Principles of Physical Chemistry

C ONTENTS C ha p t e r

0.

Mathe matical Concepts

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 some simple 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)

P ages  

1—20

Curve sketching, linear graphs and slopes Inclination 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.

2.

Quantu Quant um Mech Mechan anics ics-I -II. I. Adv Advan anced ced Topic Topicss And And Atom Atomic ic Spect Spectra ra (1 11- 17 2) Solution of the Sch rödinger equation equation for multi-electron atoms (111) 1. Time-indepen Time-independent dent perturba perturbation tion theory theory (111) Non-degenerate perturbation theory (112) Application of the first-order perturbation theory helium atom (115) Degenerate perturbation theory (117) Stark effect on the first excited state of hydrogen atom (119) 2. The variation method (120) Application of the variation method to helium atom (121) The Hartree and the Hartree-Fock self-consistent field (SCF) method (128) Slater determinant for n-electron atoms (129) The Schrödinger equation for a finite potential barrier: Quantum mechanical tunnelling (132) Simple harmonic harmonic oscillator : The algebraic method method (137) Angular momentum operators, eigenfunctions, eigenvalues, commutation relations, and ladder operators (141) Derivation of the variation theorem (148) Atomic states and term symbols (149) The term symbols for the p 2  configuration (150)

Quantu Quantum m Mechanic Mechanics-I s-I Wave Wave Mechani Mechanical cal Trea reatme tment of Simple Syst ystems ems 21—1 21—110 10 Electron 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 fine hydrogen spectrum (32) Dual character of electron (33) de Broglie’s equation (33) The Davisson-Germer experiment (35) Heisenberg uncertainty principle (36) Compton effect (36)

( 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 : Molecular Quantum Mechanics 173–246 Molecular 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 in hybridization (200) Conjugated molecules (204) Hückel molecular orbital theory of conjugated systems (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 Concepts 247–266 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 for molecular 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 : Applications 267-301 1. Decomposing a reducible representation into its irreducible representations (267) 2. Group theory and normal modes of vibrations of polyatomic molecules (268) 3. Procedure for determining the irreducible representations of the vibrational modes in nonlinear molecules (270) a. Normal modes of vibration of H 2O molecule (270) b. Normal modes of vibraiton of NH 3 molecule (272) c. Normal modes of vibration of BF 3 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 in formaldehyde (279) 7. Use of group theory in constructing hybrid orbitals in simple molecules (282) 8. Use of group theory in factoring the secular equation 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.

M ol ec ul ar S pe ct ros cop y - I

30 2– 352

What is spectroscopy ? (302) Basic features of spectrometers (302) Width and intenstiy of spectral lines (304) Molecular spectra (305) Rotational (microwave) spectra of diatomic molecules (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 transition metal complex ion (342) Jahn-Teller distortion (343) Metal-metal transitions (d d 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.

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 NMR spectrum 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)

Molecular Spectroscopy - II (NMR, ESR, NQR, NRF And PES) 353– 430 Magnetic 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 equivalent nuclei (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)

8.

E l e ct r i c a nd Ma g ne t i c P ro pe r t ie s of   Molecules 431–449 Electric 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 and paramagnetism (444) Measurement of magnetic susceptibility (447) Ferromagnetism and antiferromagnetism (448) Review Questions and Problems (449)

9.

The Gaseous State Part I : Ideal Gases 450-478 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 Gases 479-498 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 of  Liquids 49 9-515 Gaseous, 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 a droplet (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 State 516-524 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 liquid crystals (524) Review Questions (524)

v

Applications of bond energies (568)

13 . The First Law of Thermodynamics 525-551

Review Questions and Problems (569)

Importance of thermodynamics (525) Limitations of thermodynamics (525) Some basic terms used in thermodynamics (525) Thermodynamic equilibrium (526)

15 . The Second Law of Thermodynamics 571-608

Nature of work and heat (528)

Limitations of the first law : Need for the second law (571) Spontaneous or irreversible processes (571) Cyclic process (572)

The first law of thermodynamics (528)

Carnot cycle (572)

Internal energy (529)

The second law of thermodynamics (574) Carnot theorem (574) Concept of entropy (575) Entropy change in an isothermal expansion of an ideal gas (577)

Extensive and intensive properties (527) Thermodynamic processes (527)

State functions, exact and inexact differentials (530) Euler reciprocal relation (531) The cyclic rule (532) Enthalpy (533)

Entropy changes in reversible and irreversible processes (577)

Heat capacity (534) Relation between Cp and C v (535) Expansion of an ideal gas and changes in thermodynamic properties (535)

Entropy changes accompanying changes of phase (578)

B. Adiabatic expansion (538)

Calculation of entropy changes of an ideal gas with change in P , V   and T (580)

Final temperatures in reversible and irreversible adiabatic expansions (538)

Entropy of mixing of ideal gases (582) Standard entropies (583)

Comparison of isothermal and adiabatic expansions (542)

Physical significance of entropy (584) Work and free energy functions (584)

A. Isothermal expansion (535)

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) Review Questions and Problems (550)

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

55 2-570

Change 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 constant volume 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)

Criteria for reversible and irreversible processes (589) Gibbs–Helmholtz equation (590) Thermodynamics of open systems : Partial molar properties (591)

Absolute temperature scale (549)

14. Thermochemistry

Variation of free energy with T   and P  (586) Maxwell’s relations (586)

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 Thermodynamics 609-619 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

18. Phase Equilibria

661—695

Phase (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)

62 0-660

Spontaneous reactions (620) Standard free energy change (621) Chemical equilibrium (624) Law of mass action (624)

Some typical solved examples for one-component systems (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)

Thermodynamic derivation of the law of mass action (624)

Thermal analysis : cooling curves (681)

van’t Hoff reaction isotherm (626)

Bismuth–cadmium system (683)

Relations between K p , K c  and K x (626)

Potassium iodide–water system (683)

De Donder’s treatment of chemical equilibria (628) Thermodynamic relations for chemical affinity (629) Homogeneous Equilibria (630) Temperature–dependence of the equilibrium constant : The van’t Hoff equation (637) Integrated form of the van’t Hoff equation (638) Pressure - dependence of equilibrium constant  (640)

Lead–silver system (682)

Freezing mixtures (685) Type B. Systems in which two components form a stable compound (685) Formation of compounds with congruent melting points (686) Formation of compounds with incongruent melting points (687) Calculation of eutectic point and eutectic composition (688)

Heterogeneous equilibria (642)

Typical solved examples for two-component systems (688)

Equilibrium constants for reactions involving real gases (645)

Three–component solid–liquid systems (690) Acetic acid–chloroform–water system (690)

Le Chatelier’s principle (646) Linear free energy relationships (LFERs) (648)

Three–component systems consisting of two salts and water (691)

Hammett Equation (648)

The Ehrenfest classification of phase transitions (691)

Hammett equation as LFER (651)

Review Questions and Problems (695)

Reaction mechanisms and the Hammett equation   (652) Taft equation (654) Biochemical equilibria (654)

19 . The Nernst Distribution Law 696-705 Nernst Distribution law (696) Thermodynamic derivation (698)

ATP and its role in bioenergetics (654)

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

Binding of oxygen by myoglobin and hemoglobin   (657)

Dissociation of the solute in one of the solvents (700)

Review Questions and Problems (659)

Solute enters into chemical combination with one of the solvents (700)

vii

Applications of the distribution law (701)

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

Study of complex ions (701)

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

Solvent extraction (702) Review Questions and Problems (705)

20. Ionic Equilibria

Entropy change of mixing for an ideal solution

70 6-749

Acids and bases   (706)

(761)

Vapour pressures of non–ideal solutions (763)

Brönsted-Lowry concept (706)

Vapour pressure–composition and boiling pointcomposition curves of completely miscible binary solutions (764)

Lewis concept (710)

Fractional distillation of binary liquid solutions (766)

Arrhenius concept (706)

Dissociation of weak acids and bases   (712)

Azeotropic mixtures (766)

Dissociation of a weak acid (712)

TheLever rule and fractional distillation (768)

Dissociation of polybasic acids (713)

Distillation of immiscible liquids (768)

Dissociation of a weak base (714)

Solubility of partially miscible liquids (770)

Dissociation of water (715)

UCST and LCST (771)

p H scale (716)

Some other logarithmic expressions   (718)

