Chapter Pages

0. Mathematical Concepts 1—20Curve sketching, linear graphs and slopesInclination and slope of a line (1)Curve sketching (2)Functions of a real variable (2)Differentiation : The Derivative of a function (4)

Differentiation formulas (4)Maxima and minima (5)Partial differentiation (7)Cyclic rule (8)

Integration (8)Methods of integration (9)Integration formulas (9)

Permutations and combinations (11)Fundamental theorem (11)Permutations (11)Combinations (11)

Probability (12)Other mathematical relations (14)

Vectors (14)Matrices (15)Determinants (16)Complex numbers (17)Series (17)Stirling approximation (17)Evaluation of integrals (18)

Memorabilia Physicomathematica (19)

1. Quantum Mechanics-I Wave MechanicalTreatment of Simple Systems 21—110Electron and the Old Quantum Theory (21)Rutherford scattering experiments (23)Rutherford atomic model (23)Quantum theory of radiation (24)Photoelectric effect (24)Bohr theory of hydrogen atom (26)Bohr theory and the origin of the hydrogen spectrum(28)Sommerfeld extension of the Bohr theory (31)Alternative explanation for the emission of finehydrogen spectrum (32)Dual character of electron (33)

de Broglie’s equation (33)The Davisson-Germer experiment (35)

Heisenberg uncertainty principle (36)Compton effect (36)

Quantum mechanics (or wave mechanics) (37)Postulates of quantum mechanics (39)The Schrödinger wave equation (40)Operators in quantum mechanics (43)Solution of the Schrödinger wave equation for somesimple systems (45)

Particle in a one–dimensional box (45)Particle in a three–dimensional box (52)One–dimensional simple harmonic oscillator (54)Rigid rotor (63)The Schrödinger equation for hydrogen atom (65)

Angular momentum in quantum mechanics (59)Zeeman effect (84)Pauli’s exclusion principle (85)Physical interpretation of the hydrogen atom orbitals

(86)Fine structure in the hydrogen atom spectrum (87)Angular momentum in quantum mechanics (87)Solved examples in quantum mechanics (89)Hermitian operators (106)Important theorems of quantum mechanics (107)Review questions and problems (109)

2 . Quantum Mechanics-II. AdvancedTopics And Atomic Spectra (111-172)Solution of the Schrödinger equation for multi-electronatoms (111)1. Time-independent perturbation theory (111)

Non-degenerate perturbation theory (112)Application of the first-order perturbation theoryhelium atom (115)Degenerate perturbation theory (117)Stark effect on the first excited state of hydrogenatom (119)

2. The variation method (120)Application of the variation method to helium atom

(121)The Hartree and the Hartree-Fock self-consistentfield (SCF) method (128)Slater determinant for n-electron atoms (129)The Schrödinger equation for a finite potential barrier:Quantum mechanical tunnelling (132)Simple harmonic oscillator : The algebraic method(137)Angular momentum operators, eigenfunctions,eigenvalues, commutation relations, and ladderoperators (141)Derivation of the variation theorem (148)Atomic states and term symbols (149)The term symbols for the p2 configuration (150)

CONTENTS

(i)

ii

Atomic spectra (154)A. Fine structure 155)B. Zeeman effect (159)C. Stark effect (162)

The Thomas-Fermi model of the atom (163)Angular momentum revisited (165)1. Angular momentum matrices (165)2. Spin angular momentum and the Pauli spin

matrices (167)3. Spin vectors for the spin-½ system (168)4. Addition of angular momenta (169)Review Questions (171)

3 . Chemical Bonding : MolecularQuantum Mechanics 173–246Molecular orbital theory (MOT) (174)Term symbols for a diatomic molecule (184)Symmetry of molecular orbitals (185)MOs for homonuclear diatomic molecules (186)Molecular orbital energy level diagrams for

heteronuclear diatomic molecules (188)Valence bond theory (VBT) (192)Hybridization (197)Calculation of the coefficients of AOs used inhybridization (200)Conjugated molecules (204)Hückel molecular orbital theory of conjugatedsystems (205)Hückel's 4n+2 rule of aromaticity (210)Walsh diagrams (225)Born-Oppenheimer Approximation (228)Hellmann-Feynman theorm (229)Computational quantum chemistry (232)A. Hartree-Fock-Roothaan self-consistent-field

(SCF) method for polyatomic molecules (234)The Pariser-Parr-Pople approximaiton (235)Configuration interaction (236)

B. Semi-empirical and ab initio methods (236)Extended Hückel theory (EHT) (236)Semi-empirical SCF theory (238)

C. Density-functional theory (DFT) (239)Time-dependent perturbation theory (TDPT)

(242)Review Questions (246)

4 . Group Theory Part I : Basic Concepts247–266

Symmetry elements and symmetry operations(247)

Group postulates (249)Types of groups (249)Other definitions (250)Point groups (250)

Representations of molecular point groups (251)Great orthogonality theorem (G.O.T.) (253)Important properties of irreps (253)Use of G.O.T. to construct character tables formolecular point groups (254)Character tables for point groups (255)Crystallographic symmetry (261)Crystal Systems (262)Molecular symmetry and crystallographic

symmetry (265)Quasicrystals (265)Problems (265)

5. Group Theory Part II : Applications267-301

1. Decomposing a reducible representation into itsirreducible representations (267)

2. Group theory and normal modes of vibrations ofpolyatomic molecules (268)

3. Procedure for determining the irreduciblerepresentations of the vibrational modes innonlinear molecules (270)

a. Normal modes of vibration of H2O molecule (270)b. Normal modes of vibraiton of NH3 molecule (272)c. Normal modes of vibration of BF3 molecule (273)4. Direct products of irreducible representations

(275)5. Selection rules for atomic spectra (278)6. Use of group theory in determining the selection

rules for the n * and * transitions informaldehyde (279)

7. Use of group theory in constructing hybrid orbitalsin simple molecules (282)

8. Use of group theory in factoring the secularequation in MOT (285)

Trans 1,3-Butadiene, (285)Benzene (289)

9. Use of projection operators to determine SALCs(292)

Miscellaneous solved examples (294)Problems (301)

6 . Molecular Spectroscopy - I 302–352What is spectroscopy ? (302)Basic features of spectrometers (302)Width and intenstiy of spectral lines (304)Molecular spectra (305)Rotational (microwave) spectra of diatomicmolecules (307)Relative intensities of rotational spectral lines (311)Applications of Microwave spectroscopy (312)Rotational spectra of polyatomic molecules (313)Stark effect in microwave spectra (314)Other applications of microwave spectra (314)

iii

Vibrational spectra of diatomic molecules (315)Rotation–vibration spectra of diatomic molecules

(319)Vibrational spectra of polyatomic molecules

(320)Rotation-vibration spectra of polyatomic molecules

(324)Vibrational frequencies of different functional groups

(324)Raman spectroscopy (326)

Quantum theory of Raman scattering (326)Classical theory of Raman scattering (327)

Rotational Raman spectrum of a diatomic molecule(328)

Rotation-vibration Raman spectrum (329)Experimental Raman spectroscopy (329)Resonance Raman spectroscopy (331)Laser Raman spectroscopy (332)Electronic spectra (335)

Franck-Condon principle (335)Electronic spectra of polyatomic molecules (337)Charge transfer spectra (340)Electronic spectra of transition metal complexes

(341)Energy level diagram for an octahedral transitionmetal complex ion (342)Jahn-Teller distortion (343)Metal-metal transitions (dd bands) (343)Change-transfer bands (344)

Electronic spectra of lanthanides and actinides (345)Electronic spectra of conjugated molecules (345)Miscellaneous solved examples in spectroscopy

(347)Review Questions and Problems (350)

7. Molecular Spectroscopy - II (NMR, ESR,NQR, NRF And PES) 353–430Magnetic resonance spectroscopy (353)NMR spectroscopy (353)

NMR of a bare proton (355)Experimental technique of NMR spectroscopy (357)Chemical shift (358)Shielding mechanism in NMR (360)Nuclear spin-spin interaction : Fine structure in NMR

(362)Chemical shift-equivalent and magnetically equivalentnuclei (364)Mechanism of nuclear spin-spin interaction (367)Complex NMR spectra (369)NMR spectra of other nuclei (369)Fourier-Transform NMR spectroscopy (370)Relaxation processes in magnetic resonance (371)

Study of hindered rotation by NMR spectroscopy(373)

Nuclear magnetic double resonance (374)Special topics in nuclear magnetic resonance (375)

1. Quantum mechanical description of the NMRspectrum of an AB spin system (375)

2. Two-dimensional NMR spectroscopy (380)3. NMR spectra of solids (380)4. Double resonance (381)5. The nuclear Overhauser effect (NOE) (381)6. Off-resonance proton decoupling (382)7. Applications of 2D NMR (382)8. Internuclear double resonance (INDOR) (385)9. Simplification of complex NMR spectra (385)

10. NMR of paramagnetic compounds (387)11. Chemically induced dynamic nuclear polarization

(CIDNP) (388)12. NMR of liquid crystals (389)Magnetic Resonance Imaging (MRI) (390)Electron spin resonance (ESR) spectra (392)

ESR spectrum of an unpaired electron (392)Hyperfine structure in ESR spectra (393)g–factor (396)Applications of ESR spectra (397)

ESR of anisotropic systems (399)1. g-factor and hyperfine splittings (399)2. Kramers’ degeneracy and ZFS (401)3. ESR of Transition metal complexes (402)4. Multiple resonance techniques in ESR (406)Spin Hamiltonian (410)Mössbauer spectroscopy (412)

Basic principle of NRF (412)Mössbauer experiment (414)More about Mössbauer spectroscopy (414)

1. Chemical isomer shift (414)2. Nuclear quadrupole splitting (414)3. Nuclear Zeeman splitting (415)

Photoelectron spectroscopy (PES) (416)Nuclear quadrupole resonance (NQR) spectroscopy

(420)Zeeman effect in NQR spectra (425)Townes–Dailey theory of NQR coupling (426)Applications of NQR spectroscopy (427)

Review Questions and Problems (429)

8. Electric and Magnetic Properties ofMolecules 431–449Electric properties of molecules (431)Polarization of a molecule in an electric field (431)

Clausius–Mosotti equation (432)Debye equation (433)

Dependence of polarizability on frequency (436)

iv

Bond moments (440)Dipole moments and molecular structure (440)Group moments (441)Magnetic properties of molecules (442)

Molecular interpretation of diamagnetism andparamagnetism (444)

Measurement of magnetic susceptibility (447)Ferromagnetism and antiferromagnetism (448)

Review Questions and Problems (449)

9. The Gaseous State Part I : Ideal Gases450-478

Kinetic molecular theory of gases (450)Pressure of an ideal gas (450)Derivation of the gas laws (451)Ideal gas equation (452)Kinetic energy and temperature (453)

Maxwell distribution of molecular velocities (454)Maxwell distribution of molecular energies (455)Types of molecular velocities (456)Derivation of expressions for molecular velocities

(457)Expansivity and compressibility (460)Collision parameters (461)

Collision diameter (461)Collision cross-section (461)Collision number (461)Collision frequency (462)Mean free path (462)

Transport properties (463)Thermal conductivity (465)Viscosity (467)Diffusion (470)Summary of transport properties in a gas (471)

Degrees of freedom of a gaseous molecule(472)

The principle of equipartition of energy (474)Contributions to heat capacity of an ideal gas (475)The Barometric formula (477)Revies Questions and Problems (478).

