Principles of Physical Chemistry Understanding Molecules, Molecular Assemblies, Supramolecular Machines

, by Kuhn, Hans; Fö; rsterling, Horst-Dieter

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

ISBN: 9780471959021 | 0471959022
Cover: Hardcover
Copyright: 1/10/2000

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"This admirable text provides a solid foundation in the fundamentals of physical chemistry including quantum mechanics and statistical mechanics/thermodynamics. The presentation assists the students in developing an intuitive understanding of the subjects as well as skill in quantitative manipulations. Particularly exciting is the treatment of larger molecular systems. With a firm but gentle hand, the student is led to several organized molecular assemblies including supramolecular systems and models of the origin of life. By learning of some of the most productive areas of current chemical research, the student may see the discipline as an active, young science in addition to its many accomplishments of earlier years. This text makes physical chemistry fun and demonstrates why so many find it a stimulating and rewarding profession."
Professor Edel Wasserman, President (1999) of the American Chemical Society

Acknowledgements

xxiii

Preface and Guided Tour

xxv

Wave-Particle Duality

(18)

Light

(9)

The Particle Nature of Light: Photoelectric Effect

(2)

Wave Nature of Light: Diffraction

(4)

Interpretation of the Experiments

(3)

Electrons

(3)

The Particle Nature of Electrons

(1)

Wave Nature of Electrons

(2)

Interpretation of the Experiments

(1)

Questions Arising About Wave-Particle Duality

(6)

Single Event: Probability Statement; Collective Behavior: Definite Statement

(2)

Wave-Particle Duality: The Need To Abandon Familiar Ways of Thinking

(2)

Problems

(1)

Problem 1.1 - Double-slit Experiment: Distribution of |&psgr;| on the Screen

(1)

Problem 1.2 - Diffraction of Photons, Electrons, and Neutrons

(2)

Basic Features of Bonding

(20)

Distinct Energy States

(2)

Atomic Spectra

(1)

The Franck-Hertz Experiment

(2)

Standing Waves

(5)

A Particle Between Parallel Walls

(3)

The Heisenberg Uncertainty Relation

(1)

Meaningless Questions

(1)

Electron in a Box

(1)

H Atom in the Ground State

(4)

Box Model for H Atom

(1)

Variation Principle

(3)

H2+ Molecule Ion in the Ground State

(2)

Forming H2+ from an H Atom and a Proton

(1)

Box Model for H2+

(1)

He+ Ion, He Atom, and Similar Systems

(3)

He+ Ion and He Atom

(1)

He-like Systems: H-, Li+, Be2+

(1)

H2 Molecule

(1)

Pauli Exclusion Principle

(3)

Nonexistence of He2

(1)

Li+H- (Ionic Crystal)

(1)

Problems

(1)

Problem 2.1 - Franck-Hertz Experiment

(1)

Problem 2.2 - Standing Waves Formed by Overlap of Traveling Waves

(2)

Schrodinger Equation and Variation Principle

(46)

Wave Equation and Schrodinger Equation

(8)

Wave Equation

(3)

Schrodinger Equation (One-dimensional)

(2)

Schrodinger Equation (Three-dimensional)

(3)

Normalization of the Wavefunctions

(3)

Orthogonality of the Wavefunctions

(2)

Time-dependent Schrodinger Equation

(1)

H Atom in the Ground State

(5)

Wavefunction

(1)

Energy

(1)

Radial Probability Distribution of Electron

(3)

Average Potential Energy and Virial Theorem

(1)

Most Probable and Average Distance of Electron from Nucleus

(1)

H Atom in Excited States

(7)

Energies and Wavefunctions

(3)

Emission Spectra

(4)

Variation Principle

(4)

Justification of the Variation Principle

(4)

Bohr Atomic Model and Correspondence Principle

(16)

Bohr Atomic Model

(1)

Correspondence Principle

(1)

Problems

(1)

Problem 3.1 - H Atom: Ground State Derived from the Schrodinger Equation

(1)

Problem 3.2 - H Atom: Normalization of Wavefunction

(1)

Problem 3.3 - Probability Density p

(1)

Problem 3.4 - H Atom: Average Distance Between Electron and Nucleus

(1)

Problem 3.5 - H Atom: Particle in a Box Trial Function

(1)

Problem 3.6 - He+: Schrodinger Equation

(1)

Problem 3.7 - H Atom: Comovement of the Nucleus

(1)

Problem 3.8 - Ground State Energy of H Atom by Variation Principle

(2)

Foundation 3.1 - Electron in a Potential Trough of Finite Depth

(2)

Foundation 3.2 - Relation Between Time-independent and Time-dependent Schrodinger Equation

(1)

Foundation 3.3 - H-Atom: Solution of the Schrodinger Equation

(2)

Foundation 3.4 - Proof of Variation Principle

(3)

Chemical Bonding and the Pauli Principle

(32)

H2+ Molecule Ion

(11)

Electron Described by Exact Wavefunction

(1)

