adsorbent 178
5.10 Catalysis 179
5.10.1 Positive and Negative Catalyses 179
5.11 Homogeneous and Heterogeneous Catalyses 179
5.12 How Does a Catalyst Work? 180
5.12.1 Characteristics of Catalytic Reactions 181
5.12.2 Acid–Base Catalysis 182
5.12.3 Enzyme Catalysis 183
5.13 Mechanism of Homogeneous and Heterogeneous Catalyses 184
5.13.1 Significant Characteristics of Heterogeneous Catalysis 186
5.13.2 Facts Explained by Adsorption Theory 187
Revision Questions 188
Multiple Choice Questions

190

Answers 192

6. Photochemistry
6.1 Introduction 193
6.2 Thermochemical and Photochemical Reactions 194
6.3 Laws Governing Light Absorption — Lambert’s Law and Beer’s Law

6.3.1 Limitations of Lambert–Beer’s Law 198
6.4 Laws of Photochemistry 201
6.4.1 Grotthus–Drapper Principle of Photochemical Activation:
(First Law of Photochemistry) 201
6.4.2 Stark–Einstein’s Law of Photochemical Equivalence—
The Second Law of Photochemistry 201

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6.5 Quantum Efficiency 204
6.5.1 Explanation of the Unexpected Behaviour 204
6.5.2 Classification of Photochemical Reactions (Based on their Quantum
Efficiencies) 205
6.6 Study of Some Photochemical Reactions 208
6.7 Fluorescence and Phosphorescence 211
6.7.1 Fluorescence 211
6.7.2 Phosphorescence 212
6.7.3 Photophysical Process—Consequence of Light Absorption
(Jablonski Diagram) 213
6.7.4 Mechanism of Fluorescence and Phosphorescence 215
6.7.5 Difference between Fluorescence and Phosphorescence 215

Revision Questions 216
Multiple Choice Questions

217

Answers 219

7. Chemical Kinetics

221

7.1 Introduction 222
7.2 Rate of a Reaction 222
7.2.1 Measurement of Rate of a Reaction 223
7.2.2 Expressing the Rate of a Reaction 224
7.2.3 Factors Influencing Rate of a Reaction 225
7.3 Rate Constant and Rate Equation 225
7.3.1 Differences Between Rate of a Reaction and Rate Constant 226
7.4 Order of a Reaction 227
7.4.1 Units for Rate Constant or Specific Reaction Rate 228
7.5 Molecularity of a Reaction 229
7.5.1 Differences Between Order and Molecularity of a Reaction 230
7.6 Zero-order Reactions 231
7.6.1 Characteristics of a Zero-order Reaction 232
7.7 Intergrated Rate Law Equation for First-order Reactions 234
7.7.1 Characteristics or Significance of First-order Reaction 235
7.7.2 Examples of the Reactions of First Order 236
7.7.3 Pseudo First-order Reaction 239
7.8 Second-order Reactions 242
7.8.1 Characteristics of Second-order Reaction 243

7.8.2 Example of the Second-order Reaction 245
7.9 Third-order Reaction 247
7.9.1 Characteristics of a Third-order Reaction 248
7.9.2 Example of Third-order Reactions 250

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7.10 Reactions of Higher Order 251
7.11 Determination of Rate Law, Rate Constant and Order of Reaction 251
7.12 Some Complications in Determination of Order of a Reaction 256
7.12.1 Consecutive Reactions 256
7.13 Temperature Dependence of Reaction Rates 258
7.13.1 Explanation of Effect of Temperature 258
7.13.2 Arrhenius Equation 259
7.14 Mechanism of a Reaction (Concept of Molecularity and Order of a Reaction)
7.15 Theories of Reaction Rates 264