10. The Gaseous State Part II : Real Gases479-498

Deviations of real gases from ideal behaviour (479)Explanation of the deviations (480)

Equations of state for real gases (481)van der Waals equation of state (481)Other equations of state (484)Virial equation of state (486)

Intermolecular forces (487)Lennard–Jones (6–12) potential (488)

Second virial coefficient (488)Critical phenomena (489)

The P–V isotherms of carbon dioxide (490)van der Waals equation and critical state

(491)Law (principle) of corresponding states (493)

Molar mass and density of a real gas (495)Liquefaction of gases (495)Production of low temperatures by adiabatic

demagnetization (496)Review Questions and Problems (498)

11. The Liquid State : Physical Properties ofLiquids 499-515Gaseous, liquid and solid states (499)Vacancy theory of liquids (499)Free volume of a liquid (500)Physical properties of liquids (500)

Vapour pressure (500)Surface tension (502)Kelvin equation for vapour pressure of adroplet (506)

Excess pressure in a drop (506)Laplace equation and the Young-Laplace

equation (507)Surface active agents (507)Viscosity (508)

Effect of temperature on viscosity (509)Reynolds number (509)

Refraction (510)Optical activity (511)ORD and CD (512)Structure of liquids (512)Review Questions and problems (514)

12. Liquid Crystals : The Mesomorphic State516-524

Liquid crystals (516)Vapour pressure-temperature diagrams (517)Thermography (518)LCDs and the seven segment cell (518)Classification of Thermotropic liquid crystals (520)

Smectic liquid crystals (520)Nematic liquid crystals (521)Cholesteric liquid crystals (521)Disc shaped liquid crystals (522)Polymer liquid crystals (522)

Polymorphism in thermotropic liquid crystals (522)Pressure-induced mesomorphism (523)Molecular arrangements in various states of liquidcrystals (524)Review Questions (524)

v

13. The First Law of Thermodynamics525-551

Importance of thermodynamics (525)Limitations of thermodynamics (525)Some basic terms used in thermodynamics (525)Thermodynamic equilibrium (526)Extensive and intensive properties (527)Thermodynamic processes (527)Nature of work and heat (528)The first law of thermodynamics (528)Internal energy (529)State functions, exact and inexact differentials (530)

Euler reciprocal relation (531)The cyclic rule (532)

Enthalpy (533)Heat capacity (534)

Relation between Cp and Cv (535)Expansion of an ideal gas and changes inthermodynamic properties (535)

A. Isothermal expansion (535)B. Adiabatic expansion (538)Final temperatures in reversible and irreversibleadiabatic expansions (538)Comparison of isothermal and adiabaticexpansions (542)

Reversible isothermal expansion of a real gas (543)Joule–Thomson effect (545)

Joule–Thomson coefficient in an ideal gas (546)Joule–Thomson coefficient in a real gas (547)

Zeroeth law of thermodynamics (549)Absolute temperature scale (549)Review Questions and Problems (550)

14. Thermochemistry 552-570Change of internal energy in a chemical reaction

(552)Change of enthalpy in a chemical reaction (552)Exothermic and endothermic reactions (552)Relation between heats of reaction at constantvolume and at constant pressure (553)Standard enthalpy changes of reactions (555)Determination of enthalpies of reactions (558)Variation of enthalpy of a reaction with temperature:The Kirchhoff equation (560)Flame and explosion temperatures (562)Hess’s law of constant heat summation (563)

Applications of Hess’s law (564)Measuring the enthalpy of combustion (565)Bond energies (567)

Applications of bond energies (568)Review Questions and Problems (569)

15. The Second Law of Thermodynamics571-608

Limitations of the first law : Need for the secondlaw (571)Spontaneous or irreversible processes (571)Cyclic process (572)Carnot cycle (572)The second law of thermodynamics (574)

Carnot theorem (574)Concept of entropy (575)

Entropy change in an isothermal expansion of anideal gas (577)Entropy changes in reversible and irreversible

processes (577)Entropy changes accompanying changes of phase

(578)Calculation of entropy changes of an ideal gaswith change in P, V and T (580)Entropy of mixing of ideal gases (582)Standard entropies (583)Physical significance of entropy (584)Work and free energy functions (584)Variation of free energy with T and P (586)Maxwell’s relations (586)Criteria for reversible and irreversible processes

(589)Gibbs–Helmholtz equation (590)Thermodynamics of open systems : Partial molarproperties (591)

Chemical potential (592)Gibbs–Duhem equation (592)

Variation of chemical potential with temperature (593)Variation of chemical potential with pressure (593)Chemical potential in a system of ideal gases (593)Determination of partial molar quantities (595)Clapeyron equation (597)Clapeyron–Clausius equation (598)Applications of the Clapeyron–Clausius equation

(600)Fugacity and activity (601)Determination of fugacity of a gas (602)Fugacity of a gas in a gaseous mixture (605)Fugacity of a liquid component in a solution (605)Concept of activity (605)Activity coefficient (606)Standard states (606)Review Questions and Problems (607)

vi

16. The Third Law of Thermodynamics609-619

Nernst heat theorem (609)Third law of thermodynamics (610)Determination of absolute entropies (610)Experimental verification of the third law (615)Entropies of real gases (615)Entropy changes in chemical reactions (617)The Boltzmann entropy equation (618)Residual entropy (618)Review Questions and Problems (619)

17. Chemical Equilibria 620-660Spontaneous reactions (620)

Standard free energy change (621)

Chemical equilibrium (624)

Law of mass action (624)

Thermodynamic derivation of the law of mass action(624)

van’t Hoff reaction isotherm (626)

Relations betweenKp, Kc and Kx (626)

De Donder’s treatment of chemical equilibria (628)

Thermodynamic relations for chemical affinity (629)

Homogeneous Equilibria (630)

Temperature–dependence of the equilibriumconstant : The van’t Hoff equation (637)

Integrated form of the van’t Hoff equation (638)

Pressure - dependence of equilibrium constant (640)

Heterogeneous equilibria (642)

Equilibrium constants for reactions involving realgases (645)

Le Chatelier’s principle (646)

Linear free energy relationships (LFERs) (648)

Hammett Equation (648)

Hammett equation as LFER (651)

Reaction mechanisms and the Hammett equation (652)

Taft equation (654)

Biochemical equilibria (654)

ATP and its role in bioenergetics (654)

Binding of oxygen by myoglobin and hemoglobin (657)

Review Questions and Problems (659)

18. Phase Equilibria 661—695Phase (661)Components (661)Degree of freedom (663)Conditions for equilibrium between phases (664)The Gibbs phase rule (665)The Derivation of the phase rule (665)One–component systems (667)

Water system (668)Carbon dioxide system (671)Sulphur system (672)

Some typical solved examples for one-componentsystems (675)

Liquid helium system (678)High pressure phase diagrams (678)

1. Water system (678)2. Carbon system (679)

Two–component systems (679)Type A. Simple eutectic systems (679)

Thermal analysis : cooling curves (681)Lead–silver system (682)Bismuth–cadmium system (683)Potassium iodide–water system (683)Freezing mixtures (685)

Type B. Systems in which two components form astable compound (685)Formation of compounds with congruent meltingpoints (686)Formation of compounds with incongruentmelting points (687)Calculation of eutectic point and eutectic composition

(688)Typical solved examples for two-component systems

(688)Three–component solid–liquid systems (690)

Acetic acid–chloroform–water system (690)Three–component systems consisting of two saltsand water (691)

The Ehrenfest classification of phase transitions(691)Review Questions and Problems (695)

1 9 . The Nernst Distribution Law 696-705Nernst Distribution law (696)

Thermodynamic derivation (698)Association of the solute in one of the solvents

(698)Dissociation of the solute in one of the solvents

(700)Solute enters into chemical combination withone of the solvents (700)

vii

Applications of the distribution law (701)Study of complex ions (701)Solvent extraction (702)

Review Questions and Problems (705)

20. Ionic Equilibria 706-749Acids and bases (706)

Arrhenius concept (706)Brönsted-Lowry concept (706)Lewis concept (710)

Dissociation of weak acids and bases (712)Dissociation of a weak acid (712)Dissociation of polybasic acids (713)Dissociation of a weak base (714)

Dissociation of water (715)pH scale (716)Some other logarithmic expressions (718)Common ion effect (719)Buffer solutions (720)Buffer mixture of a weak acid and its salt (721)Calculation of pH values of buffer mixtures :

Henderson-Hasselbalch equation (722)Buffer mixture of a weak base and its salt (724)Hydrolysis of salts (724)

Salts of weak acids and strong bases (725)Salts of weak bases and strong acids (727)Salts of weak acids and weak bases (728)Determination of degree of hydrolysis (730)

Acid–base indicators (733)Action of phenolphthalein (734)Action of methyl organge (734)

Acid–base titrations and use of indicators (735)Mathematical treatment of acid–base titrations (736)Solubility product (740)Applications of solubility product principle (742)Ionic equilibria involving complex ions (746)Review Questions and Problems (748)

21. Solutions of Non–Electrolytes 750-777Solutions of liquids in liquids (750)Raoult’s law (752)Vapour pressures of ideal solutions (753)Activity of a component in an ideal solution (756)Chemical potentials of ideal and Non-ideal solutions.