Electron Described by Box Wavefunctions

(3)

Electron Density and Chemical Bond

(2)

Virial Theorem

(1)

Nature of the Chemical Bond

(1)

Electron Described by Combination of Atomic Orbitals

(5)

He Atom and Similar Systems

(3)

Ground State of He

(2)

Excited States of He

(1)

Antisymmetry of Wavefunctions

(5)

Energy Splitting in a Magnetic Field

(3)

Spin Variables

102

(1)

Pauli Exclusion Principle as Antisymmetry Postulate

102

(1)

Singlet-Triplet Splitting Caused by Coulomb Forces

103

(1)

Quantum Mechanical Tunneling

104

(13)

Problems

104

(1)

Problem 4.1 - Kinetic Energy in Box Model

104

(1)

Problem 4.2 - Repulsion of the Two Electrons in He

104

(1)

Problem 4.3 - Energy Separation of EPR Lines

105

(1)

Foundation 4.1 - H- Ion: Exact Wave Function and Energy. Virial Theorem

106

(2)

Foundation 4.2 - Evaluation of LCAO Integrals in H-

108

(3)

Foundation 4.3 - He Atom: Energy in the Grounds State

111

(1)

Foundation 4.4 - Oscillation of Electron between Protons at Distance (Tunneling)

112

(5)

The Periodic Table and Simple Molecules

117

(23)

Periodic Table of the Elements

117

(7)

Basic Principles

117

(1)

Hydrogen and Helium (Z = 1 and Z = 2)

118

(1)

Lithium (Z = 3)

119

(1)

Aufbau Principle and Periodic Table

120

(4)

The Structure of Simple Molecules

124

(16)

Simple Bond Models

124

(2)

The Polarity of Bonds and Electronegativity

126

(3)

Bond Lengths and Bond Angles

129

(4)

Stretching and Bending Force Constants

133

(4)

Problems

137

(1)

Problem 5.1 - Partial Charges and Dipole Moment

137

(1)

Problem 5.2 - Stretching Force Constant of H2+ Ion

137

(2)

Problem 5.3 - Bond Angle of H20

139

(1)

Bonding Described By Hybrid and Molecular Orbitals

140

(23)

Degeneracy of Energy Levels

140

(7)

Hybrid Functions

142

(2)

Hybridization of H Atom Functions

144

(3)

Localized Electrons: Hybrid Atomic Orbitals

147

(4)

Li Atom (No Hybridization)

147

(1)

BeH2 (Linear (sp) Hybridization: Two s1/2p1/2 Hybrid Orbitals)

148

(1)

H2S and H20 (Two Orbitals Between p and s1/4 p1/3/4 Hybrid)

148

(2)

CH4 (Tetrahedral (sp3) Hybridization: Four s1/4p3/4 Hybrid Orbitals)

150

(1)

Properties of Electron Pair Bonds

151

(3)

Formal and Effective Charges

152

(2)

Polymerization of BeH2

154

(1)

Delocalized Electrons: Molecular Orbitals

154

(9)

Box Wavefunctions

154

(1)

LCAO Wavefunctions

155

(4)

Improvement of Trial Function

159

(1)

Problems

159

(1)

Problem 6.1 - Linear Combinations of Wave Functions

159

(1)

Problem 6.2 - Degeneracy and Hybridization of Box Functions

159

(1)

Problem 6.3 - Orthogonality and Normalization of Hybrid Functions

160

(1)

Problem 6.4 - Symmetry Properties of Linear Hybrid Functions

160

(1)

Problem 6.5 - Energy of Hybrid States

160

(1)

Problem 6.6 - Structure of B(CH3)3 and Hg2Cl2

161

(1)

Problem 6.7 - Dative Bond

161

(1)

Problem 6.8 - Three-center Bond (CH5+) -

161

(1)

Problem 6.9 - LCAO Model for O2

162

(1)

Problem 6.10 - Molecular Orbitals of Some Diatomic Molecules

162

(1)

Molecules with π Electron Systems

163

(41)

Bonding Properties of π Electrons

163

(2)

Free-electron Model

165

(16)

Linear π Electron Systems

165

(6)

Cyclic π Electron Systems

171

(2)

Charge Density dQ/ds

173

(2)

Resonance

175

(2)

Branched Molecules

177

(4)

HMO Model

181

(3)

Wavefunctions and Energies

181

(3)

Charge Density dQ/dτ

184

(1)

Bond Lengths, Dipole Moments

184

(20)

Bond Length and Charge Density

184

(3)

Bond Alternation in Polyenes and Fullerenes

187

(1)

Dipole Moment

187

(2)

Problems

189

(1)

Problem 7.1 - HMO Method: Ethene

189

(1)

Problem 7.2 - HMO Method: Butadiene

190

(1)

Problem 7.3 - HMO Method: Fulvene

191

(1)

Problem 7.4 - Resonance of Huckel (4n + 2) Rings

192

(1)

Problem 7.5 - Bond Lengths from Bond Orders

192

(1)