Phenol–water system (772) Aniline–hexane system (772)

Common ion effect (719)

Triethylamine–water system (772)

Buffer solutions (720)

Nicotine–water system (773)

Buffer mixture of a weak acid and its salt (721)

Solutions of gases in liquids (773)

Calculation of p H values of buffer mixtures : Henderson-Hasselbalch equation (722)

Factors influencing solubility of a gas (773)

Buffer mixture of a weak base and its salt (724)

Henry’s law and Raoult’s law (775)

Hydrolysis of salts (724)

Henry’s law (774) Review Questions and Problems (776)

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)

22 . Colligative S o l ut i o n s

Properties

of

Dilute 778-800

Colligative properties (778) Vapour pressure lowering (778)

Action of phenolphthalein (734)

Osmosis and osmotic pressure (781)

Action of methyl organge (734)

Determination of molar mass from osmotic pressure measurements (783)

Acid–base titrations and use of indicators (735) Mathematical treatment of acid–base titrations (736) Solubility product (740)

Relation between osmotic pressure and vapour pressure lowering of an ideal solution (784)

Applications of solubility product principle (742)

Theories of semi–permeability (785)

Ionic equilibria involving complex ions (746)

Effects of osmosis and semi–permeability

(786)

Reverse osmosis (786)

Review Questions and Problems (748)

Boiling point elevation (788)

21. Solutions of Non–Electrolytes

750 -77 7

Solutions of liquids in liquids (750)

Freezing point depression (792) Abnormal Results and the van’t Hoff factor (796) Review Questions and Problems (799)

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)

23 . Electrochemistry Part I : Electrolytic Conductance and Transference 80 1-8 34 Electrolytic conductance (801)

Gibbs–Duhem–Margules equation (757)

Specific conductance (801)

Temperature-dependence of vapour pressure of a solution (759)

Equivalent conductance (801)

Thermodynamics of ideal solutions (759)

Molar conductance (802) Variation of molar conductance with dilution (803)

viii

Hittorf’s theoretical device (805)

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

Transport number (806)

4. Determination of solubility product constants (868)

Determination of transport numbers (807)

5. Determination of pH (869)

Ionic mobility (804)

Hittorf’s method (807)

Potentiometric titrations (872)

Moving boundary method (809)

1. Acid–base titrations (872)

Kohlrausch’s law (810)

2. Redox titrations (875)

Calculation of molar ionic conductance (810)

3. Precipitation titrations (878)

Relation between molar Ionic conductance and ionic mobility (812)

Oxidation–reduction indicators (879) Review Questions and Problems (880)

Determination of ionic mobility (814) Applications of Kohlrausch’s law (815) Diffusion and ionic mobility (816) Applications of conductance measurements (818)

25. Electrochemistry Part III : Electrified Interfaces, etc. 88 2-934 I. Debye-Hückel theory of activity coefficients of strong electrolytes (882)

Conductometric titrations (821) Precipitation titrations (822)

Determination of solute activites from solvent activities   (885)

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 coefficients of strong electrolytes (830) Debye-Hückel Limiting Law (DHLL) (832) Review Questions and Problems (833)

24 . Electrochemistry Part II : Electromotive Force of Galvanic Cells 835—881 Galvanic cells (835) Reversible electrodes (836)

Dependence of electolyte activity on the hydration number (886) Bjerrum’s theory of ion association in electrolyte solutions (887) Determinaiton of interfacial tension of mercury as a function of potential across the interface (891) II. Electrified interfaces (892) A. Quantitative thermodynamic electrified interfaces (892)

treatment

Determination of the surface excess (895) B. Structures of the electrified interfaces (898) 1. Helmholtz-Perrin model (899)

Single electrode potential (838)

2. Gouy-Chapman diffuse charge model of the double layer (900)

Thermodynamics of reversible electrodes and cells   (840)

3. Stern model (902)

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)

C. Structure of semiconductor interfaces (904) Garrett-Brattain space charge inside an intrinsic 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)

of

ix

Applications of polarography (926)

27. Classical Statistical Mechanics

Amperometric titrations (929)

989 -10 32

VI. Bioelectrochemistry (930)

Phase space, ensembles and ensemble average (989)

Electrochemical mechanisms of the nervous system (931)

Postulate of equal a priori probability in classical statistical mechanics   (992)

Review Questions (933)

Microcanonical ensemble (993)

2 6. Statistical Thermodynamics

935-988

Statistical thermodynamics (935) Types of statistics (935) Maxwell–Boltzmann statistics (936)

Entropy of a perfect gas using the classical microcanonical ensemble (994) Entropy of mixing of ideal gases and the Gibbs paradox (995) Quantum statistical mechanics (996)

Bose–Einstein statistics (938)

Quantal microcanonical ensemble (998)

Fermi–Dirac statistics (939)

Quantization of phase space and calculation of number of microstates  (N, V, E ) accessible to a system (1000)

Evaluation of Lagrange’s undertermined multipliers (940) Molecular partition function for an ideal gas (942) Translational partition function (943) Rotational partition function (945)

Validity of the classical limit of statistical mechanics (1001) System of identical particles and symmetry of wave functions (1002)

Vibrational partition function (946)

Entropy and probability (1004)

Electronic partition function (948)

Canonical ensemble (1004)

Nuclear partition function (951)

Classical canonical distribution (1005)

Thermodynamic properties in terms of the partition function (951)

Canonical partition function and thermodynamic quantities (1006)

Thermodynamic properties of an ideal monatomic gas (953)

Application of the classical canonical distribution to an ideal gas (1007)

Thermodynamic properties of an ideal diatomic gas (954)

Law of equipartition of energy (1009)

Rotational partition function of homonuclear diatomic molecules and the nuclear spin   (956) Statistical thermodynamics of ortho- and parahydrogen (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 in terms 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)

Quantal canonical distribution (1010) Grand canonical ensemble (1011) Grand canonical partition function and thermodynamic 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-Tisza Theory (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 a gas from the virial equation (1030) Review Questions (1031)

2 8 . Chemical Kinetics

1033-1111

Experimental methods for studying kinetics of reactions (1033) Rate of reactions (1034) Rate law and the rate constant

(1035)

x

Order of a reaction (1035)

Dynamics of electron tunnelling in the Marcus theory (1107)

Units of rate constant (1037)

The Marcus cross relation

Integration of rate expressions (1038)

Review Questions and Problems (1110)

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 bimolecular gaseous reactions (1063) Eyring equation (1065)

(1109)

29.

Photochemistry

1112-1146

Consequences of light absorption : The Jablonski diagram (1113) Beer–Lambert law (1115) Laws of photochemistry (1118) Grotthus–Draper law (1118) Stark–Einstein law of photochemical equivalence (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)

Statistical mechanical derivation of the rate constant using TST (1067)

Kinetics of the anthracene reaction (1128) Ozone layer in the stratosphere (1129)

Theories of unimolecular gaseous reactions (1070)

Energy transfer in photochemical reactions :

1. Lindemann theory (1070)

Photosensitization and quenching (1131)

2. Hinshelwood theory (1073)

Quenching of fluorescence : The Stern-Volmer equation (1133) Chemiluminescence (1134) Rates of intramolecular photophysical processes and 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)

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)

30. Catalysis

1147-1164

Characteristics 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 catalyzed reactions (1159)

xi

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

3 1 . The Solid State

1165-1212

Difference between crystalline and amorphous solids (1165)

Quasicrystals   (1209) Review Questions and Problems (1211)

32. The Colloidal State

1213-1250

The colloidal systems (1213) Preparation of lyophobic colloidal solutions (1213)

Symmetry in crystal systems (1166)

A. Dispersion methods   (1213)

Point groups and space groups (1168)

B. Condensation methods (1215)

Space lattice and the unit cell (1169)

Purification of colloidal solutions (1216)

Bravais lattices (1169)

Properties of colloidal systems (1216)

Seven crystal systems (1170)

Properties of hydrophobic colloidal systems (1218)

Lattice energy of an ionic crystal (1173) Born-Lande  equation and the Born-Haber cycle (1174)

I. Electrical properties (1218) Charge on colloidal particles (1218)

Law of rational indices (1175)

The electrical double layer (1219)

Miller indices (1175) Interplanar spacing in a crystal system (1175)

DLVO theory of the stability of lyophobic colloids  (1221)

X–ray diffraction (1176)