(756)Gibbs–Duhem–Margules equation (757)Temperature-dependence of vapour pressure of asolution (759)Thermodynamics of ideal solutions (759)

Free energy change of mixing for an ideal solution(759)

Volume change and enthalpy change of mixingfor an ideal solution (760)Entropy change of mixing for an ideal solution

(761)Vapour pressures of non–ideal solutions (763)Vapour pressure–composition and boiling point-

composition curves of completely misciblebinary solutions (764)

Fractional distillation of binary liquid solutions (766)Azeotropic mixtures (766)TheLever rule and fractional distillation (768)Distillation of immiscible liquids (768)Solubility of partially miscible liquids (770)

UCST and LCST (771)Phenol–water system (772)Aniline–hexane system (772)Triethylamine–water system (772)Nicotine–water system (773)

Solutions of gases in liquids (773)Factors influencing solubility of a gas (773)Henry’s law (774)Henry’s law and Raoult’s law (775)

Review Questions and Problems (776)

2 2 . Colligative Properties of DiluteSol ut i ons 778-800Colligative properties (778)

Vapour pressure lowering (778)Osmosis and osmotic pressure (781)Determination of molar mass from osmoticpressure measurements (783)Relation between osmotic pressure and vapourpressure lowering of an ideal solution (784)Theories of semi–permeability (785)Effects of osmosis and semi–permeability (786)Reverse osmosis (786)Boiling point elevation (788)Freezing point depression (792)Abnormal Results and the van’t Hoff factor (796)

Review Questions and Problems (799)

23. Electrochemistry Part I : ElectrolyticConductance and Transference 801-834Electrolytic conductance (801)

Specific conductance (801)Equivalent conductance (801)Molar conductance (802)

Variation of molar conductance with dilution (803)

viii

Ionic mobility (804)Hittorf’s theoretical device (805)Transport number (806)Determination of transport numbers (807)

Hittorf’s method (807)Moving boundary method (809)

Kohlrausch’s law (810)Calculation of molar ionic conductance (810)Relation between molar Ionic conductance and ionicmobility (812)Determination of ionic mobility (814)Applications of Kohlrausch’s law (815)Diffusion and ionic mobility (816)Applications of conductance measurements (818)

Conductometric titrations (821)Precipitation titrations (822)

Ostwald’s dilution law (822)Debye–Hückel theory of strong electrolytes

(824)Activity coefficients of electrolytes (827)Ionic strength (829)Debye–Hückel theory of mean activity coefficientsof strong electrolytes (830)

Debye-Hückel Limiting Law (DHLL) (832)Review Questions and Problems (833)

24. Electrochemistry Part II : ElectromotiveForce of Galvanic Cells 835—881Galvanic cells (835)Reversible electrodes (836)Single electrode potential (838)Thermodynamics of reversible electrodes and cells

(840)Nernst equation (844)Standard electrode potentials : The Electrochemical

series (846)Electromotive force of galvanic cells (848)Activity and mean ionic activity of electrolytes (852)Concentration cells (853)

Electrode–concentration cells (853)Electrolyte–concentration cells (855)

Types of electrolyte concentration cells (857)Concentration cells without transference (857)Concentration cells with transference (859)

Liquid junction potential (860)Fuel cells (862)Applications of EMF measurements (865)1. Determination of activity coefficients of electrolytes

(865)2. Determination of transport numbers (867)

3. Determination of valency of ions in doubtful cases (867)

4. Determination of solubility product constants (868)5. Determination of pH (869)Potentiometric titrations (872)1. Acid–base titrations (872)2. Redox titrations (875)3. Precipitation titrations (878)Oxidation–reduction indicators (879)Review Questions and Problems (880)

25. Electrochemistry Part III : ElectrifiedInterfaces, etc. 882-934I. Debye-Hückel theory of activity coefficients ofstrong electrolytes (882)Determination of solute activites from solventactivities (885)Dependence of electolyte activity on the hydrationnumber (886)Bjerrum’s theory of ion association in electrolytesolutions (887)Determinaiton of interfacial tension of mercury as afunction of potential across the interface (891)II. Electrified interfaces (892)A. Quantitative thermodynamic treatment ofelectrified interfaces (892)

Determination of the surface excess (895)B. Structures of the electrified interfaces (898)

1. Helmholtz-Perrin model (899)2. Gouy-Chapman diffuse charge model of

the double layer (900)3. Stern model (902)

C. Structure of semiconductor interfaces (904)Garrett-Brattain space charge inside anintrinsic semiconductor (905)

III. Electrocatalysis (909)Mechanism of electrocatalysis (909)Volcanoes (910)

IV. Kinetics of electrode reactions (911)Kinetics of an electrode reaction (912)Butler-Volmer equation (914)Difusion overpotential (916)

V. Irreversible electrode processes (917)1. Overvoltage (917)

Corrosion and its inhibition (918)2. Polarography (919)Ilkovic equation and its derivation from

Fick’s laws of diffusion (923)Half-wave potential (925)

ix

Applications of polarography (926)Amperometric titrations (929)

VI. Bioelectrochemistry (930)Electrochemical mechanisms of the nervoussystem (931)Review Questions (933)

26. Statistical Thermodynamics 935-988Statistical thermodynamics (935)Types of statistics (935)

Maxwell–Boltzmann statistics (936)Bose–Einstein statistics (938)Fermi–Dirac statistics (939)

Evaluation of Lagrange’s underterminedmultipliers (940)

Molecular partition function for an ideal gas (942)Translational partition function (943)Rotational partition function (945)Vibrational partition function (946)Electronic partition function (948)Nuclear partition function (951)

Thermodynamic properties in terms of the partitionfunction (951)Thermodynamic properties of an ideal monatomicgas (953)Thermodynamic properties of an ideal diatomicgas (954)Rotational partition function of homonuclear diatomicmolecules and the nuclear spin (956)Statistical thermodynamics of ortho- and para-hydrogen (958)Application of BE statistics to black body radiation

(960)Quantum statistics : ideal Bose-Einstein gas (963)a. Bose-Einstein distribution (963)b. Bose-Einstein condensation (964)c. Thermodynamic properties of an ideal BE gas

(967)Quantum statistics : ideal Fermi-Dirac gas (969)a. Fermi-Dirac distribution (969)b. Thermodynamic properties of an ideal FD gas

(973)Molar partition function of a system (976)Partition function for a real gas (977)Equilibrium constant of an ideal gas reaction interms of partition functions (977)Heat capacities of monatomic crystals (982)

The Einstein theory of heat capacities (982)The Debye theory of heat capacities (983)

Review Questions and Problems (986)

27. Classical Statistical Mechanics 989-1032Phase space, ensembles and ensemble average

(989)Postulate of equal a priori probability in classicalstatistical mechanics (992)Microcanonical ensemble (993)Entropy of a perfect gas using the classicalmicrocanonical ensemble (994)Entropy of mixing of ideal gases and the Gibbsparadox (995)Quantum statistical mechanics (996)

Quantal microcanonical ensemble (998)Quantization of phase space and calculation ofnumber of microstates (N, V, E) accessibleto a system (1000)Validity of the classical limit of statisticalmechanics (1001)System of identical particles and symmetryof wave functions (1002)

Entropy and probability (1004)Canonical ensemble (1004)

Classical canonical distribution (1005)Canonical partition function and thermodynamicquantities (1006)Application of the classical canonical distributionto an ideal gas (1007)Law of equipartition of energy (1009)Quantal canonical distribution (1010)

Grand canonical ensemble (1011)Grand canonical partition function andthermodynamic quantities (1013)Quantal grand canonical distribution (1014)

Fluctuations in various ensembles (1015)1. Canonical ensemble (1015)2. Grand canonical ensemble (1016)

Comparison of various ensembles (1017)Liquid helium (1018)Two-fluid model for liquid helium II: London-TiszaTheory (1019)Landau theory of liquid helium (1022)Statistical mechanics of Imperfect gases (1026)

Evaluation of the second virial coefficient (1029)Derivation of the van der Waals equation for agas from the virial equation (1030)

Review Questions (1031)

2 8 . Chemical Kinetics 1033-1111Experimental methods for studying kinetics ofreactions (1033)Rate of reactions (1034)Rate law and the rate constant (1035)

x

Order of a reaction (1035)Units of rate constant (1037)Integration of rate expressions (1038)

First–order reactions (1038)Second–order reactions (1042)Third–order reactions (1045)Zero–order reactions (1047)

Half–life time of a reaction (1047)Methods of determining order of a reaction (1051)Order and molecularity of reactions (1052)Mechanisms of complex reactions (1053)Collisions and encounters (1054)Effect of temperature on reaction rates (1056)

Effect of a catalyst (1057)Arrhenius equation (1058)

Theories of reaction rates (1060)Collision theory of bimolecular gaseous reactions

(1060)Activated complex theory (ACT) of bimoleculargaseous reactions (1063)

Eyring equation (1065)Statistical mechanical derivation of the rate constantusing TST (1067)Theories of unimolecular gaseous reactions (1070)1. Lindemann theory (1070)2. Hinshelwood theory (1073)3. RRK theory (1074)4. RRKM theory (1077)Kinetics of complex reactions (1079)

1. Opposing or reversible reactions (1079)2. Kinetics of consecutive reactions (1081)3. Kinetics of chain reactions (1082)4. Kinetics of branched chain reactions (1085)

Kinetics of reactions in solution (1086)Diffusion–controlled reactions in solution (1087)

Debye–Smoluchowski equation (1087)Influence of ionic strength on rates of reactions

(1088)Influence of solvent on reaction rates (1090)Reactions in flow systems (1090)Kinetics of fast reactions (1093)Flow methods for fast reactions (1095)Pulse methods (1096)Flash photolysis (1096)Pulse radiolysis (1097)Molecular reaction dynamics (1097)Potential energy surfaces (1099)Theoretical calculation of the rate constant (1102)Electron-transfer reactions : The Marcus theory

(1105)

Dynamics of electron tunnelling in the Marcus theory(1107)

The Marcus cross relation (1109)Review Questions and Problems (1110)

29. Photochemistry 1112-1146Consequences of light absorption : The Jablonskidiagram (1113)Beer–Lambert law (1115)Laws of photochemistry (1118)Grotthus–Draper law (1118)Stark–Einstein law of photochemicalequivalence (1118)Quantum yield (1118)Determination of quantum yields (1119)Photochemical reactions (1123)Photochemical rate law (1124)Kinetics of photochemical reactions (1125)Kinetics of hydrogen–chlorine reaction (1125)Kinetics of hydrogen–bromine reaction (1026)Kinetics of decomposition of HI (1127)Kinetics of the anthracene reaction (1128)Ozone layer in the stratosphere (1129)Energy transfer in photochemical reactions :Photosensitization and quenching (1131)Quenching of fluorescence : The Stern-Volmerequation (1133)Chemiluminescence (1134)Rates of intramolecular photophysical processesand intermolecular energy transfer (1135)Electronic spectra and photochemistry (1137)