Problem 7.6 - Cyclobutadiene: Bond Lengths

192

(1)

Problem 7.7 - Dipole Moment of Fulvene

193

(2)

Foundation 7.1 - Free Electron Model

195

(3)

Foundation 7.2 - HMO Model

198

(2)

Foundation 7.3 - Self-consistency in Bond Alternation

200

(4)

Absorption and Emission of Light

204

(74)

Basic Experimental Facts

204

(5)

Transmittance and Absorbance

204

(3)

Polyenes and Cyanines

207

(2)

Absorption Maxima of Dyes

209

(4)

Band Broadening

210

(1)

Single-molecule Absorption

210

(1)

Cyanine Dyes

211

(2)

Strength and Polarization of Absorption Bands

213

(3)

Oscillator Strength

213

(2)

Polarization of Absorption Bands

215

(1)

Heteroatoms as Probes for Electron Distribution

216

(3)

HOMO-LUMO Gap by Bond Alternation

219

(4)

Dyes with Cyclic Electron Cloud: Phthalocyanine

223

(3)

Coupling of π Electrons

226

(2)

Light Absorption of Biomolecules

228

(5)

β-Carotene

228

(2)

Retinal

230

(1)

Vitamin B12

231

(1)

Chlorophyll, Bacteriochlorophyll

232

(1)

Spontaneous Emission

233

(9)

Fluorescence and Phosphorescence

233

(2)

Single Molecule Emission

235

(1)

Singlet and Triplet States

236

(2)

Shift of Fluorescence and Phosphorescence Relative to Absorption

238

(2)

Absorption from Excited States

240

(2)

Quenching of Fluorescence

242

(1)

Stimulated Emission

242

(5)

Inversion of Population

242

(1)

Dye Laser

243

(3)

Excimer Laser

246

(1)

Optical Activity

247

(31)

Rotatory Dispersion

247

(1)

Ellipticity

248

(1)

Circular Dichroism

249

(1)

Circular Dichroism of Spirobisanthracene

250

(3)

Circular Dichroism of Chiral Cyanine Dye

253

(1)

Problems

253

(1)

Problem 8.1 - Lone Electron Pair at the Nitrogen

253

(1)

Problem 8.2 - Light Absorption of Different Classes of Dyes

254

(1)

Problem 8.3 - Energy Shift in Azacyanines

254

(2)

Problem 8.4 - Shift of Energy Levels by Bond Alternation

256

(1)

Problem 8.5 - Light Absorption of Phthalocyanine and Porphyrin

256

(1)

Problem 8.6 - Oscillatory Strength in Phthalocyanine and Porphyrin

257

(1)

Problem 8.7 - Cis-Peak in β-Carotene

258

(1)

Problem 8.8 - Splitting of Absorption Band

258

(1)

Problem 8.9 - Circular Dichroism of Cyanine Dye

259

(2)

Foundation 8.1 - Integrated Absorption: Classical Oscillator

261

(4)

Foundation 8.2 - Oscillator Strength: Quantum mechanical Treatment

265

(2)

Foundation 8.3 - Coupling Transitions with Parallel Transition Moment

267

(3)

Foundation 8.4 - Normal modes of Coupled Oscillators

270

(4)

Foundation 8.5 - Fluorescence Life Time

274

(2)

Foundation 8.6 - Proof of Relation for g (Anisotropy Factor)

276

(2)

Nuclei: Particle and Wave Properties

278

(55)

Quantum Mechanical Rotator

278

(4)

Exact Solution

279

(1)

Simplified Model

280

(2)

Rotational Spectra

282

(5)

Quantum Mechanical Oscillator

287

(7)

Exact Solution

288

(3)

Box Model for Oscillator

291

(2)

Comparison of a Quantum Mechanical Oscillator with a Classical Oscillator

293

(1)

Vibrational-Rotational Spectra

294

(9)

Diatomic Molecules

294

(3)

Polyatomic Molecules

297

(6)

Raman Spectra

303

(9)

Rayleigh Scattering

303

(2)

Rotational Raman Spectra

305

(2)

Vibrational-Rotational Raman Spectra of Diatomic Molecules

307

(3)

Raman Spectra of Polyatomics

310

(2)

Vibrational Structure of Electronic Spectra

312

(6)

Diatomic Molecules

312

(1)

Photoelectron Spectroscopy

312

(5)

Polyatomic Molecules

317

(1)

Nuclear Spin (Orthohydrogen and Parahydrogen)

318

(2)

Spin of Protons in H2

319

(1)

Nuclear Wavefunctions

319

(1)

Antisymmetry Postulate in H2

320

(1)

Nuclear Magnetic Resonance

320

(13)

Fundamentals

320

(1)

Chemical Shift

321

(2)

Fine Structure of NMR Signals

323

(1)

Problems

324

(1)

Problem 9.1 - Wavefunction of an Harmonic Oscillator

324

(1)

Problem 9.2 - Oscillator: Box Wavefunctions

325

(1)