Coagulation of colloidal solutions (1222)

The Bragg equation (1176) Experimental methods : The rotating crystal and the 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)

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 phase separation 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)

Energy band theory of conductors, semiconductors and insulators (1199)

Micellar catalysis (1240)

Superconductivity (1202)

Emulsification by surfactants (1242)

LTSC and HTSC (1202)

Macroemulsions (1242)

Imperfections in a crystal (1204)

Factors determining stability of emulsions (1243)

Point defects (1204)

Microemulsions (1245)

Schottky defects (1204) Frenkel defects (1206) Colour centres (1207)

Theories of emulsions (1246) The selection of surfactants as emulsifying agents (1246)

Line defects : Dislocations (1208)

Gels and their preparation (1247)

Imperfections due to transient atomic displacement (1209)

Importance and applications of colloids (1248) Review Questions   (1250)

xii

33. Surface Chemistry

1251-1272

Adsorption 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

1273-1326

Macromolecules (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 of macromolecules 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 FloryHuggins theory (1309) Helix-random coil transitions in polypeptides (1311) Structure of proteins (1312) Protein folding and denaturation (1315) -helix and  -pleated sheet structures of proteins (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

1327-1342

Basic theory (1327) Dynamics of electron-molecule collisions in mass spectrometry (1331) Factors influencing fragmentation (1332) Evaluation of heats of sublimation of solids (1332) Calculation of appearance potentials and ionization potentials (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 13 43 -1 36 2 Phenomenological laws and Onsager’s reciprocal relations (1343) Conservation of mass and energy in closed and open systems (1345) Entropy production due to heat flow (1348) Entropy production in chemical reactions   (1349) Entropy production and Entropy flow in open systems (1350) Transformation properties of fluxes and forces (1353) Principle of microscopic reversibility and the Onsager reciprocal relations   (1354) Verification of the Onsager relations (1355) Electrokinetic effects (1356) Stationary non-equilibrium states (1359) Applications of irreversible thermodynamics to biological systems (1360) Nonlinear thermodynamics of irreversible processes (1361) Concluding remarks (1362) Review Questions (1362)

General Bibliography

1 3 6 3- 1 3 6 6

Index

1367-1376

I NDEX Chapter 0 Mathematical 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)

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)

Chapters 1–36 A ab initio calculations ABMO Absolute activity Absolute entropies determination of standard Absorption spectrum Acid–Base catalysis indicators titrations Acids and Bases Arrhenius concept Brons ted-Lowry concept Lewis concept Actin Actinometer Ac tiv ated complex theory Activation energy Activity coefficient Activity coefficients Addition polymerization Adhesion Adiabatic demagnetization Adiabatic expansion Adsorption applications of BET theory heat of isobar isostere isotherms multilayer from solution Langmuir Adenosine diphosphate (ADP) Adenosine triphosphate (ATP) Affinity Allotropy Amperometric titrations

232 174 1293 610 610 613 302 1148 733 735 706 706 706 710 1312 1120 1063 1058 605 606 827 1301 505 496 538 1251 1252 1259 1253 1254 1254 1263 1259 1264 1256 655 654 1279 672 929

Amphipathy 1226 Amphiphile 1226 Angular functions 65 Angular momentum 87, 14 1,165 Addition of 169 Matrices 165 Angular momentum operators 141 Anharmonicity constant 317 Aniline–hexane system 772 Anisotropy 516 Antibodies 1238 Antiferromagnetism 448 Anthrancene reaction 1128 Anti-Stokes Raman spectroscopy 334 Apparent equilibrium constant 655 Apparent standard reaction Gibbs energy 656 Appearance potentials 1332 Associated Legendre polynomials 67 Arrhenius equation 1058 Ar rheniu s f re quenc y fa ct or 10 58 Arrhenius parameters 1058 Arrhenius activation energy 1058 As ymmetric top molecules 314 Asymmetry parameter 421 Atactic polymers 1275 Atomic populations 238 Atomic states and term symbols 149 Atomic number 23 Atomic spectra 154 fine structure 155 hyperfine structure 162 Stark effect 162 Zeeman effect 159 Aufbau principle 87 Auger electron spectroscopy (AES) 1270 Austin Model 1 237 Autocatalysis 1161 Auxochrome 339

(i)

Avogadro’s law Axis of rotation improper proper Azeotropic mixtures

452 248 247 766

B Balmer series 30 Bancroft rule 1242 Band spectra 305 Band theory 1197 Barometric formula 477 Base pairing in DNA 1320 Basis set 232 Bathochromic shift 339 BBGKY equations 514 Beer–Lambert law 1115 Berthelot equation 485 BET adsorption is otherm 1259 BET equation 1261 Binding and antibinding regions 232 Bipolaron 1308 BPP theory of relaxation processes 372 Biochemical equilibria 654 Bioelectrochemistry 930 Biological electrochemical cell 930 Bjerrum theory of ion association 887 Bismuth–cadmium system (phase rule) 683 Black body radiation 24 and BE statistics 960 Bloch function 1197 Blue shift 339 BMO 177 BCS theory 1202 Bohr’s correspondence principle 109 Bohr frequency condition 355 Bohr’s theory 26 Bohr radius 28 Bohr–Sommerfeld theory 31

GENERAL B B IL O IG R A P H Y 3 G E N E R A L BIBLIOGRAPHY 

1368 (ii) Boiling point elevation 788 and molar mass 790 Boltzmann constant 453 Boltzmann population 311 Boltzmann factor 311 Boltzons 935 Bo ltz mann ent ropy eq uati on 61 8 Bomb calorimeter 565 Bond energies 563 Bond length 260 Bond moments 440 Bond order 186 Born-Haber cycle 1174 Born’s interpretation 42 Born–Oppenheimer approximation174 Born–Lande   equation 1174 B os e- Ei ns tei n c on de ns at io n 96 4 Bose-Einstein distribution 963 Bose–Einstein statistics 936 and ideal photon gas 960 Bose gas 962 Bosons 936 Bound state 438 Boyle temperature 484 B–Z reaction 1161 Brackett series 29 Bragg equation 1176 Branched chain reaction 1085 Bravais lattices 1169 Brillouin zone 1198 Brownian movement 1218 Buffer solutions 720 capacity and buffer index 721 Butler-Volmer equation 914 C Cage effect Calomel electrode, saturated (SCE) Canonical commutation relation Canonical ensemble Canonical partition function Canonical structures Capillary-active and inactive Capillary condensation Capillary electrophoresis Carbon dioxide system (phase rule) Carbon dioxide laser Carnot, cycle theorem Catalysis acid–base auto characteristics of enzyme heterogeneous homogeneous Cathode rays Cell constant Cells, concentration fuel Chain reactions in kinectics

1054 837 138 1004 1006 196 1266 1264 1325 679 1145 572 574 1147 1149 1161 1148 1150 1157 1148 21 802 853 862 1082

Chandrasekhar limit 976 Character 252 Character tables 255 Characteristic rotational temperature 945 Characteristic vibrational temperature 947 Charge-Coupled device (CCD) sensor 1209 Charge transfer bands 344 Charge–transfer spectra 340 Charles’ law 452 Chemical affinity 629 Chemical equilibrium 620 law of 624 Chemical shift 358 Chemical shift reagents 386 Chemical isomer shift 414 Chemical kinetics 1033 Chemical potential 592 Chemiluminescence 1134 Chemisorption 1251 Chlorine electrode 837 Choles teric liquid crystals 521 Chromophores 338 Circular dichroism (CD) 512 CIDNP 388 Clapeyron equation 597 Clapeyron–Clausius equation 598 Class 250 Classical and quantum limits of statistical mechanics 1001 Classical canonical distribution 1005 Classical stastistical mechanics 989 Claude’s process 496 Clausius equation 485 Clausius –Mosotti equation 432 Clebsch–Gordon coefficients 170 Clebsch–Gordon series 170 Cluster expansion 1027 Coagulation of colloidal solutions 1221 Coefficient of viscosity 508 Coefficients of hybridization 200 Coherence length 1142 Coherent anti-Stokes Raman spectroscopy (CARS) 334 Cohesion 505 Collagen 1312 Colligative properties of dilute solutions 778 Col lis ions and enc ounters 10 87 Collision broadening 304 Collision parameters 461 Collision cross-section 461 Collision diameter 461 Collision frequency 462 Collision number 461 Collision theory 1060 Colour centres 1207 Colloidal particles 1213 Colloidal state 1213 applications 1177

