Download Essentials of physical chemistry

ESSENTIALS OF
PHYSICAL
CHEMISTRY
Don Shillady
CRC Press
Taylor & Francis Group
Boca Raton
CRC Press is
an
imprint
Taylor Si Francis Croup,
London
New York
of the
an
Informa business
Contents
Preface
xiii
Author
xvii
List of Constants
xix
Periodic Table of the Elements
Introduction: Mathematics and
Chapter
1
xxi
Physics
Review
xxiii
Ideal and Real Gas Behavior
1
Introduction to the "First Encounter with
Physical Chemistry"
Phenomenological Derivation of the Ideal Gas Equation
Charles' (Jacques-Alexandre-Cesar Charles) Law
Useful Units
Molecular
from Gas
Density (the
Dumas Bulb
11
13
Supercritical
18
Fluid
Chromatography
19
Instrumentation
20
Supercritical Mobile Phase
Sample SCF Separations
Summary
21
Problems
23
References
24
Viscosity
21
22
of Laminar Flow
25
25
Measurement of
28
Viscosity
Viscosity of Blood
Staudinger's Rule for Polymer
Summary
3
30
Molecular
Weight
34
35
References
35
The Kinetic Molecular
Theory
of Gases
37
37
Kinetic Assumptions of the Theory of Gases
Weighted Averaging:
4
31
Problems
Introduction
Chapter
10
Nonideal Gas Behavior
Introduction
Chapter
Method)
Dalton's Law of Partial Pressures
Supercritical Fluid
2
1
4
8
Weight
Fluids
Chapter
1
A
Very Important Concept
37
39
Summary
50
Problems
51
References
51
The First Law of Thermodynamics
53
Introduction
53
Historical
Development
of
Thermodynamics
Definitions
First Law of
53
54
Thermodynamics
55
v
vi
Contents
Isothermal Processes
Enthalpy
and Heat
57
59
Capacities
Adiabatic Processes
61
Adiabatic Nozzle
64
Diesel
65
Expansion Spectroscopy
Engine Compression
Calorimetry
and
67
Thermochemistry
Hess's Law of Heat Summation
Standard Heats of Formation
at
71
298.15°K and 1 bar Pressure
of Reaction
Temperature Dependence
Enthalpies
Polynomial Curve Fitting
Application to Afl°„ (T>298.15°K)
Other Types of Thermochemistry
Perspective
Key Formulas and Equations
73
Problems
79
Testing, Grading,
and
5
Thermodynamics
Introduction
78
81
81
83
of Real Heat
Efficiency
Engines
Entropy and Spontaneity
Summary of the Second Law of Thermodynamics
Eight Basic Equations of Thermodynamics
86
Third Law of
90
Entropy
85
Thermodynamics
of Reactions
Entropy Changes
Trouton's
88
88
93
Rule/Observation
Simple
Summary
Testing, Grading,
87
92
at T> 298.15°K
Statistical Treatment of
6
78
Cycle
Efficiency
Carnot
Chapter
78
81
Cycle/Engine
Carnot
75
80
The Second and Third Laws of
Carnot
74
79
Learning?
References
Chapter
72
94
Liquids
and Gases
95
99
and
Learning?
100
Problems
101
Bibliography
102
References
102
Gibbs' Free Energy and Equilibria
Introduction
103
Temperature Dependence of Equilibrium Constants
van't Hoff Equation
Vapor Pressure of Liquids
Phase Equilibria
106
How Ice Skates Work
113
Gibbs Phase Rule
113
Iodine
115
Triple Point
(C/>-Cy) for Liquids and Solids
Open Systems: Gibbs-Duhem Equation for Partial Molal Volumes
Chemical Potential for Open Systems
103
106
108
112
117
119
123
Contents
vii
125
Modeling Liquids
Summary
128
Problems
129
Testing, Grading,
Chapter
7
and
129
Learning?