261

Revision Questions 269
Multiple Choice Questions

270

Answers 272


8. Quantum Mechanics

273

8.1 Introduction 274
8.2 Classical Mechanics and Its Limitations 274
8.2.1 Limitations 274
8.3 Origin of Quantum Mechanics 275
8.3.1 Classical Mechanics versus Quantum (or wave) Mechanics 275
8.4 Black Body Radiations 276
8.5 Kirchoff’s Law 277
8.5.1 Spectral Distribution of Black Body Radiation 278
8.6 Stefan-Boltzmann Fourth Power Law 279
8.7 Wien’s Displacement Law 279
8.8 Planck’s Radiation Law 281
8.9 Postulates of Quantum Mechanics 283
8.10 Operators in Quantum Mechanics 285
8.10.1 Types of Operators 286
8.11 Schrödinger Wave Equation 288
8.11.1 Derivation of Schrödinger Wave Equation 288
8.12 Eigenvalues and Eigenfunctions (or Wave Functions) 290
8.12.1 Physical Significance of the Wave Function 290
8.13 Normalized and Orthogonal Eigenfunctions 290
8.14 Concept of Atomic Orbital 291
8.15 Probability Distribution Curves 292
8.16 Radial Probability Distribution Curves 292
8.16.1 Radial Probability Distribution Curve for 1s Orbital 293
8.16.2 Radial Probability Distribution Curves for other s Orbitals 293
8.16.3 Comparison of Radial Probability, Distribution Curves for 1s with

Other s Atomic Orbitals 294

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8.16.4 Radial Probability Distribution Curves for p Orbitals 295
8.16.5 Comparison of Radial Probability Distribution Curves for
2s and 2p Orbitals 295
8.16.6 Comparison of Radial Probability Distribution Curves for 3s, 3p and 3d
Orbitals 295
Revision Questions 296
Multiple Choice Questions

298

Answers 299

9. Ionic Equilibria

301

9.1 Introduction 301
9.2 Arrhenius Theory of Ionization 302
9.2.1 Degree of Dissociation or Ionization 303
9.3 Ionisation of Weak Electrolytes—Ostwald’s Dilution Law 304
9.3.1 Verification of Ostwald’s Dilution Law 305

9.4 Arrhenius Concept of Acids and Bases 306
9.4.1 Limitation of Arrhenius Theory 306
9.5 Ionisation Constant of Weak Acids and Bases (Arrhenius Concept) 307
9.6 Bronsted–Lowry Concept of Acids and Bases 308
9.6.1 Conjugate Acid Base Pairs 309
9.6.2 Relative Strength of Acids and Bases 310
9.6.3 Limitation of Bronsted—Lowry Theory 311
9.7 Lewis Concept of Acids and Bases 311
9.7.1 Limitations of Lewis Concept 312
9.8 Ionic Product of Water 313
9.8.1 Concentrations of H3O + and OH – ions in Aqueous Solutions of Acids
and Bases 314
9.9 pH Scale 315
9.9.1 The pOH Scale 316
9.10 Buffer Solution 321
9.10.1 Buffer Action of Buffer Solutions 322
9.10.2 Applications of Buffer Solutions 323
Revision Questions 324
Multiple Choice Questions

325

Answers 326

10. Distribution Law

327

10.1 Introduction 327
10.2 Conditions for the Validity of the Distribution Law 328

10.3 Effect of Temperature on Distribution Coefficient 329

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10.4 Thermodynamic Derivation of Distribution Law 329
10.4.1 Principle 329
10.5 Distribution Law and Molecular State of Solute 331
10.5.1 Case I: When the Solute Undergoes Association in One of the Solvents 331
10.5.2 Case II: When the Solute Undergoes Dissociation in One of the Solvents 334
10.5.3 Case III: When the Solute Enters into Chemical Combination with One of
the Solvents 335
10.6 Applications of Distribution Law 336
10.6.1 Determination of Solubility of a Solute in a Solvent 337
10.6.2 Determination of Molecular State of Solute in Different Solvents 337
10.6.3 Determination of Distribution Indicators 337
10.6.4 Study of Complex Ions 338
10.6.5 In the Process of Extraction 339
10.6.6 Application of Principle of Extraction To Desilverization of Lead 342
10.6.7 Determination of Degree of Hydrolysis 343
Revision Questions 344
Multiple Choice Questions

346

Answers 347


11. Electrochemistry

349

11.1 Introduction 349
11.2 Electrolysis 350
11.2.1 Faraday’s First Law of Electrolysis 351
11.2.2 Faraday’s Second Law of Electrolysis 351
11.2.3 Application of Electrolysis 352
11.3 Electrolytic Conduction 354
11.3.1 Differences Between Metallic Conductor and Electrolytic Conductor 355
11.3.2 Factors Affecting Electrolytic Conduction 355
11.3.3 Electrical Conductance 356
11.3.4 Specific Conductance 357
11.3.5 Equivalent Conductance and Molecular Conductance 358
11.3.6 Relation Between Specific Conductance and Equivalent
Conductance 358
11.3.7 Experimental Measurement of Conductance 359
11.3.8 Effect of Dilution on Conductance 363
11.4 Kohlrausch Law 364
11.4.1 Applications of Kohlrausch’s Law 365
11.5 Migration of Ions 367
11.5.1 Migration Velocity of Ions and Change in Concentration—Hittorf Theoretical
Device 367