PRINCIPLES OF PHYSICAL CHEMISTRY

classification 1213 coagulation 1221 origin of charge 1218 peptization 1214 preparation 1213 properties 1216 protective 1222 Combination bands 322 Combustion, enthalpy of 555 Common ion effect 719 Commutation relations 141 Commutator 141 Complex NMR spectra 385 Complex reactions, mechanism of 1053 Components, phase rule 661 Compound triplet 158 Compressibility 460 Compressibility factor 479 Compton effect 36 Compton shift 36 Compton wave length 37 Computational quantum chemistry 232 Computer-assisted tomography (CAT) 391 Computer programs 238 Computer simulation of liquids 512 Concentration cells 853 with transference 859 without transference 857 Concentration polaris ation 919 CNDO 238 Conductance, electrolytic 801 equivalent 801 molar 802 specific 801 Condensation polymerization 1303 Conductometric titrations 821 Configurational integral 1026 Configuration interaction 236 Conductors, semiconductors 1199 and insulators Conformations of polymers 1296 Congruent melting point 686 Conjugate elements 250 Conjugate acids and bas es 707 Conjugate solutions 772 Conjugated molecules 345 Conservation of energy 528 Conservation of mass and energy 1345 Conservative forces 461 Consolute temperature 771 Constrained chain 1300 Cons tructiv e interferenc e 1199 Contact shift 387 Continuity of state 490 Contour length 1296 Cooling curves 681 Cooper pairs 1202 Cooperativity 658 Corey-Pauling rules 1313

INDEX Correc t B olzmann counti ng 996 Correlation diagram 225 Correlation energy 233 Correlation spectroscopy (COSY) 384 Corresponding states, principle of 493 Corrosion of metals 918 Coulomb operator 234 Counter ions 1220 Coupled flows 1344 Coupled reactions 1351 Covalent bond 173 Criteria for reversible   and irreversible processes 589 Critic al c onstants of a gas 489 Critical micelle concentration (CMC) 1233 Critical phenomena 489 Critical solution temperature (CST) 771 Critical temperature 490 Critical volume 489 Cryosopic constant 794 Crystal imperfections 1204 Crystals, covalent 1189 ionic 1189 metallic 1193 molecular 1188 Crys tallographic s ymmetry 261 Crystal systems 262 Curie temperature 448 Curved Hammett plots 653 Cyclic rule 8,532 Cyclic process 872 D Dalton’s law 453 Daniell cell 835 D av is son -G er me r e xp eri men t 35 d-d   bands 343 de Broglie’s equation 33 ex peri ment al verif icat ion of 34 de Donder’s treatment 628 Debye equation 433 Debye’s T3  Law 986 Debye-Falkenhagen effec t 826 Debye–Hückel limiting law 832 Debye–Hückel theory, of strong electrolytes 824, 882 of mean activity coefficients 830,882 Debye-Hückel-Onsager equation826 Debye length 831 Debye–Scherrer method 1178 Debye–Smoluchowski equation 1087 Debye theory of heat capacity 983 Debye temperature 986 Defects in crystals 1204 Degeneracy 53 Degeneracy temperature 966 Degenerate BE gas 966 Degree of advancement 628

1369 (iii) Degree of association 796 Degree of dis soc iation 63 2,7 97 Degrees of freedom 472 rotational 472 translational 472 vibrational 473 Degrees of freedom (phase rule) 663 Degree of hydrolysis 726 Degree of poly merization 1275 Delocalization energy 208 Detergents 507 Density functional theory (DFT) 239 Density of states (DOS) 245,1195 Density matrix (statistical matrix)997 Destructive interference 1199 Deviations from ideality 480 Diamagnetism 444 Diamond, structure of 1189 Diatomic rotor 307 Dieterici equation 484 Difference bands 322 Diffraction, electron 1186 neutron 1187 Diffusion 470,1293 Diffusion coefficient 1293 Diffusion-controlled reactions 1087 Diffusion layer 920 Diffusion overpotential 916 Dipole-dipole interaction 487 Dipole moments and molecular structure 440 Dirac delta function 994 Di rac ’s br a an d k et no tati on 9 96 Dirac’s relativistic quantum mechanics 37 Direct product 275 Di sc –s haped liquid c ry sta ls 5 22 Dislocations 1208 Dissociation constants 712 Dissociation energy 265 Distillation, fractional 768 of immiscible liquids 768 steam 769 Distribution law (Nernst’s) 697 applications of 701 thermodynamic derivation of 698 DLVO theory 1221 DNA double helix 1321 DNA denaturation 1322 DNA renaturation 1323 Donnan membrane equilibrium 1283 Doping in semi conductors 1201 Doppler Broadening 304 Double helix (DNA) 1321 Double resonance 381 DPM 387 DPPH 397 Dropping mercury electrode (DME) 922 Dye lasers 1144 E Eadie-Hofstee method

1153

Ebullioscopic constant 790 Echo planar imaging (EPI) 391 Eckart’s inequality 149 Effective Fock operator 235 Efficiency, of heat engine 572 Eigenvalue equation 39 Eigenfunctions and eigenvalues 141 Einstein’s photoelectric equation 25 Einstein-Smoluchowski equation 1294 Einstein theory of heat capacity 982 Electric field gradient (EFG) 420 Electric properties of molecules 431 Electrical capacitance 895 Electrical double layer 1219 Electrical energy 840 Electrified interfaces 892 Electrocapillary measurements 891 Electrocatalysis 909 Electrochemical series 847 Electrode potential 838 Electrode reactions, kinetiecs of 911 Electrokinetic properties 1224 Electrolytic cell 836 Electrolytic conductance 801 Electron correlation 233 Electron diffraction 1186 e/m ratio 21 Electron mass 22 Electron spectrocopy for chemical analysis (ESCA) 417 Electron spin resonance (ESR) spectra 392 Electron tunnelling in Marcus theory 1107 Electronic spectra 335 of conjugated molecules 345 of transition metal complexes 341 Electronically conducting polymers 1306 Electron-molecule collisions 1331 Electron transfer reactions Marcus theory 1105 Electron tunnelling 1107 Electro-osmosis 1357 Electro-osmotic pressure (EOP) 1357 Electrophoretic mobility 1225 Electrophoresis 1224 capillary, gel, pulsed field 1324 ELDOR 406 ENDOR 406 EMF of galvanic cells 848 EMF measurements, applications 865 Emission spectrum 302 Emulsifiers 1246 Emulsions 1242 Enantiotropic transitions 523 Endergonic reactions 655 Endothermic reactions 552 Energy barrier 1057 Energy transfer 1131

1370 (iv ) Ensemble average 991 Ensemble theory 989 Enthalpy 533 Enthalpy change 552 of combustion 555 of formation 557 of neutralization 555 of reaction 555 of solution 556 Entropy 575 absolute values 610 and probability 618 change in reversible and irreversible processes 577 of mixing of gases 582 of vaporization 578 physical significance of 584 Entropy change of mixing of an ideal solution 761 Entropy production and entropy flow in open systems 1352 Entropy production due to heat flow 1348 Entropy production in chemical reactions 1349 Entropy production per unit time1351 Entropy, residual 618 Enzyme catalysis 1150 Equations of state 481 The Euler reciprocal relation 531 Equil ibrium approx imati on 1054 Equilibrium constant 624 pressure dependence 640 t emper atur e dependenc e 637 Equipartition of energy 474 Ergodic hypothesis 991 ESCA 417 ESI (electrospray ionization) 1331 Even-even rule 1335 EXAFS 1270 Excimer lasers 1144 Excess population 372 Excluded volume 481 Excited states 1138 Expansion of an ideal gas 535 adiabatic 538 isothermal 535 Exact and inexact differentials 530 Exc ess pres sure in a drop 506 Exchange-correlation energy functional 240 Exchange energy 151 Exchange operator 234 Ex cited s tates, geometry 1138 Exciton 1209 Exergonic reactions 655 Exothermic reactions 552 Expansivity 460 Explosion limits of chain reactions 1086 Extended Hückel theory (EHT) 236 Extinction (absorption) coefficient, molar 1116

