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 |  موضوع: كتاب Fundamental Chemistry With Matlab الأربعاء 04 مايو 2022, 7:59 pm | |
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أحضرت لكم كتاب
Fundamental Chemistry With Matlab
Daniele Mazza
Former Faculty, Politecnico di Torino, Turin, Italy
Enrico Canuto
Former Faculty, Politecnico di Torino, Turin, Italy
و المحتوى كما يلي :
Contents
Introduction xv
CHAPTER 1 Plotting atomic orbitals with Matlab .1
1.1 Wave functions and their factorization 1
1.1.1 Generalities 1
1.1.2 Angular wave functions . 3
1.1.3 Table of the radial functions 8
1.2 Graphical plot of the wave functions 9
1.3 Graphical algorithm 11
1.3.1 Description . 11
1.3.2 Matlab script 11
1.4 Graphical plot of the radial probability density for s-type orbitals 14
1.4.1 Description . 14
1.4.2 Matlab script and graphical results 15
1.5 Hybrid orbitals 17
1.5.1 Hybrid orbitals sp3 . 19
1.5.2 Hybrid orbitals dsp3 . 20
1.5.3 Hybrid orbitals d2sp3 21
References . 21
CHAPTER 2 Balancing chemical reactions with Matlab . 23
2.1 Introduction 23
2.2 Nonredox and redox reactions . 25
2.2.1 Nonredox reactions (or metatheses) 25
2.2.2 Redox reactions 25
2.2.3 Stoichiometry and nonredox reactions 26
2.2.4 Stoichiometry and redox reactions 26
2.3 General method 26
2.3.1 The balance equation . 26
2.3.2 Example 28
2.4 Solution of the homogeneous system of linear equations . 29
2.4.1 The nullspace method 29
2.4.2 Example 30
2.4.3 Balancing algorithm from chemical formulas . 30
2.5 Nullspace algorithm for balancing chemical reactions . 32
2.5.1 Nullspace function stoichiometry 33
2.5.2 Results of the plug-in code example . 34
2.6 Catalog of the reactions and of their plug-in codes 35
vii2.6.1 Oxidation of hydrogen peroxide by potassium permanganate . 35
2.6.2 Oxidation of silver sulfide by aqua regia 35
2.6.3 Oxidation of bromidric acid by potassium dichromate 36
2.6.4 Oxidation of mercury by nitric and chloridric acid 37
2.6.5 Oxidation of chromium(II) bromide by sodium bromate . 38
2.6.6 Zinc oxidation by silver arseniate . 38
2.6.7 Precipitation of an insoluble salt (AgCl) . 39
2.6.8 Neutralization of carbonic acid with sodium hydroxide . 40
2.6.9 Hydrolysis of sodium carbonate with nitric acid 40
2.6.10 Oxidation of sodium sulfite to sulfate by potassium permanganate 41
2.6.11 Oxidation of iron(II) sulfate by hydrogen peroxide in acid solution . 42
2.6.12 Oxidation of manganese(II) chloride to potassium permanganate by
sodium bromate 42
References . 43
CHAPTER 3 Chemical kinetics aided by Matlab/Simulink 45
3.1 Introduction 45
3.2 First-order irreversible kinetics 47
3.2.1 State equation construction 47
3.2.2 Simulink graphical representation . 48
3.2.3 The Matlab script . 49
3.2.4 A simpler alternative Matlab script . 50
3.3 First-order reversible reaction 51
3.3.1 State equation construction 51
3.3.2 Simulink graphical representation and results 52
3.3.3 Alternative Matlab script . 53
3.4 Second-order reversible reaction . 54
3.4.1 State equations . 54
3.4.2 Solution of the Riccati equation 56
3.4.3 Alternative Matlab script . 57
3.5 Consecutive irreversible reactions . 58
3.5.1 State equations . 58
3.5.2 Alternative Matlab script . 59
3.6 Two-stage NO to NO2 oxidation . 60
3.6.1 State equations . 60
3.6.2 Alternative Matlab script . 62
3.7 Ozone decomposition into oxygen 63
3.7.1 State equations . 63
3.7.2 Alternative Matlab script . 64
3.8 Irreversible A - B reaction with linear temperature increase 65