The oscillator strength (1138)Geometry of excited states (1138)The laser and the maser (1139)Applications of the lasers in chemistry (1143)Femtosecond transition state spectroscopy (1145)Review Questions and Problems (1146)

30. Catalysis 1147-1164Characteristics of catalytic reactions (1148)Acid–base catalysis (1148)Enzyme catalysis (1150)

Mechanism and kinetics of enzyme–catalysed reactions (1150)The Michaelis–Menten equation (1151)

Effect of temperature on enzyme catalysis (1154)Heterogeneous catalysis : Surface reactions (1155)

Kinetics of surface reactions (1155)Unimolecular surface reactions (1155)Bimolecular surface reactions (1158)

pH-dependence of rate constants of catalyzedreactions (1159)

xi

Autocatalysis and oscillatory reactions (1161)Review Questions (1162)

3 1 . The Solid State 1165-1212Difference between crystalline and amorphous

solids (1165)Symmetry in crystal systems (1166)Point groups and space groups (1168)Space lattice and the unit cell (1169)Bravais lattices (1169)Seven crystal systems (1170)Lattice energy of an ionic crystal (1173)Born-Lande equation and the Born-Habercycle (1174)Law of rational indices (1175)Miller indices (1175)Interplanar spacing in a crystal system (1175)X–ray diffraction (1176)

The Bragg equation (1176)Experimental methods : The rotating crystal andthe powder (The Debye-Scherrer) techniques (1177)X-ray diffraction pattern for a cubic system

(1180)X-ray diffration pattern for tungsten crystal (1181)Fourier synthesis of electron density in a crystal

(1183)Patterson synthesis (1184)Electron diffraction (1186)Neutron diffraction (1187)Types of crystals (1188)

Molecular crystals (1188)Covalent crystals (1189)Ionic crystals (1189)

Characteristic structures of ionic crystals (1190)Metallic crystals (1193)Free electron model of metals (1194)Band theory of solids (1197)Energy band theory of conductors, semiconductorsand insulators (1199)Superconductivity (1202)

LTSC and HTSC (1202)Imperfections in a crystal (1204)Point defects (1204)

Schottky defects (1204)Frenkel defects (1206)Colour centres (1207)Line defects : Dislocations (1208)Imperfections due to transient atomicdisplacement (1209)

Quasicrystals (1209)Review Questions and Problems (1211)

32. The Colloidal State 1213-1250The colloidal systems (1213)Preparation of lyophobic colloidal solutions (1213)

A. Dispersion methods (1213)B. Condensation methods (1215)

Purification of colloidal solutions (1216)Properties of colloidal systems (1216)Properties of hydrophobic colloidal systems

(1218)I. Electrical properties (1218)

Charge on colloidal particles (1218)The electrical double layer (1219)DLVO theory of the stability of lyophobiccolloids (1221)Coagulation of colloidal solutions (1222)

II. Electrokinetic properties (1224)Electrophoresis (1224)Electro–osmosis (1225)

Determination of size of colloidal particles (1225)Surfactants (Surface-active agents) (1226)Hydrophile-Lipophile balance (HLB) (1228)Micelle formation (1229)

The mass action model and the phaseseparation model (1229)Shape and structure of micelles (1231)Micellar aggregation numbers (1232)Critical micelle concentration (CMC) (1233)Factors affecting CMC in aqueous media

(1234)Thermodynamic approach to CMC (1236)Thermodynamics of micellization (1237)

Solubilization (1238)Location of solubilizates in micelles (1239)The phase rule of solubilization (1240)

Micellar catalysis (1240)Emulsification by surfactants (1242)

Macroemulsions (1242)Factors determining stability of emulsions (1243)Microemulsions (1245)Theories of emulsions (1246)

The selection of surfactants as emulsifying agents(1246)

Gels and their preparation (1247)Importance and applications of colloids (1248)Review Questions (1250)

xii

33. Surface Chemistry 1251-1272Adsorption by solids (1251)

Chemisorption (1251)Applications of adsorption (1252)Adsorption of gases by solids (1252)Factors influencing adsorption (1253)

The Freundlich adsorption isotherm (1253)The Langmuir theory of adsorption (1256)The BET theory of multilayer adsorption (1259)Derivation of the BET equation (1261)Types of adsorption isotherms (1263)Adsorption from solution (1264)

The Gibbs adsorption isotherm (1264)Insoluble surface films on liquids (1267)Modern techniques for investigating surfaces :LEED, PES, STM, EXAFS and SEXAFS (1269)Review Questions and Problems (1272)

34. Macromolecules 1273-1326Macromolecules (1273)Classification of polymers (1275)Polymerization reactions (1276)Molar masses of polymers (1277)Determination of molar masses of macromolecules

(1279)Viscometry (1279)Osmometry (1281)Donnan membrane equilibrium (1283)Ultracentrifugation (1285)The Svedberg equation (1286)Light scattering (1289)The Zimm plot (1292)Turbidity (1292)

Diffusion (1293)The Stokes–Einstein equation (1294)The Einstein–Smoluchowski equation (1294)

Conformations and configurations ofmacromolecules in solution (1296)

Miscellaneous solved examples (1299)Kinetics of polymerization (1301)Molar mass distribution in step-growth(condensation) polymerization (1303)Electronically conducting polymers (1306)Thermodynamics of polymer solutions : The Flory-Huggins theory (1309)Helix-random coil transitions in polypeptides

(1311)Structure of proteins (1312)

Protein folding and denaturation (1315)-helix and -pleated sheet structures ofproteins (1315)Hierarchy of protein structure (1317)Experimental methods for protein structure

determination (1318)Structure of nucleic acids (1319)Polymerase chain reaction (PCR) (1323)Separation of proteins and nucleic acids (1324)Review Questions and Problems (1325)

35. Mass Spectrometry 1327-1342Basic theory (1327)Dynamics of electron-molecule collisions in massspectrometry (1331)Factors influencing fragmentation (1332)Evaluation of heats of sublimation of solids (1332)Calculation of appearance potentials and ionizationpotentials (1332)Fragmentation processes (1333)Rearrangements : The McLafferty rearrangement

(1335)Molecular ion (1336)Molar mass determination by mass spectrometry

(1337)Finger print application of mass spectra (1338)Review Questions (1342)

36. Irreversible Thermodynamics 1343-1362Phenomenological laws and Onsager’s reciprocalrelations (1343)Conservation of mass and energy in closed andopen systems (1345)Entropy production due to heat flow (1348)Entropy production in chemical reactions (1349)Entropy production and Entropy flow in opensystems (1350)Transformation properties of fluxes and forces

(1353)Principle of microscopic reversibility and the Onsagerreciprocal relations (1354)Verification of the Onsager relations (1355)Electrokinetic effects (1356)Stationary non-equilibrium states (1359)Applications of irreversible thermodynamics tobiological systems (1360)Nonlinear thermodynamics of irreversible processes

(1361)Concluding remarks (1362)Review Questions (1362)

General Bibliography 1363-1366

Index 1367-1376

Chapter 0Mathematical Concepts

Addition theorem for probabilities (13)Argand diagram (17)Chain rule (8)Complex numbers (17)Complex conjugate (17)Conditional probability (13)Curve sketching (1)Cyclic rule (8)Determinants (16)Differentiation (4)Differentiation formulas (4)Exponential function (3)Euler reciprocal relation (7)Events (12)

INDEX

(i)

Factorial notation (11)Functions of a real variable (2)Fundamental theorem (11)Gaussian elimination (16)

Inclination and slope of a line (1)Integration (8)

formulas of (9)methods of (9)

Inverse of a matrix (16)Logarithmic function (3)Mathematical expectation (14)Matrices (15)Maxima and minima (5)Modulus of a complex number (17)Memorabilia Physicomathematica (19)

Multiplicative theorem for probabilities(13)Mutually exclusive event (13)Other mathematical relations (14)Partial differentiation (7)Permutations and combinations (11)Polynomial (2)Probability (12)Random experiment (12)Sample space (12)Series (17)Stirling approximation (17)Theorems of probability (13)Total differential (7)Trigonometric functions (3)Vectors (14)

Aab initio calculations 232ABMO 174Absolute activity 1293Absolute entropies 610determination of 610standard 613Absorption spectrum 302Acid–Base catalysis 1148

indicators 733titrations 735

Acids and Bases 706Arrhenius concept 706Bronsted-Lowry concept 706Lewis concept 710

Actin 1312Actinometer 1120Activated complex theory 1063Activation energy 1058Activity 605

coefficient 606Activity coefficients 827Addition polymerization 1301Adhesion 505Adiabatic demagnetization 496Adiabatic expansion 538Adsorption 1251

applications of 1252BET theory 1259heat of 1253isobar 1254isostere 1254isotherms 1263multilayer 1259from solution 1264Langmuir 1256

Adenosine diphosphate (ADP) 655Adenosine triphosphate (ATP) 654

Affinity 1279Allotropy 672Amperometric titrations 929

Amphipathy 1226Amphiphile 1226Angular functions 65Angular momentum 87,141,165

Addition of 169Matrices 165

Angular momentum operators 141Anharmonicity constant 317Aniline–hexane system 772Anisotropy 516Antibodies 1238Antiferromagnetism 448Anthrancene reaction 1128Anti-Stokes Raman spectroscopy

334Apparent equilibrium constant 655Apparent standard reactionGibbs energy 656Appearance potentials 1332Associated Legendre polynomials 67Arrhenius equation 1058Arrhenius frequency factor 1058Arrhenius parameters 1058Arrhenius activation energy 1058Asymmetric top molecules 314Asymmetry parameter 421Atactic polymers 1275Atomic populations 238Atomic states and term symbols 149Atomic number 23Atomic spectra 154

fine structure 155hyperfine structure 162Stark effect 162Zeeman effect 159

Aufbau principle 87Auger electron spectroscopy

(AES) 1270Austin Model 1 237Autocatalysis 1161Auxochrome 339

Avogadro’s law 452Axis of rotation

improper 248proper 247

Azeotropic mixtures 766

BBalmer series 30Bancroft rule 1242Band spectra 305Band theory 1197Barometric formula 477Base pairing in DNA 1320Basis set 232Bathochromic shift 339BBGKY equations 514Beer–Lambert law 1115Berthelot equation 485BET adsorption isotherm 1259BET equation 1261Binding and antibinding regions 232Bipolaron 1308BPP theory of relaxation

processes 372Biochemical equilibria 654Bioelectrochemistry 930Biological electrochemical cell 930Bjerrum theory of ion association 887Bismuth–cadmium system