GENERAL B B IL O IG R A P H Y 3 G E N E R A L BIBLIOGRAPHY 

Extremum principle Euler’s relation Eutectic point Eutectic systems Explosion temperature Eyring equation

PRINCIPLES OF PHYSICAL CHEMISTRY

1360 64 680 679 562 1065

F Fast atom bombardment (FAB) 1330 F–centres 1207 FEMO theory 204 Femtochemistry 1034 Femtosecond transition state spectrocopy 1145 f-f   bands 345 Fermi contact interaction 367 Fermi-Dirac distribution 969 Fermi-Dirac gas 969 Fermi–Dirac statistics 939 Fermions 936 Fermi energy 970 Fermi’s golden rule 245 Fermi Level 970 Fermi momentum 971 Fermi resonance 323 Fermi surface 1198 Fermi temperature 972 Ferretin 1312 Ferromagnetism 448 Fi ck ’s fi rs t law of dif fus ion 12 93 Fi ctitious refer ence sy stem 239 Field desorption (FD) 1330 Field ionization (FI) 1330 Fifth state of matter 967 Fine structure 87, 155 Fine structure constant 127 Fingerprint region 324 First law of thermodynamics 528 First–order reactions 1035 Flame temperature 562 Flash photolysis 1096 Flocculation values 1223 Flory-Huggins equation 1311 Flory-Huggins theory 1309 Flow methods for fast reactions10 95 Flu ctuation s in ens embl es 10 15 Fluidity 509 Fluorescence 1115 quenching of 1133 Fluxes and forces 464,1343 Force constant 54 Fourier synthesis of electron density 1183 Fourier transform NMR spectroscopy 370 Fourier transform spectroscopy 303 Fractional distillation 768 Fragmentation in mass spectrometry 1333 Franck-Condon principle 335 Franck-Hertz experiment 28 Franc k-Rabinovic h effec t 1054 Free electron model 1194

Free energy of a spontaneous reaction 620 Fr ee i nduction decay (FI D) 371 Free path phenomena 471 Free volume 500 Freely jointed chain 1296 Freezing mixtures 685 Freezing point depression 792 and molar mass 794 Frenkel defects 1204 Freons (chlorofluorocarbons) 1131 Freundlich adsorption isotherm 1253 Frictional coefficient 1294 Fr ontier molec ular or bitals 337 Fuel cells 862 Fugacity 601,1013 determination of 602 Full rotation group 257 Functional derivative 241 Functional MRI 390 Fundamental vibrational frequency 316 G g-factor in ESR 396 Galvanic cells 835 Gamma function 961 Garrett-Brattain space charge 905 Gas electrodes 836 Gas lasers 1144 Gas laws, derivation of 451 Avogadro’s law 452 Boyle’s law 451 Charles’s law 452 Dalton’s law 453 Graham’s law 453 Gases, kinetic theory of 450 Gas-liquid chromatography GLC 1338 Gaussian type orbitals (GTOs) 232 Gel electrophoresis 1324 Gels 1247 Generalized angular momentum 149 Generalized gradient approximation (GGA) 242 Generating operators 292 Giant magnetoresistance (GMR) 1209 Gi bbs ads orpt ion is otherm 12 64 Gibbs–Duhem equation 592 Gibbs–Duhem–Margules equation 758 Gibbs free energy 586 Gibbs free energy change of mixing for an ideal solution 759 Gibbs–Helmholtz equation 590 Gibbs paradox 995 Gibbs phase rule 665 Glass electrode 871 Glide plane 264 Glycolysis 656 Gold number 1222 Good solvent 1299 Gouy balance 447

INDEX Gouy-Chapman model 900 Graft copolymers 1276 Gr and canonical ens emble 993 Grand canonical partition function 1013 Grand potential 1013 Grand/Great orthogonality theorem (G.O.T.) 253 Graphite, structure of 1189 Grotrian diagram 155 Grotthus–Draper law 1118 Grotthus mechanism 805 Group moments 441 Group postulates 249 Group theory 247 and normal modes of vibration 268 direct porduct of irreducible representations 275 use in determining selection rules in transitions 279 use in factoring the secular equation in MOT 285 Group velocity 134 H Half–life time 1047 Half–wave potential 925 Hamiltonian operator 42 Hammett equation 648 Hammett constants 648 Hammett plot 650 Hard-sphere potential 1029 Hartree–Fock self–consistent field method 128 Hartree-Fock-Roothaan SCF method 234 Heat capacities of monatomic crystals 982 The Debye theory 983 The Einstein theory 982 Heat capacity 534 Heat capacities at constant pressure and constant volume 535 Heisenberg’s uncertainty principle 36 1313 -helix Helix-coil transitions 1312 H el lm ann -Fe yn ma n th eo rem 22 9 Heitler-London-Slater-Pauling (HLSP) theory 192 Helmholtz free energy 585 Helmholtz-Perrin model 899 Hemoglobin, binding of oxygen 658 Henderson-Hasselbalch equation 722 Henry’s law 774 Henry’s law and Raoult’s law 775 Hermite equation 55 Hermite polynomials 56 Hermitian operators 106 Hess’ law 563 applications of 564 Heterogeneous c atalysis 1155 Heteronuclear 2D J-resolved

1371 (v ) spectra Heterogeneous equilibria High energy phosphate ester bonds High pressrue phase diagrams Hindered rotation Hinshelwood theory Hi ttor f’s theoretical device Hohenberg-Kohn theorem Holes in s emiconductors Homogeneous equilibria Homonuclear 2D J-resolved spectra HOMO-LUMO transition Hooke‘s law potential Hückel molecular orbital theory Hü ck el ’s r ule of aroma tic ity Hund's rule Hund’s rules Hybrid functional Hybridization coefficients of Hydration number Hydrogen–bromine reaction (photochemical) Hydrogen–chlorine reaction (photochemical) Hydrogen electrode Hy drogen-oxygen fuel cell Hydrogen spectrum Hydrolysis of salts Hydronium ion Hydrophile-Lipophile balance (HLB) Hydrophobic interaction Hyperchromic effect Hyperfine structure in atomic spectra Hy perfine str ucture in E SR Hypsochromic shift

383 642 655 678 373 1073 805 239 1200 630 383 340 54 205 2 10 87 151 242 197 200 886 1126 1125 836 862 28 724 706 1228 1314 1322 162 393 339

I Icosahedral symmetry 1209 Ideal gas equation 452 Ideal solution 756 Idempotent matrix 998 Identical particles 1002 Impact parameter 1103 Imperfections in cry stals 1209 Incongruent melting point 687 Index of hydrogen deficiency 1336 Isothermal expansion 535 Ilkovic equation 923 derivation 923 Indicators, acid–base 733 theory of 733 Inorganic phosphate 655 Insulators 1201 Integrated absorption coefficient1137 Integration of rate expressions first-order reactions 1038 s ec ond–or der r eac ti ons 1042 third–order reactions 1045

zero–order reactions 1047 Interfacial tension 507 Interionic effect 824 Intramolecular energy transfer 1079 Internal pressure 482 Intensity of spectral lines 304 Intermediate neglect of differential overlap (INDO) 238 Intermolecular energy transfer 1136 Intermolecular forces 487 Internal conversion 1114 Internal energy 529 Internal rotation 314 Internuclear distance 309 Internuclear double resonance (INDOR) 385 I nt er sy st em c ro ss in g (I SC ) 11 14 Intramolecular photophysical processes 1135 Inverse anti-Stokes Raman scattering 334 Inverse-Stokes Raman scattering 334 Inversion doubling 323 Inversion temperature 548 Inversion spectrum 315 Ionic atmosphere 825 Ionization potentials 1332 Ionic, bond 173 mobility 804,814 product of water 715 Ionic crystals, structures of 1190 Ionic doublets 824 Ionic strength 829 Ioniz ation eff ic ienc y c ur ve 13 32 Ionization potentials 1332 Isenthalpic process 546 Isentropic process 582 Irreversible processes 577 Irreversible thermodynamics 1343 Isoelectric focusing 1324 Isoelectric point (pI) 1324 Isomorphism 297 Isosteric enthalpy of adsorption 1185 Isotactic polymers 1275 Isothermal expansion 535 work done in 535 Isotope peaks 1329 Isotope separation 1144 Isotopic substitution 312 Isotropy 516 Iteration 128 J Jablonski diagram Jahn-Teller distortion Jahn-Teller Theorem  j.j.  coupling Joule-Thomson coeffic ient Joule-Thomson effect K Karplus relation in NMR