References . 66
viii ContentsCHAPTER 4 More complex kinetics aided by Matlab/Simulink 67
4.1 Introduction 67
4.2 MichaelisMenten kinetics . 68
4.2.1 State equations, equilibrium, and stability 68
4.2.2 The MichaelisMenten equation of the production rate 69
4.2.3 Script, block diagram and graphical results 71
4.3 The iodine clock reaction . 74
4.3.1 State equations . 74
4.4 Oscillating kinetics: introduction . 77
4.4.1 The LotkaVolterra model . 77
4.5 Oscillating kinetics of BriggsRauscher 80
4.5.1 Simplified reaction scheme 80
4.5.2 State equations and stability analysis 81
4.5.3 Behavior of the state equations . 82
4.6 Introduction to BelousovZhabotinsky kinetics . 85
4.6.1 State equations . 85
4.6.2 Equilibrium and stability analysis . 88
4.6.3 Simulated results 90
4.6.4 Matlab script 92
References . 96
CHAPTER 5 Gaseous reactions and equilibria aided by Matlab 99
5.1 The second law of thermodynamics 99
5.2 Application of the Gibbs energy criterion to chemical reactions . 100
5.3 Relationship of ΔG with the equilibrium constant KP . 103
5.4 The value of ΔS, ΔH, and ΔG as a function of temperature 104
5.5 The table of the NASA CEA thermochemical coefficients 105
5.6 Introduction to Matlab scripts 106
5.6.1 Organization of the Matlab scripts 106
5.6.2 The function NASAdata . 107
5.6.3 The function ThermoCoef . 110
5.7 Hydrogen combustion 110
5.7.1 Description . 110
5.7.2 The Matlab script . 111
5.8 Ammonia synthesis (Haber process) . 114
5.8.1 Description and graphical plot . 114
5.8.2 The Matlab script . 115
5.9 Methane (CH4) combustion . 117
5.9.1 Description and graphical plot . 117
5.9.2 Matlab script 118
5.10 Hydrogen production at high and low temperature . 121
Contents ix5.10.1 Description and graphical plot . 121
5.10.2 Matlab script 122
5.11 Sulfur trioxide (SO3) production from sulfur dioxide (SO2) 124
5.11.1 Description and graphical profiles . 124
5.11.2 Matlab script 125
5.12 CaSO4 production from lime and sulfur impurity in clean coal combustion . 126
5.12.1 Description and graphical results 126
5.12.2 Matlab script 127
5.13 Calcium carbonate (CaCO3) decomposition and kinetics . 130
5.13.1 Description and graphical plot . 130
5.13.2 Matlab script 130
References . 133
CHAPTER 6 Physical properties of gases and vapors aided by Matlab . 135
6.1 Introduction 135
6.2 Distribution of molecular velocities in the case of oxygen 136
6.2.1 Description and graphical results 136
6.2.2 Matlab script 136
6.3 Compressibility of a real gas . 137
6.3.1 Description and graphical results 137
6.3.2 Matlab script 139
6.4 van der Waals isotherm of real gases 140
6.4.1 Description and graphical results 140
6.4.2 Matlab script 143
6.5 Water vapor pressure . 147
6.5.1 Description and graphical results 147
6.5.2 Matlab script 148
6.6 Water vapor pressure at different altitude and humidity 149
6.6.1 Description and graphical results 149
6.6.2 Matlab script 150
References . 153
CHAPTER 7 Exploring with Matlab acidbase equilibria in water 155
7.1 The hydrogen ion in solution . 155
7.2 Monoprotic acid . 156
7.2.1 Description and results . 156
7.2.2 Matlab script 157
7.3 Biprotic acid . 159
7.3.1 Description and results . 159
7.3.2 Matlab script 160
x Contents7.4 Titration of a weak biprotic acid with a strong base 161
7.4.1 Description and graphical results 161
7.4.2 Matlab script 161
7.5 Triprotic acid and sodium salt: H3PO4 1 Na3PO4 163
7.5.1 Description and results . 163
7.5.2 Matlab script 164
7.6 Titration of a triprotic acid with addition of NaOH 164