Problem 9.3 - Classical Oscillator: Probability Density &rgr;(x)

326

(1)

Problem 9.4 - Isotope Effect in Vibrational-Rotational IR Spectrum

326

(1)

Problem 9.5 - Bond Length of HCl from Raman Spectrum

327

(1)

Problem 9.6 - Bond Length of CO from Infrared Spectrum

328

(1)

Problem 9.7 - Force Constant of CO from IR Spectrum

328

(2)

Foundation 9.1 - Rotator: Solution of the Schrodinger Equation

330

(1)

Foundation 9.2 - Vibrational Structure of Electronic Absorption Bands

331

(2)

Intermolecular Forces and Aggregates

333

(23)

Forces in Ionic Crystals

333

(7)

Attracting and Repelling Forces

333

(1)

Lattice Types

334

(6)

Forces in Metals

340

(4)

Coulomb Energy: Electrons Considered as Being Localized at Lattice Points

341

(1)

Kinetic Energy: Electrons Considered as Being Delocalized Over the Lattice

341

(3)

Lattice Energy

344

(1)

Dipole Forces

344

(3)

Hydrogen Bonds

347

(1)

Induction Forces

348

(1)

Dispersion Forces

349

(4)

Molecular Crystals

353

(3)

Problems

353

(1)

Problem 10.1 - The Energy of an Ion Pair

353

(1)

Problem 10.2 - Dipole-Dipole Attraction

354

(1)

Problem 10.3 - Polarizability of a Conducting Plate

354

(2)

Thermal Motion of Molecules

356

(52)

Kinetic Gas Theory and Temperature

356

(13)

Thermal Motion and Pressure

357

(5)

Avogadro's Law

362

(2)

Temperature Equilibration and Heat

364

(1)

Ideal Gas Law: Definition of Absolute Temperature

364

(5)

Speed of Molecules in a Gas

369

(1)

Mean Speed

369

(1)

Effusion

370

(1)

Mean Free Path and Collision Frequency

370

(4)

Mean Free Path

371

(3)

Collision Frequency

374

(1)

Diffusion

374

(9)

Mean Displacement

374

(4)

Equation of Einstein and Smoluchowski

378

(1)

Fick's Law

378

(3)

Gravity Competing with Thermal Motion

381

(2)

Viscosity Arising from Collisions of Molecules

383

(4)

Viscous Flow

383

(1)

Calculating Viscosity

384

(2)

Dependence of Viscosity on Pressure

386

(1)

Increasing η with Increasing Temperature

386

(1)

Calculating Collision Diameters

386

(1)

Thermal Motion in Liquids

387

(6)

Collisions in Liquids

387

(1)

Diffusion Coefficient D of a Liquid

388

(1)

Viscosity of a Liquid

388

(1)

Stokes-Einstein Equation: Diffusion, Assembling, Interlocking

389

(4)

Molecular Motion and Phases

393

(15)

Melting Point

394

(1)

Boiling Point

395

(1)

Critical Point

395

(1)

Phases

396

(1)

Clusters and Liquid Crystals

396

(1)

Problems

397

(1)

Problem 11.1 - Elastic Collisions of Spheres

397

(1)

Problem 11.2 - Gas Bubbles Rising from the Bottom of a Sea

398

(1)

Problem 11.3 - Pressure Change on Cooling in a Refrigerator

398

(1)

Problem 11.4 - Gas Thermometer

398

(1)

Problem 11.5 - Separation of Isotopes by Effusion

399

(1)

Problem 11.6 - Separation of Isotopes by Using an Ultracentrifuge

399

(1)

Problem 11.7 - Diffusion Path

400

(1)

Problem 11.8 - Distribution Function for Diffusion Path

401

(3)

Problem 11.9 - Evaporation of Water at Room Temperature

404

(1)

Foundation 11.1 - Averaging the Free Path λ

405

(1)

Foundation 11.2 - Intermolecular Forces Affecting the Mean Free Path

405

(3)

Energy Distribution in Molecular Assemblies

408

(42)

The Boltzmann Distribution Law

408

(4)

System Consisting of Two Quantum States

408

(3)

Systems Consisting of Many Quantum States

411

(1)

Distribution of Vibrational Energy

412

(5)

Population Number Nn

413

(1)

Total Vibrational Energy Uvib

414

(3)

Distribution of Rotational Energy

417

(3)

Population Numbers Nn

418

(1)

Total Rotational Energy Urot

418

(2)

Translational Energy

420

(8)

Average Translational Energy According to Quantum Mechanics

420

(2)

Maxwell-Boltzmann Distribution

422

(2)

Deriving the Maxwell-Boltzmann Distribution

424

(3)

Number of Translational Quantum States Available per Molecule

427

(1)

Distribution of Electronic Energy

428

(1)

Proving the Boltzmann Distribution

429

(21)

Distinguishable Particles

429

(5)

Indistinguishable Particles

434

(1)

Problems

435

(1)

Problem 12.1 - Population of Quantum States of a Rotator at Temperature T

435

(1)