1113 343 109 153 546 545 368

1372 (vi ) Kelvin equation 506 Kinetic energy and temperature 453 Kinetic gas equation 451 Kinetic theory of gases 450 and gas laws 451 Kinectics of acid–base catalysed reactions 1149 branched–chain reactions 1085 chain reactions 1082 complex reactions 1079 consecutive reactions 1081 diffusion–controlled reactions 1087 electrode reactions 912 enzyme–catalysed reactions 1150 fast reactions 1093 polymerization 1301 reactions in solution 1086 reversible reactions 1079 surface reactions 1155 Kirchhoff equation 560 Knudsen cell 1332 Knudsen effect 1359 Knudsen gas 462 Kohlrausch law 810 applications 815 Kohn-Sham method 239 Koopmanns’ theorem 108,417 Kramers’ degeneracy 109 Kramers’ theorem 109,401 Kronecker delta 42 1197 k - space L Ladder operators 143 Lambda temperature 1018 Lambda transition 1018 Laminar flow 508 Langmuir-Hinshelwood mechanism 1155 Lagrange’s equations of motion 321 Lagrange’s undetermined multipliers 937 Landau theory of liquid helium-II1022 Lande   interval rule 159 Lande   g-factor 159 Langevin function 434 Langmuir's adsorption isotherm 1256 Langmuir’s theory of adsorption1256 Lanthanide shift reagents 386 Laplace equation 421 Laplacian operator 42 Laporte rule 343 Larmor frequency 357 Larmor precession 357 Laser 1139 Laser Raman spectroscopy 1143 Lattice energy 1173 Lattice model of polymer solution 1309 LCST 771 Law Avogadro’s 452

GENERAL B B IL O IG R A P H Y 3 G E N E R A L BIBLIOGRAPHY 

PRINCIPLES OF PHYSICAL CHEMISTRY

Beer–Lambert 1115 Boyle’s 451 Charles 452 Curie’s 445 of chemical equilibrium 625 of cons erv ation of ener gy 5 28 of corresponding states 493 Dalton’s 453 distribution (Nernst) 697 equipartition of energy 474 Henry’s 774 Hess’s 563 of mass action 625 of photochemical equivalence1118 of rational indices 1175 LCAO-MO approximation 174 LCDs 519 Le Chatelier’s principle 646 Lead–silver system (phase rule) 682 LEED 1269 Lennard–Jones (6, 12) potential 488,1030 Lever rule 768 Levitation 1202 Lewis concept of acids and bases 710 Light scattering 1289 Limiting current density 921 Limiting diffusion current 921 Lindemann’s theory of unimolecular reactions 1070 Li ne d efec ts : Di sloc ations 12 08 Line spectra 305 Linear free energy relationships (LFERs) 648 Linear rotor 313 Lineweaver-Burk m ethod 1152 Lippmann equation 894 Liquefaction of gases 495 Liquid crystals 516 classification of 520 molecular arrangements in 524 Liouville theorem 992 Liquid helium system 678,10 18 Liquid–junction potential 860 Liquid state 499 Local density approximation (LDA) 242 London forces 487 London-Tisza theory 1019 Lorentz-Lorenz equation 437 Lotk a- Volterr a mec hanis m 1162 Lowering of vapour pressure 778 323 l-type doubling Lyman series 29 M Macroemulsions Macromolecules conformations of molar masses of Madelung constant Magic angle s pinn ing (MA S)

1242 1273 1296 1277 1173 3 81

Magnetic properties of molecules442 permeability 442 susceptibility 443 Magnetic polarizability (magnetizability) 445 Magnetic resonance imaging (MRI) 390 Magnetic resonance spectroscopy 299 Magnetogyric ratio 303 MALDI 1330 MALDI-TOF mass spectrometry 1330 Marcus cross relation 1109 Marcus theory of electron transfer reactions 1105 Mark–Houwink equation 1279 Mass number 23 Mass spectrometry 1327 Mathematical probability 618 Matrix element 112,175 Matrix mechanics 37 Matter waves 34 Maximum work 537 Maxwell–Boltzmann statistics 935 Maxwell’s distribution of molecular energies 455 Maxwell’s distribution of molecular velocities 454 Maxwell’s relation 437 Maxwell’s relations in thermodynamics 587 Mayer f -function 1026 McBain micelles 1231 McConnell equation 398 Mc Laf fer ty rearrangement 1335 Mean ionic activity 852 Mean free path 462 Mechanisms of complex reactions 1053 Melting curves of DNA 1322 Meritectic (or peritectic) temperature 687 Meissner effect 1202 Membranes, biochemical 930 Membrane potentials 930 Mesomorphic state 516 Mesomorphism lyotropic 516 Thermotropic 516 Metabolism : anaerobic and aerobic 656 Metal deficiency defects 1207 Metallic crystals 1193 free electron model of 1194 Metallic properties 1193 Metal-metal transitions 343 Metastable equilibrium 674 Metastable peaks 1329 Michaelis–Menten equation 1151 Micellar aggregation numbers 1232 Micellar catalysis 1240 Micelle formation 1229

(vii ) 1373

INDEX Mass action model 1229 Ph as e s eparat ion mod el 1 22 9 Microcanonical enemble 993 Microemulsions 1245 Microscopy far-field confocal 1144 near-field optical 1144 Microstates 936 Microwave oven 313 Microwave spectra 307 Milikan’s oil drop tec hnique 21 Miller indices 1175 MINDO 238 Mode locking 1142 Mobility, ionic 804 determination of 814 Molal boiling point elevation constant 790 Molal freezing point depression constant 794 Molar absorption coefficient 1116 Molar conductance 802 Molar extinction coefficient 1116 Molar ionic conductance at infinite dilution 803 and ionic mobility 812 Molar polarization 432 Molar mass determination by mass spectrometry 1337 Molar mass distribution in condensation polymerization 1303 Molar refraction 437 Molecular beam methods 1097 Molecular dynamics (MD) method 513 Molecular ion 1336 Molecular orbital theory (MOT) 174 Molecular orbitals 174 antibonding 174 bonding 174 Molecular orbitals for homonuclear diatomic molecules 186 for heteronuclear diatomic molecules 188 Mo lec ular part ition fu nc ti on 94 2 Molecular reaction dynamics 1097 Molecular symmetry 247 Molecularity of a reaction 1052 Moment of inertia 308 Monochromatic radiation 1066 Monte Carlo (MC) procedure 1103 Morse potential 317 Mössbauer s pectroscopy 412 Moving boundary method 809 Mutual exclusion rule 330 Mulliken population analysis (MPA) 238 Multicentre integrals 238 Multi photon s pec tros copy 1143 Multiplication table in group theory 250 Myoglobin, binding of oxygen 657 Myosin 1312

N Natural linewidth 304 Neel point 443 Nematic liquid crystals 521 Nernst Distribution law 697 Nernst, equation 844 heat theorem 609 Nervous system 931 Neutron 23 Neutron diffraction 1187 Nicotine–water system 773 Nitrogenous bases in DNA and RNA 1319 Nonlinear thermodynamics of irreversible processes 1361 Non-Newtonian liquids 508 Nonradrative transitions 1114 No rmal c oordi nate an alys is 3 21 Normal coordinates 269 Normal mode of vibration 268, 320 Normalization of wave function 47 NRF spectroscopy 412 Nuclear magnetic double resonance (NMDR) 374 Nuclear magnetic resonance (NMR) 353 Nuclear spin and rotational partition function 956 Nuclear Overhauser effect (NOE) 381 Nuclear spin-spin interaction 362 Nucleic acids (DNA and RNA) 1319 NMR of AB spin system 375 NMR, 2-dimensional 380 NMR of liquid crystals 389 NMR of paramagnetic compounds 387 NMR of solids 380 Non-trivial solution 176 Nuclear quadrupole resonance (NQR) spectroscopy 420 Nylon 66 1277 O Off-resonance proton decoupling382 One–dimensional simple harmonic oscillator 54 Open systems 591 Onsager’s phenomenological coefficients 1274 Onsager’s reciprocal relations, verification of 1345,1355 Opacity function 1103 Operand 43 Operators in quantum mechanics 43 Optical activity 511 Optical pumping 1141 Optical rotatory dispersion (ORD) 512 Optimal pH point 1161 Orbital and spin angular momentum operators 147 Orbital energies of multi–electron atoms 87