Bibliography
130
References
130
Basic Chemical Kinetics
133
Introduction
133
First-Order Reactions
133
Promethium: An Introduction
Madame Curie and
to
Nuclear
Chemistry
Radioactivity
137
Radium
139
Second-Order Rate Processes:
Second-Order Rate Processes:
Arrhenius Activation
The Classic A
8
-»
B
[A] [B]
[A] ^ [B]
=
Energy
—>
147
150
153
References
154
More Kinetics and Some Mechanisms
155
Introduction
155
Beyond
Eyring
Example
Graphical-Analytical Method for A/f* and AS*
Summary of Graphical Method Results at r=25°C
Further Consideration of SN1 Solvolysis
Chain Reactions and the Steady State
Steady-State Example No. 1: H2 + Br2 -» 2HBr
Steady-State Example No. 2: Thermal Cracking of Acetaldehyde
Steady-State Example No. 3: The Lindemann Mechanism
Enzyme
to the
Transition State
Kinetics
155
159
161
163
164
165
165
167
168
169
Basic Michaelis-Menten
Equation
Hypothetical Enzyme
Michaelis-Menten with Competitive
Michaelis-Menten Summary
Example:
171
A
172
Inhibitor
Kinetics Conclusions
174
176
178
Problems
178
Testing, Grading,
9
139
Problems
Arrhenius
Chapter
139
145
C Consecutive First-Order Reaction
the Atom
Splitting
Chapter
135
and
Learning?
179
Bibliography
180
References
180
Basic
181
Spectroscopy
Introduction
181
Planck's
181
Discovery
Radio Waves
Balmer's
Integer
183
Formula
Very Useful Formula
Preliminary Summary of the
184
A
189
Bohr Atom
190
vjjj
Contents
Significance of the Bohr Quantum Number
Orbital Screening
X-Ray Emission
Forensic/Analytical Use of Auger X-Rays
X-Ray
X-Ray
192
n
192
193
196
Fluorescence
198
Diffraction
199
Absorption Spectroscopy/Spectrophotometry
Interpreting Electronic Spectra
General Principles of Spectroscopy
202
Problems
210
Electronic
Chapter
Chapter
10
209
Bibliography
210
References
211
Early Experiments in Quantum Physics
213
Introduction
213
Stefan-Boltzmann Law: Relating Heat and Light—Part 1
Blackbody Radiation: Relating Heat and Light—Part H
213
Photoelectric Effect
221
De
225
Broglie
Matter Waves
214
Davisson-Germer Experiment
226
Summary
230
Problems
231
References
232
11 The
Schrodinger Wave Equation
233
Introduction
Definition of
Chapter 12
204
233
a
Commutator
242
Postulates of Quantum Mechanics
243
Particle
244
on a
Ring
Comparison of PIB and POR Applications
Additional Theorems in Quantum Mechanics
247
Summary
249
Problems
250
Study, Test, and Learn?
251
References
252
The
253
247
Quantized Harmonic Oscillator: Vibrational Spectroscopy
Introduction
253
Harmonic Oscillator Details
255
Harmonic Oscillator Results
258
Reduced Mass
Isotope Shift
262
in the Vibrational Fundamental
Hermite Recursion Rule
Infrared
Dipole Selection
3iV- 6
or
Raman
Spectroscopy
264
265
Rule
265
3jV- 5 Vibrations?
267
271
Summary
274
Problems
References
Frequency
275
,
275
Contents
Chapter
'*
13 The
Quantized Rigid
Rotor and the Vib-Rotor
277
Introduction
277
Three-Dimensional Particle-in-a-Box
277
Rigid Rotor
Key Step!