(phase rule) 683Black body radiation 24

and BE statistics 960Bloch function 1197Blue shift 339BMO 177BCS theory 1202Bohr’s correspondence principle 109Bohr frequency condition 355Bohr’s theory 26Bohr radius 28Bohr–Sommerfeld theory 31

Chapters 1–36

1368 PRINCIPLES OF PHYSICAL CHEMISTRY

GENERALBIBLIOGRAPHY3GENERALBIBLIOGRAPHY(ii)

Boiling point elevation 788and molar mass 790Boltzmann constant 453Boltzmann population 311Boltzmann factor 311Boltzons 935Boltzmann entropy equation 618Bomb calorimeter 565Bond energies 563Bond length 260Bond moments 440Bond order 186Born-Haber cycle 1174Born’s interpretation 42Born–Oppenheimer approximation174Born–Lande equation 1174Bose-Einstein condensation 964Bose-Einstein distribution 963Bose–Einstein statistics 936

and ideal photon gas 960Bose gas 962Bosons 936Bound state 438Boyle temperature 484B–Z reaction 1161Brackett series 29Bragg equation 1176Branched chain reaction 1085Bravais lattices 1169Brillouin zone 1198Brownian movement 1218Buffer solutions 720

capacity and buffer index 721Butler-Volmer equation 914

CCage effect 1054Calomel electrode, saturated

(SCE) 837Canonical commutation relation 138Canonical ensemble 1004Canonical partition function 1006Canonical structures 196Capillary-active and inactive 1266Capillary condensation 1264Capillary electrophoresis 1325Carbon dioxide system

(phase rule) 679Carbon dioxide laser 1145Carnot, cycle 572

theorem 574Catalysis 1147

acid–base 1149auto 1161characteristics of 1148enzyme 1150heterogeneous 1157homogeneous 1148

Cathode rays 21Cell constant 802Cells, concentration 853

fuel 862Chain reactions in kinectics 1082

classification 1213coagulation 1221origin of charge 1218peptization 1214preparation 1213properties 1216protective 1222

Combination bands 322Combustion, enthalpy of 555Common ion effect 719Commutation relations 141Commutator 141Complex NMR spectra 385Complex reactions,

mechanism of 1053Components, phase rule 661Compound triplet 158Compressibility 460Compressibility factor 479Compton effect 36Compton shift 36Compton wave length 37Computational quantumchemistry 232Computer-assisted tomography

(CAT) 391Computer programs 238Computer simulation of liquids 512Concentration cells 853

with transference 859without transference 857

Concentration polarisation 919CNDO 238Conductance, electrolytic 801

equivalent 801molar 802specific 801

Condensation polymerization 1303Conductometric titrations 821Configurational integral 1026Configuration interaction 236Conductors, semiconductors 1199

and insulatorsConformations of polymers 1296Congruent melting point 686Conjugate elements 250Conjugate acids and bases 707Conjugate solutions 772Conjugated molecules 345Conservation of energy 528Conservation of mass and

energy 1345Conservative forces 461Consolute temperature 771Constrained chain 1300Constructive interference 1199Contact shift 387Continuity of state 490Contour length 1296Cooling curves 681Cooper pairs 1202Cooperativity 658Corey-Pauling rules 1313

Chandrasekhar limit 976Character 252Character tables 255Characteristic rotational

temperature 945Characteristic vibrational

temperature 947Charge-Coupled device (CCD)

sensor 1209Charge transfer bands 344Charge–transfer spectra 340Charles’ law 452Chemical affinity 629Chemical equilibrium 620

law of 624Chemical shift 358Chemical shift reagents 386Chemical isomer shift 414Chemical kinetics 1033Chemical potential 592Chemiluminescence 1134Chemisorption 1251Chlorine electrode 837Cholesteric liquid crystals 521Chromophores 338Circular dichroism (CD) 512CIDNP 388Clapeyron equation 597Clapeyron–Clausius equation 598Class 250Classical and quantum limits of

statistical mechanics 1001Classical canonical distribution 1005Classical stastistical mechanics 989Claude’s process 496Clausius equation 485Clausius–Mosotti equation 432Clebsch–Gordon coefficients 170Clebsch–Gordon series 170Cluster expansion 1027Coagulation of colloidal solutions

1221Coefficient of viscosity 508Coefficients of hybridization 200Coherence length 1142Coherent anti-Stokes

Raman spectroscopy (CARS) 334Cohesion 505Collagen 1312Colligative properties of dilute

solutions 778Collisions and encounters 1087Collision broadening 304Collision parameters 461

Collision cross-section 461Collision diameter 461Collision frequency 462Collision number 461

Collision theory 1060Colour centres 1207Colloidal particles 1213Colloidal state 1213

applications 1177

INDEX 1369(iii)Correct Bolzmann counting 996Correlation diagram 225Correlation energy 233Correlation spectroscopy

(COSY) 384Corresponding states, principle

of 493Corrosion of metals 918Coulomb operator 234Counter ions 1220Coupled flows 1344Coupled reactions 1351Covalent bond 173Criteria for reversible

and irreversible processes 589Critical constants of a gas 489Critical micelle concentration

(CMC) 1233Critical phenomena 489Critical solution temperature

(CST) 771Critical temperature 490Critical volume 489Cryosopic constant 794Crystal imperfections 1204Crystals, covalent 1189

ionic 1189metallic 1193molecular 1188

Crystallographic symmetry 261Crystal systems 262Curie temperature 448Curved Hammett plots 653Cyclic rule 8,532Cyclic process 872

DDalton’s law 453Daniell cell 835Davisson-Germer experiment 35d-d bands 343de Broglie’s equation 33

experimental verification of 34de Donder’s treatment 628Debye equation 433Debye’s T3 Law 986Debye-Falkenhagen effect 826Debye–Hückel limiting law 832Debye–Hückel theory,

of strong electrolytes 824, 882of mean activity coefficients

830,882Debye-Hückel-Onsager equation826Debye length 831Debye–Scherrer method 1178Debye–Smoluchowski equation 1087Debye theory of heat capacity 983Debye temperature 986Defects in crystals 1204Degeneracy 53Degeneracy temperature 966Degenerate BE gas 966Degree of advancement 628

Degree of association 796Degree of dissociation 632,797Degrees of freedom 472

rotational 472translational 472vibrational 473

Degrees of freedom (phase rule) 663Degree of hydrolysis 726Degree of polymerization 1275Delocalization energy 208Detergents 507Density functional theory (DFT) 239Density of states (DOS) 245,1195Density matrix (statistical matrix) 997Destructive interference 1199Deviations from ideality 480Diamagnetism 444Diamond, structure of 1189Diatomic rotor 307Dieterici equation 484Difference bands 322Diffraction, electron 1186neutron 1187Diffusion 470,1293Diffusion coefficient 1293Diffusion-controlled reactions 1087Diffusion layer 920Diffusion overpotential 916Dipole-dipole interaction 487Dipole moments and

molecular structure 440Dirac delta function 994Dirac’s bra and ket notation 996Dirac’s relativistic quantum

mechanics 37Direct product 275Disc–shaped liquid crystals 522Dislocations 1208Dissociation constants 712Dissociation energy 265Distillation, fractional 768

of immiscible liquids 768steam 769

Distribution law (Nernst’s) 697applications of 701thermodynamic derivation of 698

DLVO theory 1221DNA double helix 1321DNA denaturation 1322DNA renaturation 1323Donnan membrane equilibrium 1283Doping in semiconductors 1201Doppler Broadening 304Double helix (DNA) 1321Double resonance 381DPM 387DPPH 397Dropping mercury electrode

(DME) 922Dye lasers 1144

EEadie-Hofstee method 1153

Ebullioscopic constant 790Echo planar imaging (EPI) 391Eckart’s inequality 149Effective Fock operator 235Efficiency, of heat engine 572Eigenvalue equation 39Eigenfunctions and eigenvalues 141Einstein’s photoelectric equation 25Einstein-Smoluchowski equation

1294Einstein theory of heat capacity 982Electric field gradient (EFG) 420Electric properties of molecules 431Electrical capacitance 895Electrical double layer 1219Electrical energy 840Electrified interfaces 892Electrocapillary measurements 891Electrocatalysis 909Electrochemical series 847Electrode potential 838Electrode reactions, kinetiecs of 911Electrokinetic properties 1224Electrolytic cell 836Electrolytic conductance 801Electron correlation 233Electron diffraction 1186e/m ratio 21Electron mass 22Electron spectrocopy forchemical analysis (ESCA) 417Electron spin resonance(ESR) spectra 392Electron tunnelling in Marcus theory

1107Electronic spectra 335

of conjugated molecules 345of transition metal complexes 341

Electronically conductingpolymers 1306

Electron-molecule collisions 1331Electron transfer reactionsMarcus theory 1105Electron tunnelling 1107Electro-osmosis 1357Electro-osmotic pressure

(EOP) 1357Electrophoretic mobility 1225Electrophoresis 1224

capillary, gel, pulsed field 1324ELDOR 406ENDOR 406EMF of galvanic cells 848EMF measurements, applications

865Emission spectrum 302Emulsifiers 1246Emulsions 1242Enantiotropic transitions 523Endergonic reactions 655Endothermic reactions 552Energy barrier 1057Energy transfer 1131

1370 PRINCIPLES OF PHYSICAL CHEMISTRY

GENERALBIBLIOGRAPHY3GENERALBIBLIOGRAPHY(iv)

Ensemble average 991Ensemble theory 989Enthalpy 533Enthalpy change 552

of combustion 555of formation 557of neutralization 555of reaction 555of solution 556

Entropy 575absolute values 610and probability 618change in reversible andirreversible processes 577of mixing of gases 582of vaporization 578physical significance of 584