Orbitals, filling of 87 Orbital exponent 232 Order parameter 523 Order of a reaction 1035 methods of determination 1051 Order and molecularity of simple reactions 1052 Order and molecularity of complex reactions 1053 Order of a group 250 Orthonormal set of wave functions 42 Orgel diagrams 344 Ortho and para hydrogen 958 Oscillator strength 1138 Oscillatory reactions 1161 Osmometry 1281 Osmosis 781 osmotic pressure 781 Osmotic pressure and molar mass 783 Osmotic pressure and vapour pressure lowering 784 Ostwald’s dilution law 822 Outer Helmholtz plane (OHP) 898 Overtones 322 Overpotential 912 Overvoltage 917 applications of 917 Oxidation potential 838 Oxidation–reduction indicators 879 Oxidation–reduction electrodes 838 Ozone hole 1131 Ozone layer 1129 P P–V isotherms of carbon dioxide gas 490 Parallel bands 324 Paramagnetism 444 Parity 260 Pariser-Parr-Pople (PPP) approximation 235 Partial molar properties 591, 595 Particles indistinguishable 1002 distinguishable 1002 Partition function, canonical 976 electronic 948 nuclear 951 rotational 945 translational 943 vibrational 946 Pascal’s constants 444 Pascal’s triangle 363, 396 Paschen series 29 Paschen-Back effect 162 Patterson synthesis 1184 Pauli’s exclusion principle 85 Pauli spin matrices 167 Penrose tiling pattern 1210 Perfect pairing approximation 144 Perpendicular bands 324

(viii) 1374 Perturbation Theory 111 Degenerate 117 first order 115 second order 113 Non degenerate 112 time-dependent 242 time-independent 111 application to helium 115 Perovskite structure 1203 PET (polyethylene terephthalate) 1277 Pfund series 29 p H scale 716 p H, determination of 869 Phase problem in crystallography 1184 Phase equilibria 661 Phase 661 Phase rule (Gibbs) 665 derivation of 665 Phase rule, application to one–component sy stems 667 two–component sy stems 679 t hr ee –c om po ne nt s y st em s 69 0 Phase transitions, Ehrenfest classification 692 Phenol–water system (phase rule) 772 Phenomenological laws 1343 Phonon 1209 Phosphorescence 1115 Photochemical rate law 1124 Photobiology 1112 Photochemical reactions 1123 kinetics of 1125 Photochemistry 1112 Photodissociation coefficient 1130 Photoelectric effect 24 Photoelectron spectroscopy (PES) 416 appilications of 417 Photon 25 Photosensitization 1131 Photosynthesis in plants 1132 Pierl’s distortion 1307 Planck’s constant 24 Phanck's law 961 Plait point 691 Plasmolysis 786 1313 -pleated sheet Pockels cell 1142 Point defects 1204 Point groups 250 character tables for 254 representations of 251 Poisseuille’s equation 509 Poisson equation 882 Poisson-Boltzmann equation 883 Polar, resonance and steric effects 653 Polarisation of a molecule in an electric field 431 Polarizability 431 Polarizability volume 435

GENERAL B B IL O IG R A P H Y 3 G E N E R A L BIBLIOGRAPHY 

Polarography 919 applications of 926 Polaron 1308 Polyacetylene 1307 Polyethylene (LDPE and HDPE)1274 Poly(para-phenylene) 1308 Poly(sulphur nitride) 1306 Polymerase chain reaction (PCR) 1323 Polymers, classification 1275 Polymer liquid crystals 522 Polymorphism 672 Polymorphism in liquid crystals 522 PMMA 1274 Poly di spe rsit y in dex (PD I) 12 78 Polynucleotides 1319 Polystyrene 1274 Population inversion 1141 Potassium iodide–water system (phase rule) 683 Potential energy surfac es 1099 Potentiometric titrations 872 Pressure of an ideal gas 450 Pressure-induced polymorphism 523 Primary process 1122 Principal axis system 421 Prigogine’s principle of minimum entropy production 1360 Principle of microrcopic reversibility 1354 Probe and pump pulses 1145 Projection operators 292 Proteins, structure of 1312 denaturation of 1315 Protein folding 1315 Pseudo-contact shift 387 Pseudmonomolecular reactions 1052 Pulse radiolysis 1097 PVC 1274 Q Quantal canonical distribution 1010 Quantal grand canonical distribution 1014 Quantal microcanonical ensemble 998 Quantization of phase space 1000 Quantum chemistry programs 238 Quantum concentration 1293 Quantum electrodynamics (QED) 227 Quantum mechanical tunnelling 133 Quantum mechanics 37 postulates of 39 Quantum numbers 83 azimuthal 83 magnetic 83 principal 83 spin 84 Quantum statistical mechanics 996 Quantum theory of radiati on 24 Quantum yield 1118 Quasicrystals 1209 Quasiparticles 1022

PRINCIPLES OF PHYSICAL CHEMISTRY

Quenching of fluorescence Quenching of orbital angular momentum Q-switching Quinhydrone electrode

1133 446 1142 838

R Racah parameters 151 Radial dis tribution functi on 512 Radiative transitions 1045 Radius of gyration 1298 Radius of the ion sphere 831 Raising and lowering operators 143 Ramachandran diagram 1314 Raman shift 327 Raman spectroscopy 326 Ramsay-Shield’s equation 504 Raoult’s law 752 of vapour pressure lowering 779 Rate constant 1035 statistical mechanical derivation of 1067 Rate of Reactions 1034 Rate expressions, integrations of 1038,1042,1045,1047 Rational indices, law of 1175 Rayleigh-Jeans law 961 Rayleigh ratio 1291 Rayleigh scattering 326 Reaction coordinate 1054 Reaction cross-section 1103 Reaction rate, effect of temperature 1056 Re ac ti on rates , t heor ies of 10 60 Reactions in flow systems 1090 Rearrangements 1335 Real gases 479 deviation from ideal behaviour 479 Rectifier 1201 Red shift 339 Redlich–Kwong equation 485 Redox titrations 875 Re du ced os mo ti c pr es su re 12 82 Reducible and irreducible representations 252 Reduced phase rule equation 679 Reduced plack's constant 46 Reduction potential 838 Refractive index 510 Refraction, molar 510 Relativistic quantum mechanics 37 Relaxation methods in kinetics 1093 Relaxation processes in NMR 371 Residual entropy 618 Resonance energy 569 Resonance Raman spectroscopy 331 Rest mass 22 Reverse osmosis 786 Reversible and irreversible processes : criteria for 589 Reversible electrodes 836 Reversible isothermal expansion of a real gas 543

INDEX Reynolds number Rhodopsin Ribosomes Ric e- Her zfeld mechanis m Riemann zeta function Root mean s quar e veloci ty Rotational quantum number Rotational constant Rotational spectra Rotational term Rotation–v ibration spec tra Rotons RRK theory RRKM theory Rus sel l-S aunders coupl ing Rutherford’s atomic model Rydberg constant

(ix) 1375 509 1312 1319 1083 961 457 64 308 307 308 319 1022 1074 1077 132 23 30

S Sackur-Tetrode equation 954 Saddle point 1101 SALCs 286 Salt bridge 861 Salt effects on reaction rates 1088 Saturated calomel electrode (SCE) 839 Saxon’s relation 1358 Schottky defects 1204 Scattering factor 1183 Schrödinger wave equation, solutions of 40,45-83 particle in a one-dimensional box 45 particle in a three-dimensional box 52 rigid diatomic rotor 63 si mple harmonic oscillator 54 hydrogen atom 65 many-electron atoms 111 Screw axis 264 Screw dislocation 1208 Second–order reactions 1042 Second law of thermodynamics 571 Second sound 1020 Second virial coefficient 486 Secondary process 1122 Secular determinant 176 Secular equation 176 Sedimentation equilibrium method 1288 Sedimentation velocity method 1285 Selection rules 303 Semiconductors 1200 Semiconductor interfaces 904 Semi-empirical methods 236 Semipermeable membrane (SPM) 781 Semipermeability, theories of 785 Seven segment cell 518 Shirakawa technique 1307 Similarity transformation 250 Shielding constant 131,358 Shielding mechanisms in NMR 360