281
Rigid
Rigid
279
Rotor Wave Functions
283
Rotor Results
285
Angular
Wave Functions
285
Angular
Momentum
286
Rotational
Chapter 14
Spectrum of CO
Fourier Transform Spectrometry
FT-IR Imaging and Microscopy
289
Dipole Requirement
Vib-Rotor Infrared Spectroscopy
Bond Length of H-$C1
Summary
294
Problems
304
References
305
The
Schrodinger Hydrogen
291
292
295
302
303
Atom
307
Introduction
Strategy
to
307
Solve the Problem
Associated Laguerre
307
Polynomials
310
Interpretation
Pictures of Angular Orbitals
Powell Equivalent d-Orbitals
311
Unsold's Theorem
323
Aufbau
Term
316
319
and the Scaled H Atom
Principle
Symbols and Spin Angular
323
Momentum
324
Hund's Rule
\L, Sz)
versus
325
\J, Jz) Coupling
326
Summary
328
Problems
329
References
329
Chapter 15 Quantum Thermodynamics
331
Introduction
331
(Energy) Partition Function
Average Translation Energy in One Dimension
Average Rotational Energy of a Diatomic Molecule
Average Vibrational Energy
High-Temperature Limit for Vibrational Heat Capacity
Heat Capacity of a Polyatomic Species: Water
Combining Partition Functions
Statistical Formulas for Other Thermodynamic Functions
333
Statistical Formula for S(T)
340
Sakur-Tetrode Formula for Absolute
Entropy
of
a
334
334
335
337
337
339
340
Gas
341
343
Summary
Problems
References
344
•
344
Contents
x
Chapter
16
Approximate
Methods and Linear
345
Algebra
345
Introduction
Simple
345
First-Order Perturbation Theory
Principles
of Perturbation
347
Theory
Variation Method
348
Molecular Orbitals and the Secular
Chemical Bonds of
Chapter
350
Equation
352
Ethylene
Elementary Linear Algebra
356
Unitary Similarity Diagonalization of a Square Hermitian Matrix
Jacobi Algorithm for Diagonalization Using a Computer
359
Order Matters!
361
Summary
362
Problems
363
Testing, Grading, and Learning?
Study, Test, and Learn?
363
References
366
365
17 Electronic Structure of Molecules
367
Introduction
367
Hartree-Fock-Roothan LCAO Calculations
367
Chemical Effects in Orbital
368
Many-Electron
Screening
Wave Functions
370
Determinantal Wave Functions for Many-Electron Systems
371
Roothaan's LCAO Hartree-Fock Equation
Electron Exchange Energy
372
Practical
373
Implementation
and
Equations for
Examples
2n Electrons
375
377
Gaussian Basis Sets
377
Moment of BH
392
Excited States of BH
392
Mesoionic Bond Orders
393
Summary
399
Problems
399
References
401
Point
Group Theory
and
Electrospray
Mass
Spectrometry
Introduction
Basic Point
Future
403
403
Group Theory
403
Calculation of Molecular Vibrations
of
Development
Electrospray
"Making Elephants Fly"
Summary
Chapter
374
SCF Iteration
Dipole
18
370
Atomic Units
The Hartree-Fock-Roothaan
Chapter
361
410
Mass
Spectrometry?
412
414
419
Problems
419
References
420
19 Essentials of Nuclear
Magnetic Resonance
Introduction
Early
NMR
423
423
Spectrometers
423
Contents
xi
NMR
Spin Hamiltonian
Application of 1D-NMR
Nuclear Magnetic Resonance: Pulse Analysis
Rotating Coordinate System
Detection of Magnetic Fields
424
Forensic
427
Bloch
Equations
Complex Fourier Transform
434
2D-NMR COSY
438
430
432
433
438
Coherent
Spectroscopy
Operator COSY Analysis Using
Anatomy of a 2D Experiment
Product
439
Dr. Brown's Automated Software
440
443
Summary
447
Problems
447
References
447
Appendix
A:
Relation between
Appendix
B:
The Hartree-Fock-Roothaan SCF
Legendre and Associated Legendre Polynomials
Equation
449
451
Appendix C:
Gaussian Lobe Basis Integrals
457
Appendix D:
Spin-Orbit Coupling in the H
459
Atom
Index
465
UseofPCLOBE
475