Entropy change of mixing of anideal solution 761

Entropy production and entropyflow in open systems 1352

Entropy production due to heatflow 1348

Entropy production in chemicalreactions 1349

Entropy production per unit time1351Entropy, residual 618Enzyme catalysis 1150Equations of state 481The Euler reciprocal relation 531Equilibrium approximation 1054Equilibrium constant 624

pressure dependence 640temperature dependence 637

Equipartition of energy 474Ergodic hypothesis 991ESCA 417ESI (electrospray ionization) 1331Even-even rule 1335EXAFS 1270Excimer lasers 1144Excess population 372Excluded volume 481Excited states 1138Expansion of an ideal gas 535

adiabatic 538isothermal 535

Exact and inexact differentials 530Excess pressure in a drop 506Exchange-correlation energy

functional 240Exchange energy 151Exchange operator 234Excited states, geometry 1138Exciton 1209Exergonic reactions 655Exothermic reactions 552Expansivity 460Explosion limits of chain reactions

1086Extended Hückel theory (EHT) 236Extinction (absorption)

coefficient, molar 1116

Extremum principle 1360Euler’s relation 64Eutectic point 680Eutectic systems 679Explosion temperature 562Eyring equation 1065

FFast atom bombardment (FAB) 1330F–centres 1207FEMO theory 204Femtochemistry 1034Femtosecond transition state

spectrocopy 1145f-f bands 345Fermi contact interaction 367Fermi-Dirac distribution 969Fermi-Dirac gas 969Fermi–Dirac statistics 939Fermions 936Fermi energy 970Fermi’s golden rule 245Fermi Level 970Fermi momentum 971Fermi resonance 323Fermi surface 1198Fermi temperature 972Ferretin 1312Ferromagnetism 448Fick’s first law of diffusion 1293Fictitious reference system 239Field desorption (FD) 1330Field ionization (FI) 1330Fifth state of matter 967Fine structure 87, 155Fine structure constant 127Fingerprint region 324First law of thermodynamics 528First–order reactions 1035Flame temperature 562Flash photolysis 1096Flocculation values 1223Flory-Huggins equation 1311Flory-Huggins theory 1309Flow methods for fast reactions 1095Fluctuations in ensembles 1015Fluidity 509Fluorescence 1115

quenching of 1133Fluxes and forces 464,1343Force constant 54Fourier synthesis of electron

density 1183Fourier transform NMR

spectroscopy 370Fourier transform spectroscopy 303Fractional distillation 768Fragmentation in mass

spectrometry 1333Franck-Condon principle 335Franck-Hertz experiment 28Franck-Rabinovich effect 1054Free electron model 1194

Free energy of a spontaneousreaction 620

Free induction decay (FID) 371Free path phenomena 471Free volume 500Freely jointed chain 1296Freezing mixtures 685Freezing point depression 792and molar mass 794Frenkel defects 1204Freons (chlorofluorocarbons) 1131Freundlich adsorption isotherm 1253Frictional coefficient 1294Frontier molecular orbitals 337Fuel cells 862Fugacity 601,1013

determination of 602Full rotation group 257Functional derivative 241Functional MRI 390Fundamental vibrational

frequency 316

Gg-factor in ESR 396Galvanic cells 835Gamma function 961Garrett-Brattain space charge 905Gas electrodes 836Gas lasers 1144Gas laws, derivation of 451

Avogadro’s law 452Boyle’s law 451Charles’s law 452Dalton’s law 453Graham’s law 453

Gases, kinetic theory of 450Gas-liquid chromatography GLC 1338Gaussian type orbitals (GTOs) 232Gel electrophoresis 1324Gels 1247Generalized angular momentum 149Generalized gradient approximation

(GGA) 242Generating operators 292Giant magnetoresistance (GMR)

1209Gibbs adsorption isotherm 1264Gibbs–Duhem equation 592Gibbs–Duhem–Margules equation

758Gibbs free energy 586Gibbs free energy change of

mixing for an ideal solution 759Gibbs–Helmholtz equation 590Gibbs paradox 995Gibbs phase rule 665Glass electrode 871Glide plane 264Glycolysis 656Gold number 1222Good solvent 1299Gouy balance 447

INDEX 1371(v)

Gouy-Chapman model 900Graft copolymers 1276Grand canonical ensemble 993Grand canonical partition function

1013Grand potential 1013Grand/Great orthogonality

theorem (G.O.T.) 253Graphite, structure of 1189Grotrian diagram 155Grotthus–Draper law 1118Grotthus mechanism 805Group moments 441Group postulates 249Group theory 247

and normal modes of vibration 268direct porduct of irreduciblerepresentations 275use in determining selectionrules in transitions 279use in factoring the secularequation in MOT 285

Group velocity 134

HHalf–life time 1047Half–wave potential 925Hamiltonian operator 42Hammett equation 648Hammett constants 648Hammett plot 650Hard-sphere potential 1029Hartree–Fock self–consistent

field method 128Hartree-Fock-Roothaan SCF method

234Heat capacities of monatomic

crystals 982The Debye theory 983The Einstein theory 982

Heat capacity 534Heat capacities at constant

pressure and constant volume 535Heisenberg’s uncertainty principle 36-helix 1313Helix-coil transitions 1312Hellmann-Feynman theorem 229Heitler-London-Slater-Pauling

(HLSP) theory 192Helmholtz free energy 585Helmholtz-Perrin model 899Hemoglobin, binding of oxygen 658Henderson-Hasselbalch

equation 722Henry’s law 774Henry’s law and Raoult’s law 775Hermite equation 55Hermite polynomials 56Hermitian operators 106Hess’ law 563

applications of 564Heterogeneous catalysis 1155Heteronuclear 2D J-resolved

spectra 383Heterogeneous equilibria 642High energy phosphate esterbonds 655High pressrue phase diagrams 678Hindered rotation 373Hinshelwood theory 1073Hittorf’s theoretical device 805Hohenberg-Kohn theorem 239Holes in semiconductors 1200Homogeneous equilibria 630Homonuclear 2D J-resolvedspectra 383HOMO-LUMO transition 340Hooke‘s law potential 54Hückel molecular orbital theory 205Hückel’s rule of aromaticity 210Hund's rule 87Hund’s rules 151Hybrid functional 242Hybridization 197

coefficients of 200Hydration number 886Hydrogen–bromine reaction

(photochemical) 1126Hydrogen–chlorine reaction

(photochemical) 1125Hydrogen electrode 836Hydrogen-oxygen fuel cell 862Hydrogen spectrum 28Hydrolysis of salts 724Hydronium ion 706Hydrophile-Lipophile balance(HLB) 1228Hydrophobic interaction 1314Hyperchromic effect 1322Hyperfine structure in atomicspectra 162Hyperfine structure in ESR 393Hypsochromic shift 339

IIcosahedral symmetry 1209Ideal gas equation 452Ideal solution 756Idempotent matrix 998Identical particles 1002Impact parameter 1103Imperfections in crystals 1209Incongruent melting point 687Index of hydrogen deficiency 1336Isothermal expansion 535Ilkovic equation 923

derivation 923Indicators, acid–base 733

theory of 733Inorganic phosphate 655Insulators 1201Integrated absorption coefficient1137Integration of rate expressions

first-order reactions 1038second–order reactions 1042third–order reactions 1045

zero–order reactions 1047Interfacial tension 507Interionic effect 824Intramolecular energy transfer 1079Internal pressure 482Intensity of spectral lines 304Intermediate neglect of

differential overlap (INDO) 238Intermolecular energy transfer 1136Intermolecular forces 487Internal conversion 1114Internal energy 529Internal rotation 314Internuclear distance 309Internuclear double resonance

(INDOR) 385Intersystem crossing (ISC) 1114Intramolecular photophysical

processes 1135Inverse anti-Stokes Raman

scattering 334Inverse-Stokes Raman scattering

334Inversion doubling 323Inversion temperature 548Inversion spectrum 315Ionic atmosphere 825Ionization potentials 1332Ionic, bond 173

mobility 804,814product of water 715

Ionic crystals, structures of 1190Ionic doublets 824Ionic strength 829Ionization efficiency curve 1332Ionization potentials 1332Isenthalpic process 546Isentropic process 582Irreversible processes 577Irreversible thermodynamics 1343Isoelectric focusing 1324Isoelectric point (pI) 1324Isomorphism 297Isosteric enthalpy of adsorption 1185Isotactic polymers 1275Isothermal expansion 535

work done in 535Isotope peaks 1329Isotope separation 1144

Isotopic substitution 312Isotropy 516Iteration 128

JJablonski diagram 1113Jahn-Teller distortion 343Jahn-Teller Theorem 109j.j. coupling 153Joule-Thomson coefficient 546Joule-Thomson effect 545

KKarplus relation in NMR 368

1372 PRINCIPLES OF PHYSICAL CHEMISTRY

GENERALBIBLIOGRAPHY3GENERALBIBLIOGRAPHY(vi)

Kelvin equation 506Kinetic energy and temperature 453Kinetic gas equation 451Kinetic theory of gases 450

and gas laws 451Kinectics of

acid–base catalysed reactions1149

branched–chain reactions 1085chain reactions 1082complex reactions 1079consecutive reactions 1081diffusion–controlled reactions 1087electrode reactions 912enzyme–catalysed reactions 1150fast reactions 1093polymerization 1301reactions in solution 1086reversible reactions 1079surface reactions 1155

Kirchhoff equation 560Knudsen cell 1332Knudsen effect 1359Knudsen gas 462Kohlrausch law 810

applications 815Kohn-Sham method 239Koopmanns’ theorem 108,417Kramers’ degeneracy 109Kramers’ theorem 109,401Kronecker delta 42k-space 1197

LLadder operators 143Lambda temperature 1018Lambda transition 1018Laminar flow 508Langmuir-Hinshelwood mechanism

1155Lagrange’s equations of motion 321Lagrange’s undeterminedmultipliers 937Landau theory of liquid helium-II1022Lande interval rule 159Lande g-factor 159Langevin function 434Langmuir's adsorption isotherm 1256Langmuir’s theory of adsorption1256Lanthanide shift reagents 386Laplace equation 421Laplacian operator 42Laporte rule 343Larmor frequency 357Larmor precession 357Laser 1139Laser Raman spectroscopy 1143Lattice energy 1173Lattice model of polymer solution

1309LCST 771Law

Avogadro’s 452

Beer–Lambert 1115Boyle’s 451Charles 452Curie’s 445of chemical equilibrium 625of conservation of energy 528of corresponding states 493Dalton’s 453distribution (Nernst) 697equipartition of energy 474Henry’s 774Hess’s 563of mass action 625of photochemical equivalence1118of rational indices 1175