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11.6 Transport Number 369
11.6.1 Important Relations Concerning Transport Number
11.6.2 Factors Controlling Transport Number 370
11.6.3 Determination of Transport Numbers 371
11.7 Limitations of Arrhenius Theory 375
11.8 Modern Theory of Strong Electrolytes 376

369

Revision Questions 379
Multiple Choice Questions

380

Answers 382

12. Electromotive Force and Oxidation–Reduction
System

383

12.1 Introduction 383
12.2 Single Electrode Potential 384
12.2.1 Definition 385
12.3 Standard Electrode Potential 387
12.4 Measurement of Single Electrode Potential 388
12.4.1 Sign Conventions 388

12.5 Reference Electrodes 389
12.5.1 Primary Reference Electrodes 389
12.5.2 Secondary Reference Electrodes 390
12.5.3 Advantages of Glass Electrode 392
12.5.4 Limitations of Glass Electrode 393
12.6 Electrochemical Series 393
12.6.1 Applications of Electrochemical Series 394
12.7 Cell Potential or EMF of a Cell 396
12.7.1 Calculation of EMF of a Cell 396
12.8 Derivation of Nernst Equation (Concentration Dependence of Electrode
Potential) 399
12.8.1 Application of Nernst Equation 400
Revision Questions 406
Multiple Choice Questions

407

Answers 410

13. Solid State (Crystalline State)
13.1
13.2
13.3
13.4
13.5

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411


Introduction 411
Crystalline and Amorphous Solids 412
Some Terms Used in Crystal Structure 415
Crystal Lattice and Unit Cell 416
Elements of Symmetry 419

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13.5.1 Plane of Symmetry and Reflections 419
13.5.2 Axis of Symmetry or Axis of Rotation 419
13.5.3 Centre of Symmetry or Inversion Centre 421
13.5.4 Improper Axis or Rotation Reflector Axis and Improper Rotation
13.5.5 Axis of Rotation Inversion 421
13.5.6 Total Elements of Symmetry 421
13.6 Crystallographic Designations 423
13.6.1 Weiss Indices (Parameter System of Weiss) 423
13.6.2 Index System of Miller (Miller Indices) 423
13.7 Laws of Crystallography 424
13.7.1 The Law of Constancy of Interfacial Angles 424
13.7.2 The Law of Rationality of Indices 424
13.7.3 The Law of Symmetry 425
13.8 Crystal Systems 427
13.9 Types of Unit Cells in Crystal System (Bravais Lattice) 428
13.10 Bragg’s Method of Crystal Analysis 430
13.10.1 Principle 430
13.10.2 Derivation of Bragg’s Equation 430
13.10.3 Bragg’s Method for Determining Crystal Structure 431

13.10.4 Applications of Bragg’s Equation 432
13.11 Types of Crystalline Solids 433
13.11.1 Ionic Solids 433
13.11.2 Metallic Solids 434
13.11.3 Covalent Solids 435
13.11.4 Molecular Solids 435

421

Revision Questions 437
Multiple Choice Questions

438

Answers 439

14. Chemical Bonding

441

14.1 Introduction 441
14.2 Valence Bond (VB) Theory 442
14.3 Molecular Orbital (MO) Theory 443
14.3.1 Molecular Orbitals 443
14.3.2 Conditions for Atomic Orbitals to Form Molecular Orbitals 444
14.3.3 Difference Between Atomic and Molecular Orbitals 445
14.3.4 Formation of Bonding and Anti-bonding Molecular Orbitals
(LCAO Method) 445
14.3.5 Bonding and Anti-bonding Molecular Orbitals in Terms of Wave
Functions 447


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14.4
14.5

14.6

14.7

14.3.6 Characteristics of Bonding and Anti-bonding Molecular Orbitals 448
14.3.7 Combination of Atomic Orbitals—Sigma (s) and Pi (p) Molecular
Orbitals 448
Relative Energies of Molecular Orbitals and Filling of Electrons 451
Stability of Molecules 453
14.5.1 Stability of Molecules in Terms of Bonding and Anti-bonding
Electrons 453
14.5.2 Stability of Molecules in Terms of Bond Order 453
Molecular Orbital Configurations 454
14.6.1 Bonding in Some Homonuclear Diatomic
Molecules and Ions – Electronic Configurations 454
14.6.2 Helium Ion, He2+ 457
14.6.3 Nitrogen Molecule, N2 459
14.6.4 Oxygen Molecule, O2 460
14.6.5 The Fluorine Molecule, F2 462