Problem 12.2 - Maxwell-Boltzmann Distribution: vP, v, v2 and Etrans

435

(1)

Problem 12.3 - Number of Quantum States in a One-dimensional Gas

436

(1)

Problem 12.4 - Population Probability

437

(1)

Problem 12.5 - Boltzmann Distribution

437

(1)

Problems 12.6 and 12.7 - Superhelix as a Frozen Boltzmann Distribution

438

(3)

Problem 12.8 - Internal Energy for Particles Rotating on a Circle

441

(1)

Foundation 12.1 - Oscillator: Population Numbers Nn and Total Energy Uvib

442

(2)

Foundation 12.2 - Rotator: Population Number Nn and Total Energy Urot

444

(2)

Foundation 12.3 - Boltzmann Distribution

446

(4)

Internal Energy U, Heat q, and Work w

450

(19)

Change of State at Constant Volume

450

(3)

Change of Internal Energy ΔU; Heat q

450

(2)

Heat Capacity Cv

452

(1)

Temperature Dependence of Cv

453

(7)

Rotational and Vibrational Contribution to Cv

453

(3)

ortho- and para-H2: Fascinating Quantum Effects on Cv

456

(1)

Electronic Contribution to Cv (Cv, electr)

457

(1)

Cv of Solids

457

(2)

Characteristic Temperature

459

(1)

Change of State at Constant Pressure

460

(2)

Change of Internal Energy ΔU; Heat q and work w

460

(1)

Heat Capacity CP

461

(1)

System and Surroundings; State Variables

462

(7)

Defining System and Surroundings

462

(1)

Defining State and State Variables

462

(2)

Closed, Isolated, and Open Systems

464

(1)

Cyclic Processes

465

(1)

Problems

466

(1)

Problem 13.1 - Isothermal Expansion of an Ideal Gas

466

(2)

Problem 13.2 - Adiabatic Expansion of an Ideal Gas

468

(1)

Principle of Entropy Increase

469

(23)

Irreversible and Reversible Changes of State

469

(3)

Irreversible Changes

469

(1)

Reversible Changes

470

(2)

Distribution Possibilities

472

(5)

Mixing of Two Gases

473

(1)

Expansion of a Gas

474

(3)

Counting the Number of Configurations Ω

477

(3)

Probability P of Reversion of an Irreversible Process

477

(1)

Particles Each in One of Three Energy States

477

(1)

Number of Configurations Ω of an Atomic Gas

477

(3)

Entropy of a System: S = k 1n Ω

480

(2)

Entropy of Atomic Gases

480

(1)

Entropy of Diatomic Gases

481

(1)

Entropy Change ΔS

482

(10)

Temperature Equilibration

482

(1)

Mixing of Two Gases

483

(1)

Entropy Increase in an Irreversible Process in an Isolated System

483

(1)

Entropy of Subsystems

484

(2)

Entropy Change in Non-isolated Systems

486

(1)

Problems

486

(1)

Problem 14.1 - Increase in the Number of Configurations with Temperature Equilibration

486

(2)

Problem 14.2 - Mixing Entropy

488

(2)

Foundation 14.1 - Entropy for Rotation and Vibration

490

(2)

Entropy S and Heat qrev

492

(25)

Heat and Change of Entropy in Processes with Ideal Gases

493

(8)

Expansion at Constant Temperature

493

(1)

Thermal Equilibration

494

(4)

Cyclic Processes and Processes in Isolated Systems

498

(1)

Reversible Heat Engine with Ideal Gases (Carnot Cycle)

498

(3)

Heat and Change of Entropy in Arbitrary Processes

501

(6)

Entropies of Substances

507

(4)

Thermodynamic Temperature Scale and Cooling

511

(1)

Laws of Thermodynamics

511

(6)

Problems

513

(1)

Problem 15.1 - Reversible Adiabatic Expansion

513

(1)

Problem 15.2 - Entropy of Mixing

514

(1)

Problem 15.3 - Efficiency of Different Heat Engines

515

(1)

Problem 15.4 - Efficiency of a Power Station

515

(1)

Problem 15.5 - Heat Pump

515

(1)

Problem 15.6 - Air Conditioning

515

(1)

Problem 15.7 - Entropy and Configurations of Water

516

(1)

Criteria for Chemical Reactions

517

(28)

Heat Exchange

518

(4)

Reaction at Constant Volume: g = ΔU

518

(2)

Reaction at Constant Pressure: g = ΔH

520

(2)

Change of Internal Energy and Enthalpy

522

(6)

Temperature Dependence of ΔU and ΔH

522

(2)

Molar Enthalpies of Formation from Elements ΔfH⊖

524

(1)

Molar Enthalpy of Reaction ΔrH⊖

525

(3)

Conditions for Spontaneous Reactions

528

(2)

Helmholtz Energy and Gibbs Energy

528

(1)

Reversible Work wrev

529

(1)

Change of Gibbs Energy

530

(15)