LCAO-MO approximation 174LCDs 519Le Chatelier’s principle 646Lead–silver system (phase rule) 682LEED 1269Lennard–Jones (6, 12) potential

488,1030Lever rule 768Levitation 1202Lewis concept of acids and bases

710Light scattering 1289Limiting current density 921Limiting diffusion current 921Lindemann’s theory of unimolecular

reactions 1070Line defects : Dislocations 1208Line spectra 305Linear free energy relationships

(LFERs) 648Linear rotor 313Lineweaver-Burk method 1152Lippmann equation 894Liquefaction of gases 495Liquid crystals 516

classification of 520molecular arrangements in 524

Liouville theorem 992Liquid helium system 678,1018Liquid–junction potential 860Liquid state 499Local density approximation (LDA)

242London forces 487London-Tisza theory 1019Lorentz-Lorenz equation 437Lotka-Volterra mechanism 1162Lowering of vapour pressure 778l-type doubling 323Lyman series 29

MMacroemulsions 1242Macromolecules 1273

conformations of 1296molar masses of 1277

Madelung constant 1173Magic angle spinning (MAS) 381

Magnetic properties of molecules442permeability 442susceptibility 443

Magnetic polarizability(magnetizability) 445

Magnetic resonance imaging(MRI) 390

Magnetic resonance spectroscopy299

Magnetogyric ratio 303MALDI 1330MALDI-TOF mass spectrometry

1330Marcus cross relation 1109Marcus theory of electron transfer

reactions 1105Mark–Houwink equation 1279Mass number 23Mass spectrometry 1327Mathematical probability 618Matrix element 112,175Matrix mechanics 37Matter waves 34Maximum work 537Maxwell–Boltzmann statistics 935Maxwell’s distribution of molecular

energies 455Maxwell’s distribution of molecular

velocities 454Maxwell’s relation 437Maxwell’s relations in

thermodynamics 587Mayer f-function 1026McBain micelles 1231McConnell equation 398McLafferty rearrangement 1335Mean ionic activity 852Mean free path 462Mechanisms of complex reactions

1053Melting curves of DNA 1322Meritectic (or peritectic)

temperature 687Meissner effect 1202Membranes, biochemical 930Membrane potentials 930Mesomorphic state 516Mesomorphism

lyotropic 516Thermotropic 516

Metabolism : anaerobic andaerobic 656

Metal deficiency defects 1207Metallic crystals 1193

free electron model of 1194Metallic properties 1193Metal-metal transitions 343Metastable equilibrium 674Metastable peaks 1329Michaelis–Menten equation 1151Micellar aggregation numbers 1232Micellar catalysis 1240Micelle formation 1229

INDEX 1373(vii)

Mass action model 1229Phase separation model 1229

Microcanonical enemble 993Microemulsions 1245Microscopy far-field confocal 1144

near-field optical 1144Microstates 936Microwave oven 313Microwave spectra 307Milikan’s oil drop technique 21Miller indices 1175MINDO 238Mode locking 1142Mobility, ionic 804

determination of 814Molal boiling point elevation

constant 790Molal freezing point depression

constant 794Molar absorption coefficient 1116Molar conductance 802Molar extinction coefficient 1116Molar ionic conductance at

infinite dilution 803and ionic mobility 812

Molar polarization 432Molar mass determination by

mass spectrometry 1337Molar mass distribution in

condensation polymerization 1303Molar refraction 437Molecular beam methods 1097Molecular dynamics (MD) method

513Molecular ion 1336Molecular orbital theory (MOT) 174Molecular orbitals 174

antibonding 174bonding 174

Molecular orbitalsfor homonuclear diatomicmolecules 186for heteronuclear diatomicmolecules 188

Molecular partition function 942Molecular reaction dynamics 1097Molecular symmetry 247Molecularity of a reaction 1052Moment of inertia 308Monochromatic radiation 1066Monte Carlo (MC) procedure 1103Morse potential 317Mössbauer spectroscopy 412Moving boundary method 809Mutual exclusion rule 330Mulliken population analysis

(MPA) 238Multicentre integrals 238Multiphoton spectroscopy 1143Multiplication table in group theory

250Myoglobin, binding of oxygen 657Myosin 1312

NNatural linewidth 304Neel point 443Nematic liquid crystals 521Nernst Distribution law 697Nernst, equation 844

heat theorem 609Nervous system 931Neutron 23Neutron diffraction 1187Nicotine–water system 773Nitrogenous bases in DNA and

RNA 1319Nonlinear thermodynamics of

irreversible processes 1361Non-Newtonian liquids 508Nonradrative transitions 1114Normal coordinate analysis 321Normal coordinates 269Normal mode of vibration 268, 320Normalization of wave function 47NRF spectroscopy 412Nuclear magnetic double

resonance (NMDR) 374Nuclear magnetic resonance

(NMR) 353Nuclear spin and rotational

partition function 956Nuclear Overhauser effect

(NOE) 381Nuclear spin-spin interaction 362Nucleic acids (DNA and RNA) 1319NMR of AB spin system 375NMR, 2-dimensional 380NMR of liquid crystals 389NMR of paramagnetic compounds

387NMR of solids 380Non-trivial solution 176Nuclear quadrupole resonance

(NQR) spectroscopy 420Nylon 66 1277

OOff-resonance proton decoupling382One–dimensional simple

harmonic oscillator 54Open systems 591Onsager’s phenomenological

coefficients 1274Onsager’s reciprocal relations,

verification of 1345,1355Opacity function 1103Operand 43Operators in quantum mechanics 43Optical activity 511Optical pumping 1141Optical rotatory dispersion

(ORD) 512Optimal pH point 1161Orbital and spin angular

momentum operators 147Orbital energies of multi–electron

atoms 87

Orbitals, filling of 87Orbital exponent 232Order parameter 523Order of a reaction 1035

methods of determination 1051Order and molecularity of simple

reactions 1052Order and molecularity of complex

reactions 1053Order of a group 250Orthonormal set of wave functions

42Orgel diagrams 344Ortho and para hydrogen 958Oscillator strength 1138Oscillatory reactions 1161Osmometry 1281Osmosis 781osmotic pressure 781Osmotic pressure and molar mass

783Osmotic pressure and vapour

pressure lowering 784Ostwald’s dilution law 822Outer Helmholtz plane (OHP) 898Overtones 322Overpotential 912Overvoltage 917

applications of 917Oxidation potential 838Oxidation–reduction indicators 879Oxidation–reduction electrodes 838Ozone hole 1131Ozone layer 1129

PP–V isotherms of carbon dioxide

gas 490Parallel bands 324Paramagnetism 444Parity 260Pariser-Parr-Pople (PPP)

approximation 235Partial molar properties 591, 595Particles

indistinguishable 1002distinguishable 1002

Partition function,canonical 976electronic 948nuclear 951rotational 945translational 943vibrational 946

Pascal’s constants 444Pascal’s triangle 363, 396Paschen series 29Paschen-Back effect 162Patterson synthesis 1184Pauli’s exclusion principle 85Pauli spin matrices 167Penrose tiling pattern 1210Perfect pairing approximation 144Perpendicular bands 324

1374 PRINCIPLES OF PHYSICAL CHEMISTRY

GENERALBIBLIOGRAPHY3GENERALBIBLIOGRAPHY(viii)

Perturbation Theory 111Degenerate 117first order 115second order 113Non degenerate 112time-dependent 242time-independent 111application to helium 115

Perovskite structure 1203PET (polyethylene terephthalate)

1277Pfund series 29pH scale 716pH, determination of 869Phase problem in crystallography

1184Phase equilibria 661Phase 661Phase rule (Gibbs) 665

derivation of 665Phase rule, application to

one–component systems 667two–component systems 679three–component systems 690

Phase transitions, Ehrenfestclassification 692

Phenol–water system (phase rule)772

Phenomenological laws 1343Phonon 1209Phosphorescence 1115Photochemical rate law 1124Photobiology 1112Photochemical reactions 1123

kinetics of 1125Photochemistry 1112Photodissociation coefficient 1130Photoelectric effect 24Photoelectron spectroscopy

(PES) 416appilications of 417

Photon 25Photosensitization 1131Photosynthesis in plants 1132Pierl’s distortion 1307Planck’s constant 24Phanck's law 961Plait point 691Plasmolysis 786-pleated sheet 1313Pockels cell 1142Point defects 1204Point groups 250

character tables for 254representations of 251

Poisseuille’s equation 509Poisson equation 882Poisson-Boltzmann equation 883Polar, resonance and steric

effects 653Polarisation of a molecule in an

electric field 431Polarizability 431Polarizability volume 435

Polarography 919applications of 926

Polaron 1308Polyacetylene 1307Polyethylene (LDPE and HDPE)1274Poly(para-phenylene) 1308Poly(sulphur nitride) 1306Polymerase chain reaction

(PCR) 1323Polymers, classification 1275Polymer liquid crystals 522Polymorphism 672Polymorphism in liquid crystals 522PMMA 1274Polydispersity index (PDI) 1278Polynucleotides 1319Polystyrene 1274Population inversion 1141Potassium iodide–water system

(phase rule) 683Potential energy surfaces 1099Potentiometric titrations 872Pressure of an ideal gas 450Pressure-induced polymorphism 523Primary process 1122Principal axis system 421Prigogine’s principle of

minimum entropy production 1360Principle of microrcopic reversibility

1354Probe and pump pulses 1145Projection operators 292Proteins, structure of 1312

denaturation of 1315Protein folding 1315Pseudo-contact shift 387Pseudmonomolecular reactions 1052Pulse radiolysis 1097PVC 1274

QQuantal canonical distribution 1010Quantal grand canonical

distribution 1014Quantal microcanonical ensemble

998Quantization of phase space 1000Quantum chemistry programs 238Quantum concentration 1293Quantum electrodynamics

(QED) 227Quantum mechanical tunnelling 133Quantum mechanics 37

postulates of 39Quantum numbers 83

azimuthal 83magnetic 83principal 83spin 84

Quantum statistical mechanics 996Quantum theory of radiation 24Quantum yield 1118Quasicrystals 1209Quasiparticles 1022