Lamb's formula 360 Sigmoid binding curve 658 Simple harmonic oscillator (SHO) 54 Algebraic technique for solving the sc hrödinger equati on 137 Single electrode potential 839 Single-molecule spectroscopy 1144 Singlet state 113 Slater determinant 76, 1003 Slater type or bitals (STO s) 232 Slater’s rules 131 Slater sum 1011 Slope-intercept method 595 Smectic liquid crystals 521 Soft Laser Desorption (SLD) 1331 Solid state laser 1144 Soliton 1308 Soliton pair 1308 Solubility of partially miscible liquids 770 Solubility product 740 applications of 742 Solubilization 1238 Solutions of non–electrolytes 750 Soluti ons of gas es in l iqui ds 7 73 Solutions of liquids in liquids 750 Solvent extraction 702 Sommerfeld extension of Bohr theory 31 Space groups 263 Space lattice 263,1169 Spectra, charge transfer 340 electronic 335 electron spin resonance 392 hydrogen 28 molecular 305 Raman 326 rotational 307,313 vibrational 315,320 Spectroscopic transition 302 Spectroscopy 302 Spherical harmonics 64 Spherical wave 1270 Spherical top molecules 324 Spin Hamiltonian in ESR 410 Spin labels 397 Spin multiplicity 1113 Spinors 169 Spin-lattice relaxation in NMR 372 Spin-lattice r elax ation ti me 372 Spin-orbit coupling 153 Spin quantum number 84 Spin-s pin coup lin g c onstant 3 63 Spin-spin interaction in NMR 362 Spin vectors 168 Spontaneous processes 571 Spontaneous reactions 620 free energy of 620 Square-well potential 1029 SQUID 447 Standard electrode potentials 846 Standard enthalpies 555

Standard hydrogen electrode (SHE) 836 Standard state 606 St anda rd reduc tio n f ormu la 2 68 Stark effect 162 Stark effect in microwave spectra 314 Stark–Einstein law 1118 State of a system 526 Statee mixed 997 pure 997 State variables 526 Stationary nonequilibrium states1359 Statistical averaging 996 Statistics, types of 935 Bose–Einstein 935 Fermi–Dirac 935 Maxwell–Boltzmann 935 Statistical entropy 619 Statis ti cal ther mody namic s 935 Staudinger index 1279 STM (Scanning tunnelling microscopy) 1270 STO-3G basis set 233 Steady-state approximation 1054 Steam distillation 769 Stephen-Boltzmann law 961 Sternheimer effect 427 Stereoregular polymers 1276 Stern-Gerlach experiment 84 Stern Model 902 Stern-Volmer equation 1137 Stimulated Raman scattering (SRS) 332,1143 Stirling approximation 937 Stirred flow reactor 1091 Stokes and anti-Stokes lines 326 Stokes -Einstein equation 1294 Streaming current (SC) 1358 Streaming potential (SP) 1358 Structure factor 1184 Structure of liquids 512 Subgroup 250 Sulphur system (phase rule) 672 Supercoiled DNA 1321 Superconductivity 1202 LTSC and HTSC 1202 Superfluidity 1018 Supermolecule 1100 Supertwist 1322 Surface energy 503 Surface excess 1266 Surface films on liquids 1267 Surface reactions 1085 Surface structure techniques (EXAFS and SEXAFS) 1270 Surface tension 502 Surfactants 1226 Svedberg equation 1286 Symmetric and antisymmetric wave functions 1003 Symmetric top molecules 324

GENERAL B B IL O IG R A P H Y 3 G E N E R A L BIBLIOGRAPHY 

1376 ( x) Symmetry, in crystal systems axis of centre of elements of operations plane of Symmetry of molecular orbitals Symmetry of wave functions Syndiotactic polymers System of identical particles

1166 1166 1167 1167 1167 1167 185 1003 1275 1002

T Tafel equations 914 Tafel plot 915 Taft equation 654 Tanabe-Sugano diagrams 344 Temperature coefficient 1056 Temperature–dependence of equilibrium constant 637 TEMPOL 397 Term symbols for diatomic molecules 184 Tetramethylsilane (TMS) 359 Theorems of quantum mechanics 107 Theoretical plate 768 Thermal analysis, phase rule 681 Thermal conductivity 465 Thermochemistry 552 Thermody namic equil ibr ium 526 Thermodynamic potentials 630 Ther modynamic pr obabi lity 618 Thermody namic proc es ses 527 Thermodynamics of CMC 1236 Thermodynamics of ideal solutions 759 Thermodynamics, laws of 525 Thermography 518 Thermomec hanical effect 1358 Thermomolecular pressure difference (TPD) 1358 Thermo-osmosis 1359 Third law of thermodynamics 609 experimental verification of 615 Third–order reactions 1045 Thomas-Fermi equation 164 Thomas-Fermi model 163 Threshold energy 1056 Threshold frequency 25 Three–c omponent s ys tems 690 Tie line 768 Time-dependent perturbation theory (TDPT) 242 Time-dependent Schrödinger equation (TDSE) 242 Time-independent perturbation theory (TIPT) 111 Time-independent Schrödinger equation (TISE) 42 Time-resolved spectroscopy 1143 Townes-Dailey theory 426 Trace of a matrix 997 Transfer coefficient in electrode kinetics 913

PRINCIPLES OF PHYSICAL CHEMISTRY

Transition state theory 1063 Transmission coefficient 1068 Transmission probability 135 Transitions (allowed and forbidden) 303 Transitions electric dipole 154 magnetic dipole 154 Transistors 1201 Transmittance 1116 Transport number 806 determination of 807 Transport properties in gases 463 Tr ansvers e r el axati on ti me 372 Trial wave function 121 Triethylamine–water system (phase rule) 772 Triple point 669 Triplet state 1114 Trouton’s rule 502 Turbidity 1292 Turnover number 1152 Two-dimensional NMR 380 Tyndall effect 1289 U UCST 771 Ultracentrifugation 1285 Ultramicroscope 1217 Unimolecular reactions, theories of 1070 Hinshelwood theory 1073 Lindemann theory 1070 RRK theory 1074 RRKM theory 1077 Unimolecular surface reactions 1155 Unit cell 1169 Unsold’s theorem 108 UPES (Ultraviolet photoelectron spectroscopy) 416 Upper bound 175 V Vacancy theory of liquids Valence bond theory (VBT) Valence state ionization potentials van der Waals constants van der Waals equation and critical phenomena van der Waals forces van’t Hoff equation van’t Hoff osmotic pressure equation reaction isotherm van’t Hoff factor Vapour pressure of liquids Vapour pressure lowering Vapour pressure lowering and molar mass Vapour pressures of ideal solutions Vapour pressures of non–ideal solutions

499 192 233 482 481 491 433 637 782 626 796 500 778 779 753 763

Variation method 120 Application to helium 121 Variation theorem 148 Velocity, average 457 most probable 453 root-mean-square 457 Vibrational quantum number 316 Vibrational spectra 315 of polyatomic molecules 320 Vibrational term 316 Virial coefficients 486 Vi rial equ ation of state 48 6, 10 28 Virial theorem 108 Virtual orbitals 236 Viscometry 1279 Viscosity of gases 467 Viscosity of liquids 508 Volcanoes 910 Volume change and enthalpy change of mixing for an ideal solution 760 VSEPR theory 226 W Walden’s rule 817 Walsh diagrams 225 Water s ystem (phase rul e) 668 Watson-Crick model 1320 Wave-particle duality of electron 33 Wave mechanics 37 Width of spectral lines 304 Wien’s displacement law 24, 961 Wien effect 827 Wierl equation 1186 Wigner coefficients 170 Wiger-Seitz cell 1199 Work function 25 X X–ray diffraction X-ray diffraction pattern of a cubic system X–ray diffractometer Y Young-Laplace equation

1176 1180 1177 507

Z Zeeman effect 84, 159 Normal and anomalous 159 Zeeman effect in NQR 425 Zero differential overlap (ZDO) 238 Zero–order reactions 1049 Zeroeth law of thermodynamics 549 Zeroeth law and temperature scale 549 Zero-point energy (ZPE) 56 Zero-field splitting (ZFS) 109,401 Zeta potential 1221 Ziegler-Natta catalyst 1276 Zimm equation 1292 Zimm plot 1292 Zinc-air fuel cell (ZAFC) 864 Zwitterion 1324