Molar Gibbs Energy of Formation from Elements ΔfG⊖

530

(1)

Molar Gibbs Energy of Reaction ΔrG⊖

531

(1)

Temperature Dependence of ΔG⊖

531

(2)

Pressure Dependence of ΔG

533

(2)

Problems

535

(1)

Problem 16.1 - Bunsen Burner Fed with Methane

535

(1)

Problem 16.2 - ΔrH from Standard Enthalpies of Formation

535

(1)

Problem 16.3 - Temperature Regulation in the Human Body

536

(1)

Problem 16.4 - Spontaneous Reactions

537

(1)

Problem 16.5 - Burning Limestone on Mount Everest

537

(2)

Foundation 16.1 - How to Calculate ST2T1ΔCp,m⊖ dT

539

(3)

Foundation 16.2 - How to Calculate ΔGT2 from ΔGT1

542

(3)

Chemical Equilibrium

545

(34)

ΔG for Reactions in Gas Mixtures

546

(14)

Mass Action Law and Equilibrium Constant K

546

(3)

Equilibrium Constant K from ΔrG⊖ = -RT . 1n K

549

(4)

Reactions Involving Gases and Immiscible Condensed Species

553

(1)

Van't Hoff Equation

554

(1)

Statistical Interpretation of K

555

(2)

Estimation of K = f (T)

557

(1)

ΔH and ΔS from Measured K

558

(1)

Vapor Pressure

559

(1)

ΔG for Reactions in Dilute Solution

560

(19)

Osmotic Pressure and Concentration

560

(2)

Concentration and Molality

562

(1)

Depression of Vapor Pressure

562

(3)

Reversible Change of Concentration

565

(1)

Mass Action Law: Solutions of Neutral Particles

565

(2)

Mass Action Law: Solutions of Charged Particles

567

(3)

Gibbs Energy of Formation in Aqueous Solution

570

(3)

Part of Reactants or Products in Condensed or Gaseous State

573

(2)

Problems

575

(1)

Problem 17.1 - Equilibrium Constant Calculated from ΔH and ΔS

575

(1)

Problem 17.2 - Dissociation of I2

575

(1)

Problem 17.3 - Hydrogen-Iodine Equilibrium

576

(1)

Problem 17.4 - Formation of NH3 from Its Elements

576

(1)

Problem 17.5 - Boiling Point of Water on Mount Everest

577

(1)

Problem 17.6 - Reverse Osmosis

577

(1)

Problem 17.7 - Elevation of Boiling Point

577

(1)

Problem 17.8 - Depression of Melting Point

578

(1)

Reactions in Aqueous Solution and in Biosystems

579

(21)

Proton Transfer Reactions: Dissociation of Weak Acids

579

(5)

Henderson-Hasselbalch Equation

579

(1)

Degree of Dissociation

580

(1)

Acid in a Buffer

581

(1)

Titration Curve of a Weak Acid

582

(1)

Stepwise Proton Transfer: Amino Acids

583

(1)

Electron Transfer Reactions

584

(4)

Electron Transfer from Metal to Proton: Dissolution of Metals in Acid

584

(1)

Electron Transfer from Metal 1 to Metal 2 Ion: Coupled Redox Reactions

585

(1)

Electron Transfer Coupled with Proton Transfer

586

(1)

Electron Transfer to Proton at pH 7: ΔG⊖

587

(1)

Group Transfer Reactions in Biochemistry

588

(3)

Group Transfer Potential

589

(1)

Coupling of Reactions by Enzymes

590

(1)

Bioenergetics

591

(9)

Synthesis of Glucose

591

(1)

Combustion of Glucose

592

(1)

Energy Balance of Formation and Degradation of Glucose

592

(2)

Problems

594

(1)

Problem 18.1 - pH of Weak Acid for Different Total Concentrations

594

(1)

Problem 18.2 - Buffer Solutions

595

(1)

Problem 18.3 - pH of Amino Acids

596

(1)

Problem 18.4 - Absorption Maximum of NADH

596

(1)

Foundation 18.1 - Titration of Acetic Acid by NaOH

597

(3)

Chemical Reactions in Electrochemical Cells

600

(27)

ΔG and Potential E of an Electrochemical Cell Reaction

600

(4)

Concentration Cells

604

(5)

Metal Electrodes

604

(3)

Gas Electrodes

607

(2)

Standard Potential E⊖

609

(2)

Nernst Equation

609

(1)

Practical Determination of E⊖

610

(1)

Redox Reactions

611

(2)

Fe3+/Fe2+ Electrode

611

(1)

Quinone/Hydroquinone Electrode

611

(1)

NAD+/NADH Electrode

612

(1)

Oxygen Electrode

613

(1)

Applications of Electrochemical Cells

613

(7)

Reference Electrodes

613

(2)

Glass Electrodes

615

(1)

Galvanic Elements

616

(2)

Fuel Cells

618

(1)

Electrolysis

619

(1)

Conductivity of Electrolyte Solutions

620

(7)

Mobility of Ions

620

(2)