7.6.1 Description and graphical results 164
7.6.2 Matlab script 165
7.7 Carbonatic acidbase equilibria involving the precipitation of
CaCO3 and Mg(OH)2 . 166
7.7.1 Description and numerical results . 166
7.7.2 Matlab script 166
7.8 Pure water electric conductivity at different temperatures . 169
7.8.1 Description and graphical results 169
7.8.2 Matlab script 170
7.9 pH and water ionic product from 0C to 80C . 172
Reference 172
CHAPTER 8 Colligative properties of solutions aided by Matlab . 173
8.1 Aqueous solutions of NaCl 173
8.1.1 Description . 173
8.1.2 Matlab script 175
8.1.3 Output in command window . 175
8.2 Density of aqueous solutions: linear regression 176
8.2.1 The regression of density data in terms of temperature and
concentration 176
8.2.2 Numerical results of the regression . 178
8.2.3 Analysis of variance . 181
8.2.4 Graphical analysis 182
8.2.5 Matlab script 184
References . 187
CHAPTER 9 Exploring seawater chemical equilibria with Matlab . 189
9.1 Introduction 189
9.2 Why seawater reacts with atmospheric CO2? . 189
9.3 Methods and techniques for dealing with seawater chemistry . 191
9.4 Surface chemistry . 192
9.4.1 Description and graphical results 192
9.4.2 Matlab script 193
9.5 Ocean chemistry under pressure up to 100 MPa . 197
Contents xi9.5.1 Different pH scales in ocean chemistry 197
9.5.2 Heterogeneous reactions in ocean chemistry 198
9.5.3 Hydrostatic pressure acting on homogeneous and heterogeneous
equilibria 198
9.5.4 Ocean chemistry in a broad perspective 200
9.5.5 Matlab script 202
9.5.6 The sea water equilibria computation . 206
9.5.7 The electro-neutrality function 214
9.5.8 The graphical script . 214
9.5.9 Typical numerical and graphical results 218
9.6 Phosphate chemistry in seawater . 220
9.6.1 Description and graphical results 220
9.6.2 Matlab script 221
9.7 Density of seawater versus salinity, temperature, and pressure 223
9.7.1 Description . 223
9.7.2 Matlab script 225
References . 226
CHAPTER 10 Prevalence diagrams for common elements aided by Matlab . 229
10.1 Introduction and scope . 229
10.2 The electrode potential E0 and the galvanic cell . 230
10.3 Energy analysis of a galvanic cell . 231
10.3.1 Introduction 231
10.3.2 Example 1 234
10.4 The Nernst equation . 234
10.4.1 Introduction 234
10.4.2 Example 2 235
10.4.3 Example 3 235
10.5 The electron activity 236
10.6 The prevalence (or Pourbaix) diagrams . 236
10.6.1 Introduction 236
10.6.2 Two alternative algorithms for building prevalence/stability
diagrams . 239
10.7 The first algorithm . 239
10.8 The second algorithm . 240
10.8.1 The main script 240
10.8.2 The functions 245
10.9 The fundamental prevalence diagram: water 248
10.9.1 Description . 248
10.9.2 Graphical and numerical results 250
xii Contents10.10 Manganese oxides and hydroxides 250
10.10.1 Description, graphical, and numerical results . 250
10.11 Lead and lead sulfate . 252
10.11.1 Description . 252
10.12 Sulfur 253
10.12.1 Description, numerical, and graphical results . 253
10.13 Au/Cl in seawater . 255
10.13.1 Description . 255
10.13.2 Graphical and numerical results 256
References . 257
Appendix A: Linear algebra 259
Appendix B: Introduction to dynamic systems 267
Appendix C: Introduction to linear regression . 283
Appendix D: Introduction to Matlab Simulink . 291
Appendix E: Table of seawater coefficients . 303
Appendix F: The Schroedinger equation 311
Index .
Index
Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively.