14.6.6 Hypothetical Neon Molecule, Ne2 462
14.6.7 Molecular Orbital Electronic Configuration of Some
Common Heteronuclear Molecules 462
Comparison of Valence Bond (VB) Theory and Molecular
Orbital (MO) Theory 463
14.7.1 Points of Similarly 463
14.7.2 Points of Difference 463

Revision Questions 465
Multiple Choice Questions

466

Answers 467

15. Phase Equilibria

469

15.1 Introduction 469
15.2 Explanation of the Terms Involved 470
15.2.1 True and Metastable Equilibrium 470
15.2.2 Phase 470
15.2.3 Components 471
15.2.4 Degrees of Freedom or Variance 474
15.3 Mathematical Statement of Phase Rule 474
15.4 Phase Diagrams 476
15.5 One-component Systems 477
15.6 The Water System 478
15.7 Sulphur System 481

15.8 Application of Phase Rule To Two-component Systems
(Liquid–Solid Phase Diagram) 484
15.9 Type A—Simple Eutectic System 485

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Contents | xvii

15.9.1 Characteristics of Eutectic Point 485
15.9.2 Use of Eutectic Systems 486
15.9.3 Lead–Silver System 486
15.9.4 Pattinson’s Process for Desilverization of Lead 488
15.10 Type B—System in Which Two Components form a Stable Compound
(Zinc–Magnesium Alloy System) 488
15.10.1 Eutectic Points and Congruent Melting Point 490
15.11 Type C—The Two-component Form: A Compound With Incongruent Melting
Point 490
15.11.1 Sodium – Potassium System 490
15.12 Thermal Analysis (Cooling Curve) 492
Revision Questions 493
Multiple Choice Questions

495

Answers 496

Experiments

Refractometry

501

Refractive Index 501, Measurement of Refractive Index 502

Experiment 1

503

Object 503, Apparatus 503, Theory 503, Procedure 503,
Observations 503, Result 503, Precautions 504, Viva-voce 504

Polarimetry

506

Optical Activity 506, Specific Rotation 507

Experiment 2

508

Object 508, Apparatus 508, Theory 508, Procedure 508,
Observations and Results 509, Viva-voce 509

Experiment 3

512


Object 512, Apparatus 512, Theory 512, Procedure 512,
Calculation 513, Result 513, Viva-voce 513

Experiment 4

514

Object 514, Theory 514, Apparatus/Reagents Required 515,
Procedure 515, Observations 515, Calculations 516, Result 516, Precautions 516,
Graphical Method 516, Viva-voce 517

Experiment 5

520

Object 520, Theory 520, Cell Constant 520, Measurement of Cell Constant 520,
Apparatus Required 521, Materials Required 521, Procedure 521,
Determination and Calculations 522, Precautions 522, Viva-voce 523

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Experiment 6

524


Object 524, Apparatus and Reagents 524, Theory 524, Procedure 525,
Observation 525, Calculation 526, Result 526, Precautions 526, Viva-voce 526

Experiment 7

528

Object 528, Theory 528, Requirements 529, Procedure 529, Important Note 529,
Calibration of the Instrument 529, Titration of HCl VS. NaOH Solution 530,
Observation and Calculations 530, Result 531, Note 531, Precautions 531,
Viva-voce 531

Experiment 8

535

Object 535, Theory 535, Materials 535, Description of the Apparatus 535,
Procedure 536, Observations and Calculations 536, Calculations 537, Result 537,
Precautions 537, Viva-voce 538

Experiment 9

540

Object 540, Theory 540, Apparatus/Reagents Required 540, Procedure 540,
Observations 541, Calculations 541, Calculate Values of K for Each Set 542,
Results 542, Precautions 542, Viva-voce 542

Experiment 10


543

Object 543, Theory 543, Apparatus Reagents Required 543, Method 543,
Observations 544, Burette Readings 544, Calculations 544, Result 545,
Precautions 545, Viva-voce 545

Experiment 11

548

Object 548, Apparatus 548, Description 548, Theory 549, Procedure 549,
Observations 549, Calculations 550, Result 550, Precautions 550, Viva-voce 550

Experiment 12

552

Object 552, Apparatus 552, Theory 552, Indicators 553, Procedure 554,
Observations 554, Viva-voce 554