Generalization

622

(2)

Problems

624

(1)

Problem 19.1 - Acceleration of Na+ Ions

624

(1)

Problem 19.2 - Thermodynamic and Electrochemical Data

625

(1)

Problem 19.3 - Complex Formation

625

(1)

Problem 19.4 - Calculation of ΔG⊖ and E⊖

626

(1)

Real Systems

627

(36)

Phase Equilibria

627

(2)

Equation of State for Real Gases

629

(7)

van der Waals Equation

630

(3)

Critical Point and van der Waals Constants

633

(1)

Virial Coefficients

634

(2)

Change of State of Real Gases

636

(10)

Isothermal Compression of a van der Waals Gas

636

(1)

Fugacity and Equilibrium Constant

636

(4)

Adiabatic Expansion into Vacuum

640

(2)

Joule-Thomson Effect

642

(4)

Change of State of Real Solutions

646

(17)

Partial Molar Volume

646

(2)

Chemical Potential

648

(1)

Activities and Equilibrium Constants in Solutions with Ions

649

(4)

Problems

653

(1)

Problem 20.1 - Freezing Point of Mercury

653

(1)

Problem 20.2 - Determination of Fugacity Coefficient &phis;

653

(1)

Problem 20.3 - Charge Distribution p(r)

654

(1)

Problem 20.4 - Activity Coefficient γ± for HCl

655

(2)

Foundation 20.1 - Distribution of Ions at a Charged Plate

657

(6)

Kinetics of Chemical Reactions

663

(69)

Collision Theory for Gas Reactions

663

(6)

Counting the Number of Collisions

663

(2)

Activation

665

(1)

Accumulation of Kinetic Energy

666

(3)

Rate Equation for Gas Reactions

669

(3)

Rate Constant and Frequency Factor

669

(3)

Reactants A and B are Identical Molecules

672

(1)

Rate Equation for Reactions in Solution

672

(3)

Reaction Through Activated Complex

672

(2)

Diffusion Controlled Reaction

674

(1)

Transition State Theory

675

(2)

Eyring Equation for Bimolecular Reaction

675

(1)

Activation Enthalpy and Activation Entropy

676

(1)

Decay Reaction

677

(1)

Treatment of Experimental Data

677

(12)

Rate Constants

677

(5)

Activation Energy and Frequency Factor

682

(3)

Activation Enthalpy and Activation Entropy

685

(2)

Tunneling of Proton and Deuteron

687

(2)

Complex Reactions

689

(30)

Reactions Leading to Equilibrium

689

(3)

Parallel Reactions

692

(1)

Consecutive Reactions

693

(4)

Chain Reactions

697

(2)

Branching Chain Reactions

699

(1)

Enzyme Reactions (Michaelis-Menten Mechanism)

700

(3)

Autocatalytic Reactions

703

(4)

Inhibition of Autocatalysis

707

(2)

Bistability

709

(1)

Oscillating Reactions (Belousov-Zhabotinsky Reaction)

710

(4)

Chemical Waves

714

(5)

Experimental Methods

719

(13)

Flow Methods

720

(1)

Flash Photolysis

721

(1)

Relaxation Method

722

(4)

Problems

726

(1)

Problem 21.1 - Second-order Reaction

726

(1)

Problem 21.2 - Reaction Leading to Equilibrium

727

(1)

Problem 21.3 - Yield of Main Reaction

727

(1)

Problem 21.4 - Consecutive Reaction

729

(729)

Problem 21.5 - Autocatalytic Reaction

729

(1)

Problem 21.6 - Unimolecular Reactions

730

(2)

Organized Molecular Assemblies

732

(62)

Interfaces

732

(11)

Surface Tension and Interfacial Tension

732

(5)

Surface Films

737

(1)

Insoluble Monolayers

738

(3)

Solid Surfaces

741

(1)

Micelles

742

(1)

Liquid Crystals

743

(7)

Birefringence

746

(1)

Selective Reflection

746

(1)

Electro-optical Effects

747

(3)

Membranes

750

(5)

Soap Lamella

750

(1)

Black Lipid Membranes

751

(1)

Liposomes

752

(1)

Biomembranes

752

(3)

Macromolecules

755

(31)

Random Coil: A Chain of Statistical Chain Elements

755

(5)

Length of Statistical Chain Element from Light Scattering

760

(2)

Length of Statistical Chain Element from Hydrodynamic Properties

762

(3)

Refined Theory: Macroscopic Models

765

(4)

Uncoiling Coil

769

(5)

Restoring Coil

774

(2)

Motion Through Entangled Polymer Chains

776

(5)

Rubber Elasticity

781

(5)

Supramolecular Structures

786

(8)

Problems

787

(1)

Problem 22.1 - Contact angles

787

(1)

Problem 22.2 - Transfer of Charge e from Water into a Membrane

787

(1)

Problem 22.3 - Light Scattering (diameter of molecules ≪)

788

(1)

Problem 22.4 - Light Scattering (diameter of molecules < λ/4)