Quenching of fluorescence 1133Quenching of orbital angular

momentum 446Q-switching 1142Quinhydrone electrode 838

RRacah parameters 151Radial distribution function 512Radiative transitions 1045Radius of gyration 1298Radius of the ion sphere 831Raising and lowering operators 143Ramachandran diagram 1314Raman shift 327Raman spectroscopy 326Ramsay-Shield’s equation 504Raoult’s law 752

of vapour pressure lowering 779Rate constant 1035

statistical mechanical derivationof 1067

Rate of Reactions 1034Rate expressions, integrations of

1038,1042,1045,1047Rational indices, law of 1175Rayleigh-Jeans law 961Rayleigh ratio 1291Rayleigh scattering 326Reaction coordinate 1054Reaction cross-section 1103Reaction rate, effect of temperature

1056Reaction rates, theories of 1060Reactions in flow systems 1090Rearrangements 1335Real gases 479

deviation from ideal behaviour 479Rectifier 1201Red shift 339Redlich–Kwong equation 485Redox titrations 875Reduced osmotic pressure 1282Reducible and irreducible

representations 252Reduced phase rule equation 679Reduced plack's constant 46Reduction potential 838Refractive index 510Refraction, molar 510Relativistic quantum mechanics 37Relaxation methods in kinetics 1093Relaxation processes in NMR 371Residual entropy 618Resonance energy 569Resonance Raman spectroscopy

331Rest mass 22Reverse osmosis 786Reversible and irreversible

processes : criteria for 589Reversible electrodes 836Reversible isothermal expansion

of a real gas 543

INDEX 1375(ix)

Reynolds number 509Rhodopsin 1312Ribosomes 1319Rice-Herzfeld mechanism 1083Riemann zeta function 961Root mean square velocity 457Rotational quantum number 64Rotational constant 308Rotational spectra 307Rotational term 308Rotation–vibration spectra 319Rotons 1022RRK theory 1074RRKM theory 1077Russell-Saunders coupling 132Rutherford’s atomic model 23Rydberg constant 30

SSackur-Tetrode equation 954Saddle point 1101SALCs 286Salt bridge 861Salt effects on reaction rates 1088Saturated calomel electrode

(SCE) 839Saxon’s relation 1358Schottky defects 1204Scattering factor 1183Schrödinger wave equation,

solutions of 40,45-83particle in a one-dimensionalbox 45particle in a three-dimensionalbox 52rigid diatomic rotor 63simple harmonic oscillator 54hydrogen atom 65many-electron atoms 111

Screw axis 264Screw dislocation 1208Second–order reactions 1042Second law of thermodynamics 571Second sound 1020Second virial coefficient 486Secondary process 1122Secular determinant 176Secular equation 176Sedimentation equilibrium method

1288Sedimentation velocity method 1285Selection rules 303Semiconductors 1200Semiconductor interfaces 904Semi-empirical methods 236Semipermeable membrane

(SPM) 781Semipermeability, theories of 785Seven segment cell 518Shirakawa technique 1307Similarity transformation 250Shielding constant 131,358Shielding mechanisms in NMR 360

Lamb's formula 360Sigmoid binding curve 658Simple harmonic oscillator (SHO) 54

Algebraic technique for solvingthe schrödinger equation 137

Single electrode potential 839Single-molecule spectroscopy 1144Singlet state 113Slater determinant 76, 1003Slater type orbitals (STOs) 232Slater’s rules 131Slater sum 1011Slope-intercept method 595Smectic liquid crystals 521Soft Laser Desorption (SLD) 1331Solid state laser 1144Soliton 1308Soliton pair 1308Solubility of partially miscible

liquids 770Solubility product 740

applications of 742Solubilization 1238Solutions of non–electrolytes 750Solutions of gases in liquids 773Solutions of liquids in liquids 750Solvent extraction 702Sommerfeld extension of Bohr

theory 31Space groups 263Space lattice 263,1169Spectra,

charge transfer 340electronic 335electron spin resonance 392hydrogen 28molecular 305Raman 326rotational 307,313vibrational 315,320

Spectroscopic transition 302Spectroscopy 302Spherical harmonics 64Spherical wave 1270Spherical top molecules 324Spin Hamiltonian in ESR 410Spin labels 397Spin multiplicity 1113Spinors 169Spin-lattice relaxation in NMR 372Spin-lattice relaxation time 372Spin-orbit coupling 153Spin quantum number 84Spin-spin coupling constant 363Spin-spin interaction in NMR 362Spin vectors 168Spontaneous processes 571Spontaneous reactions 620

free energy of 620Square-well potential 1029SQUID 447Standard electrode potentials 846Standard enthalpies 555

Standard hydrogen electrode(SHE) 836

Standard state 606Standard reduction formula 268Stark effect 162Stark effect in microwave spectra

314Stark–Einstein law 1118State of a system 526Statee

mixed 997pure 997

State variables 526Stationary nonequilibrium states1359Statistical averaging 996Statistics, types of 935

Bose–Einstein 935Fermi–Dirac 935Maxwell–Boltzmann 935

Statistical entropy 619Statistical thermodynamics 935Staudinger index 1279STM (Scanning tunnelling

microscopy) 1270STO-3G basis set 233Steady-state approximation 1054Steam distillation 769Stephen-Boltzmann law 961Sternheimer effect 427Stereoregular polymers 1276Stern-Gerlach experiment 84Stern Model 902Stern-Volmer equation 1137Stimulated Raman scattering

(SRS) 332,1143Stirling approximation 937Stirred flow reactor 1091Stokes and anti-Stokes lines 326Stokes-Einstein equation 1294Streaming current (SC) 1358Streaming potential (SP) 1358Structure factor 1184Structure of liquids 512Subgroup 250Sulphur system (phase rule) 672Supercoiled DNA 1321Superconductivity 1202

LTSC and HTSC 1202Superfluidity 1018Supermolecule 1100Supertwist 1322Surface energy 503Surface excess 1266Surface films on liquids 1267Surface reactions 1085Surface structure techniques

(EXAFS and SEXAFS) 1270Surface tension 502Surfactants 1226Svedberg equation 1286Symmetric and antisymmetric wavefunctions 1003Symmetric top molecules 324

1376 PRINCIPLES OF PHYSICAL CHEMISTRY

GENERALBIBLIOGRAPHY3GENERALBIBLIOGRAPHY(x)

Symmetry, in crystal systems 1166axis of 1166centre of 1167elements of 1167operations 1167plane of 1167

Symmetry of molecular orbitals 185Symmetry of wave functions 1003Syndiotactic polymers 1275System of identical particles 1002

TTafel equations 914Tafel plot 915Taft equation 654Tanabe-Sugano diagrams 344Temperature coefficient 1056Temperature–dependence

of equilibrium constant 637TEMPOL 397Term symbols for diatomic

molecules 184Tetramethylsilane (TMS) 359Theorems of quantum mechanics 107Theoretical plate 768Thermal analysis, phase rule 681Thermal conductivity 465Thermochemistry 552Thermodynamic equilibrium 526Thermodynamic potentials 630Thermodynamic probability 618Thermodynamic processes 527Thermodynamics of CMC 1236Thermodynamics of ideal

solutions 759Thermodynamics, laws of 525Thermography 518Thermomechanical effect 1358Thermomolecular pressure

difference (TPD) 1358Thermo-osmosis 1359Third law of thermodynamics 609

experimental verification of 615Third–order reactions 1045Thomas-Fermi equation 164Thomas-Fermi model 163Threshold energy 1056Threshold frequency 25Three–component systems 690Tie line 768Time-dependent perturbation

theory (TDPT) 242Time-dependent Schrödinger

equation (TDSE) 242Time-independent perturbation

theory (TIPT) 111Time-independent Schrödinger

equation (TISE) 42Time-resolved spectroscopy 1143Townes-Dailey theory 426Trace of a matrix 997Transfer coefficient in electrode

kinetics 913

Transition state theory 1063Transmission coefficient 1068Transmission probability 135Transitions (allowed and forbidden)

303Transitions

electric dipole 154magnetic dipole 154

Transistors 1201Transmittance 1116Transport number 806

determination of 807Transport properties in gases 463Transverse relaxation time 372Trial wave function 121Triethylamine–water system

(phase rule) 772Triple point 669Triplet state 1114Trouton’s rule 502Turbidity 1292Turnover number 1152Two-dimensional NMR 380Tyndall effect 1289

UUCST 771Ultracentrifugation 1285Ultramicroscope 1217Unimolecular reactions, theories

of 1070Hinshelwood theory 1073Lindemann theory 1070RRK theory 1074RRKM theory 1077

Unimolecular surface reactions 1155Unit cell 1169Unsold’s theorem 108UPES (Ultraviolet photoelectron

spectroscopy) 416Upper bound 175

VVacancy theory of liquids 499Valence bond theory (VBT) 192Valence state ionization

potentials 233van der Waals constants 482van der Waals equation 481

and critical phenomena 491van der Waals forces 433van’t Hoff equation 637van’t Hoff osmotic pressure

equation 782reaction isotherm 626

van’t Hoff factor 796Vapour pressure of liquids 500Vapour pressure lowering 778Vapour pressure lowering and

molar mass 779Vapour pressures of ideal

solutions 753Vapour pressures of non–ideal

solutions 763

Variation method 120Application to helium 121

Variation theorem 148Velocity,

average 457most probable 453root-mean-square 457

Vibrational quantum number 316Vibrational spectra 315

of polyatomic molecules 320Vibrational term 316Virial coefficients 486Virial equation of state 486,1028Virial theorem 108Virtual orbitals 236Viscometry 1279Viscosity of gases 467Viscosity of liquids 508Volcanoes 910Volume change and enthalpy

change of mixing for an idealsolution 760

VSEPR theory 226

WWalden’s rule 817Walsh diagrams 225Water system (phase rule) 668Watson-Crick model 1320Wave-particle duality of electron 33Wave mechanics 37Width of spectral lines 304Wien’s displacement law 24, 961Wien effect 827Wierl equation 1186Wigner coefficients 170Wiger-Seitz cell 1199Work function 25

XX–ray diffraction 1176X-ray diffraction pattern of a

cubic system 1180X–ray diffractometer 1177

YYoung-Laplace equation 507

ZZeeman effect 84, 159

Normal and anomalous 159Zeeman effect in NQR 425Zero differential overlap (ZDO) 238Zero–order reactions 1049Zeroeth law of thermodynamics 549Zeroeth law and temperature

scale 549Zero-point energy (ZPE) 56Zero-field splitting (ZFS) 109,401Zeta potential 1221Ziegler-Natta catalyst 1276Zimm equation 1292Zimm plot 1292Zinc-air fuel cell (ZAFC) 864Zwitterion 1324