Experiment 13

555

Object 555, Apparatus 555, Theory 555, Procedure and Observations 555,
Result 556, Viva-voce 556

Experiment 14

558


Object 558, Apparatus 558, Theory 558, Procedure 558, Calculations 559,
Result 559, Precautions 559, Viva-voce 560

Experiment 15

562

Object 562, Theory 562, Apparatus and Materials 562, Procedure 562,
Observations 563, Calculations 564, Precautions 564, Viva-voce 564

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Contents | xix

Experiment 16

566

Object 566, Theory 566, Apparatus and Materials Required 566, Procedure 567,
Observations 568, Calculations 568, Result 569, Precautions 569, Viva-voce 570

Experiment 17

573

Object 573, Theory 573, Materials Required 573, Procedure 574,

Precautions 575, Viva-voce 575

Experiment 18

577

Object 577, Theory 577, Materials Required 577, Procedure 578,
Observations 578, Result 579, Viva-voce 579

Experiment 19

580

Object 580, Theory 580, Apparatus and other Materials Required 580,
Procedure 581, Observations and Calculations 581, Viva-voce 582

Experiment 20

584

Object 584, Theory 584, Apparatus and Other Materials Required 584,
Procedure 585, Observation and Calculations 585, Viva-voce 586
Index

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Preface

It gives me immense pleasure to place before a large community of pharmacy students, my humble work
on Pharmaceutical Physical Chemistry, written in accordance with the recent syllabus prescribed for the
B.Pharma. (II Semester) students of all Indian universities. My aim in writing this book is to present
the fundamental principles of physical chemistry for the pharmacy students on modern lines. No single
book on pharmacy that covers the revised syllabus exclusively is available in the market. Keeping in view
the requirement of the students and the teachers, this book has been written to cover all the topics with
the desired limits of the prescribed syllabus. I hope the book will be useful and meets the requirements
of students at large.
Based on my vast teaching experience, I have prepared the text in a simple, lucid and comprehensive
style, keeping in view the difficulties of the students; in addition, the manuscript has been presented as if
the teacher is talking to the students in the class. Throughout the text, special care has been taken to add
‘Review Problems for Tutorials’ at relevant stages for the students to assess their grasp of the topic covered. Students are advised to solve the problems themselves and look for their solution only afterwards.
An added feature of this book is that it contains the ‘Laboratory Manual’, which contains 20 experiments covering the syllabus in the practical of all Indian universities along with the ‘Viva-Voce’ at the
end of each experiment. In this section, we have described the theory of the experiment in details before
giving the procedural details.
A large number of solved and unsolved ‘Numerical Problems’ have also been included wherever
required. Students should solve the unsolved numerical problems in the tutorial classes under the guidance of their learned teachers.
Here is a book that resolves all your queries and doubts. This book discusses the fundamentals of
pharmaceutical physical chemistry required for a pharmacist. The book will not only help you to score
better in the examination but would also develop your skills to apply your knowledge of pharmaceutical

physical chemistry in solving the problems that you may face during your pharmaceutical career.
I sincerely express my thanks to the authors and the publishers whose works I have consulted in producing this book. I am grateful to the editors of Pearson Education for the sustained interest shown by
them during the publication of this book.
Although care has been taken while preparing and typing the manuscript, yet errors and misprints
might have crept in; I shall be grateful to the students and teachers who would be kind enough to send
their suggestions for the further improvement of the book.
I shall consider my efforts amply rewarded if all those for whom the book is intended are benefited
by it.
Dr. S. K. Bhasin

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About the Author

S.K. Bhasin is presently Director and Professor in Chemistry in the Global Research Institute of
Management and Technology, Radaur. A matured academician, experienced teacher, established author
and devoted researcher, Dr Bhasin has a teaching experience of over 50 years; 35 years of which relates
to teaching of undergraduate and postgraduate students in chemistry and 15 years of teaching in professional institutes.
He is a ‘life fellow’ of four professional bodies, namely, the International Congress of Chemistry and
Environment (FICCE), Fellow of Indian Council of Chemists (FICC), Fellow of Indian Association of
Environmental Management (FIAEM) and Fellow of Indian Journal of Environmental Protection (FIJEP).
He is a member on the Editorial Board of International Journal of Environmental Research. He has published 64 research papers in reputed international and national journals and has published 14 articles in
national-level magazines and newspapers. He has also convened a number of national-level conferences
and workshops and has acted as resource person in many conferences.
He has presented his research papers in international conferences abroad—two research papers in
Kuwait in 2007 and one paper in Thailand in 2009. Recently, he has presented his research paper in an
international conference held at Malaysia, May 2011 organized by the Indian Congress of Chemistry