788

(1)

Problem 22.5 - Special Case of Scattering Relation (22.29)

789

(1)

Problem 22.6 - Molar Mass from Diffusion and Sedimentation

789

(1)

Problem 22.7 - Extension of an unraveled coil

790

(2)

Foundation 22.1 - Mobility of DNA in Meshwork

792

(2)

Supramolecular Machines

794

(86)

Energy Transfer Illustrating the Idea of a Supramolecular Machine

794

(1)

Programmed Interlocking Molecules

795

(5)

Manipulating Photon Motion

800

(18)

Energy Transfer Between Dye Molecules

800

(3)

Functional Unit by Coupling Dye Molecules

803

(2)

Dye Aggregate as Energy Harvesting Device

805

(5)

Solar Energy Harvesting in Biosystems

810

(2)

Manipulating Luminescence Lifetime by Programming Echo Radiation Field

812

(3)

Nonlinear Optical Phenomena

815

(3)

Manipulating Electron Motion

818

(15)

Photoinduced Electron Transfer in Designed Monolayer Assemblies

818

(1)

Switching by Photoinduced Electron Transfer

819

(2)

Monolayer Assemblies for Elucidating the Nature of Photographic Sensitization

821

(2)

Conducting Molecular Wires

823

(3)

Solar Energy Conversion: The Electron Pump of Plants and Bacteria

826

(4)

Artificial Photoinduced Electron Pumping

830

(1)

Tunneling Current Through Monolayer

831

(2)

Electron Transfer Through Proteins

833

(1)

Manipulating Nuclear Motion

833

(14)

Light-induced Change of Monolayer Properties

833

(3)

Solar Energy Conversion in Halobacteria

836

(8)

Photoinduced Sequence of Amplification Steps: The Visual System

844

(1)

Mechanical Switching Devices

845

(2)

Molecular Recognition and Replica Formation

847

(6)

Multisite Recognition of a Molecule at a Surface Layer

847

(1)

Catalytic Reaction in Solution

848

(1)

Catalytic Reaction in Organized Media

848

(2)

Molecular Replica Formation

850

(2)

Biosensors

852

(1)

Addressing and Positioning Molecules

853

(27)

STM (scanning tunneling microscopy)

853

(1)

AFM (atomic force microscopy)

854

(2)

SNOM (scanning near-field optical microscopy)

856

(2)

Problems

858

(1)

Problem 23.1 - Derivation of Equation for ε in Foundation 23.4

858

(1)

Problem 23.2 - Dielectric Medium as a Tunneling Barrier

858

(1)

Problem 23.3 - Induced Dipole Moment

859

(1)

Problem 23.4 - Proton Pump: Field of Charged Amino Acids at Chromophore

860

(1)

Problem 23.5 - Circular Dichroism and Structural Features of Chlorosomes

861

(1)

Foundation 23.1 - Energy Transfer

862

(3)

Foundation 23.2 - Energy transfer from Exciton to Acceptor

865

(2)

Foundation 23.3 - Radiation Echo field

867

(4)

Foundation 23.4 - Electron Transfer Between π-Electron Systems

871

(6)

Foundation 23.5 - Electron Transfer in Soft Medium

877

(3)

Origin of Life

880

(42)

Investigation of Complex Systems

880

(1)

Need for Simplifying Models

880

(1)

Increasing Simplification with Increasing Stages of Complexity

881

(1)

Can Life Emerge by Physicochemical Processes?

881

(14)

Bioevolution as Process of Learning

881

(1)

Model Case for the Learning Mechanism

882

(3)

Modeling the Emergence of the Genetic Apparatus

885

(9)

Later Evolutionary Steps: Emergence of an Eye With Lens

894

(1)

General Aspects of Life

895

(27)

Information and Knowledge

895

(1)

Processing Information and Genesis of Information and Knowledge

895

(4)

Limits of Physicochemical Ways of Thinking

899

(4)

Problems

903

(1)

Problem 24.1 - Aggregation of Folded Strands

903

(1)

Problem 24.2 - Replication Error Rate of a Bacterium and a Human

904

(1)

Problem 24.3 - Time Needed to Evolve a Bacterium

904

(1)

Problem 24.4 - Maximum Genetic Information Carried by DNA

905

(1)

Foundation 24.1 - The Emergence of a Simple Genetic Apparatus Viewed as a Supramolecular Engineering Problem. A thought Experiment

906

(7)

Foundation 24.2 - Attempts to Model the Origin of Life

913

(6)

Foundation 24.3 - Maxwell's Demon: Production of Entropy

919

(3)

Glossary

922

(6)

Appendices

928

(9)

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Principles of Physical Chemistry Understanding Molecules, Molecular Assemblies, Supramolecular Machines

Summary

Author Biography

Table of Contents

Supplemental Materials

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Principles of Physical Chemistry Understanding Molecules, Molecular Assemblies, Supramolecular Machines

Summary

Author Biography

Table of Contents

Supplemental Materials

Digital License