and Environment (ICCE) and yet another international conference organized by the Indian Council of
Chemists (ICC), June 2011, at Bangkok (Thailand).
He has acted as Chairman of ICC chapter at M.L.N. College Yamuna Nagar for consecutive three
years. He has been honoured with appreciation awards twice at international conferences organized
by the ICCE in the year 2009 and in Malaysia in 2011. Has also been decorated with Dronacharya
Award in recognition of his services in the field of education and research. He has over 24 graduate-level
books in chemistry, engineering and pharmacy to his credit.

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Behaviour
of Gases

1

CHAPTER OBJECTIVES
1.1

Introduction

1.2

Gas laws

1.3

Kinetic Theory of Gases


1.4

Derivation of Kinetic Gas Equation

1.5

Derivation of Gas laws from Kinetic Equation

1.6

1.9

van der Waals’ Equation (Reduced Equation
of State) (Equation of State for Real Gases)

1.10

Explanation of Behaviour of Real Gases
on the Basis of van der Waals’ Equation

1.11

Isotherms of Carbon
Dioxide-Critical Phenomenon

Ideal and Real Gases

1.12


Principle of Continuity of States

1.7

Deviations of Real Gases from Gas laws

1.13

Critical Constants

1.8

Causes of the Derivations from
Ideal Behaviour

1.14

law of Corresponding States

1.15

limitations of van der Waals’ Equation

H2O

CO2

A vacuum is nothing and what is nothing
cannot exist
Thomas Hobbes

As the pressure increased, the volume of the
gas decreased.
Robert Boyle

Chapter 01.indd 1

O3 ozone

CH4 methane

N2O nitrous oxide

CFC chlorofloro carbon

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2 | Pharmaceutical Physical Chemistry

1.1 INTRODUCTION
All matter exists in one of the three states of aggregation: solids, liquids or gases. A solid has definite
shape and volume due to strong intermolecular attractive forces. A substance will be a solid if it melts at
a temperature higher than room temperature under atmospheric pressure.
In the liquid state, the attractive forces are relatively weak and it has a definite volume but no definite
shape. A substance will be a liquid if its freezing point (i.e., melting point) is below the room temperature
under atmospheric pressure.
In the gaseous state, the molecular forces are much weaker. Hence, due to possible random motion in
all directions, gases have no bounding surface and lend to fill completely any available space. The gases
thus have neither definite shape nor definite volume. A substance will be a gas if its boiling point is below
room temperature under atmospheric pressure.

Out of the three states of matter, i.e., solid, liquid and gases in which the different substances exist, the
gases show the most uniform behaviour irrespective of the nature of the gas. Some common properties
of gases are given below:
(i)
(ii)
(iii)
(iv)
(v)
(vi)

They expand indefinitely and fill up the whole vessel in which they are placed.
They can be compressed by the application of pressure.
They can be liquefied by cooling and applying pressure.
They possess low densities under ordinary conditions of temperature and pressure.
They intermix spontaneously, i.e., they show the property of diffusion.
They exert pressure on the walls of the vessel in which they are contained.

In addition to the above general properties of gases, another important feature of all gases is that they
obey certain gas laws such as Boyle’s law and Charles’ law which are briefly outlines below. A gas which
obeys the gas laws under all conditions of temperature and pressure is known as an ideal gas. However,
gases deviate from behaviour especially at low temperature and high pressure. The concept of ideal gases
is only hypothetical. Gases obey gas laws at high temperature and low pressure usually and are called real
gases. In this chapter, we will discuss the deal gas behaviour in terms of kinetic theory of gases and also
the deviation of real gases from ideal behaviour.

1.2 GAS LAWS
1.2.1 Boyle’s Law
This law was proposed by Robert Boyle in 1662 based on his experimental study of the variation of
volume of a gas with change of pressure at constant temperature. The law states as follow:
Temperature remaining constant, the volume of a given mass of a gas is inversely proportional to its

pressure.
Mathematically, if V is the volume of a gas at pressure P, then
1
V ∝ , if temperature is kept constant.
P
or
PV = constant, if temperature is kept constant.
(1.1)
In other words, if at constant temperature, V1 is the volume of a gas at pressure P1 and on changing
the pressure to P2, the volume changes to V2, then
P1 × V1 = P2 × V2

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