A
Acid-base equilibria in water
biprotic acid, 159160
CaCO3, 164165
CaCO3 and Mg(OH)2, 166169
hydrogen ion in solution, 155156
monoprotic acid, 156159
pH, 172
pure water electric conductivity, 169171
triprotic acid and sodium salt, 163164
triprotic acid with addition of NaOH, 164165
water ionic product, 172
weak biprotic acid with a strong base, 161163
Algorithm
linear regression, 176187
nullspace method, 29, 3234
prevalence diagram, 239
Riccati equation, 5657
Ammonia reaction, 102t
Ammonia synthesis
description and graphical plot, 114
Matlab script, 115116
Angular frequency, 269
Aqua regia, 3536
Aqueous solutions of NaCl
description, 173174
additive properties, 173
colligative properties, 173
constitutional properties, 173
ebullioscopic constant, 174
Matlab script, 175
molarity, 174
Atomic orbitals, graphical plot of
graphical algorithm, 1114
graphical plot of wave functions, 910
hybrid orbitals, 1721
radial probability density for s-type orbitals, 1416
wave functions, 19
Auto-catalytic reaction, 77
Autonomous dynamic system, 267
Avogadro’s number, 23
B
Balancing chemical reactions
general method, 2628
homogeneous system of linear equations, 2931
nonredox reactions, 2526
nullspace algorithm for, 3234
plug-in codes, 3543
redox reactions, 2526
BelousovZhabotinsky (BZ) kinetics
characteristic polynomial of, 89f
equilibrium and stability analysis, 8889
limit cycle reached from unstable equilibrium, 90f
Matlab script, 9296
nullcline, 88f
reactions set, 8586
Routh’s necessary and sufficient conditions, 89
simulated results, 9091
state equations, 8588
Biprotic acid
carbonatic equilibria, 159
description and results, 159160
Matlab script, 160
Bohr radius, 89
Boiling point, 173
ebullioscopic constant, 174
BriggsRauscher oscillating kinetics
block diagram of, 82f
hypoiodous acid, 81
instability region, 83f
iodide ion, 81
iodo-malonic acid, 81
limit cycle, 84f
molecular iodine, 81
simplified reaction scheme, 8081
stability analysis, 8182
state equations, 8182
Buffer system, 164
C
Calcium carbonate (CaCO3) decomposition
description and graphical plot, 130
kinetics, 130132
Matlab script, 130132
Calcium sulfate (CaSO4) production
description and graphical results, 126127
free energy, reversible reaction, 127f
Matlab script, 127129
sulfur impurity, 126129
Carbonate compensation depth, 198199
Carbonatic acid-base equilibria
CaCO3 and Mg(OH)2, 166169
description and numerical results, 166
Matlab script, 166169
Carbon dioxide, 189191
Characteristic polynomial, 264
Chemical kinetics
321Chemical kinetics (Continued)
consecutive irreversible reactions, 5860
first-order irreversible reactions, 4750
first-order reversible reaction, 5153
NO to NO2 oxidation, 6062
ozone decomposition into oxygen, 6364
second-order reversible reaction, 5457
temperature increase, 6566
Chemical reaction
autocatalytic, 77
balancing, 2325
breeding, 77
BriggsRauscher, 8084
equilibrium constant and ΔG, 103104
Gibbs energy criterion, 100102
Gibbs energy of formation, 101
hydrolysis, 4041
iodine clock, 7477
neutralization, 40
nonredox, 2526
oscillating, 7780
precipitation, 39
product, 45
rate, 4546
reactant, 45
redox, 25
standard conditions, 101
stoichiometric coefficients, 46
Chromium bromide
oxidation, 38
Colligative properties of solutions
aqueous solutions of NaCl, 173176
density of aqueous solutions, 176187
Complex eigenvectors, 264
Complex kinetics
BelousovZhabotinsky (BZ) kinetics, 8596
iodine clock reaction, 7477
MichaelisMenten kinetics, 6874
oscillating kinetics, 7780
oscillating kinetics of BriggsRauscher, 8084
Compressibility of a real gas
description and graphical results, 137139
Matlab script, 139140
Condensation region, 140141
Consecutive irreversible reactions
alternative Matlab script, 5960
block diagram of, 58f
first-order delayed approximation, 59f
state equations, 5859
Convolution integral, 269
Covolume, 135
D
Damping coefficient, 269
Dealing with seawater chemistry
Matlab functions, 192
methods and techniques for, 191192
professional tools, 191192
ΔS, ΔH, and ΔG function of temperature, 104105
Density of aqueous solutions
analysis of variance, 181182
sum of squares, 181
graphical analysis, 182184
model residuals, 183f
Matlab script, 184187
analysis of variance, 184
least squares regression, 184
predictor variables, 184
matrix version, 178
NaCl density, 177f
numerical results of the regression, 178180
estimate, 178
pValue, 178
standard error, 178
parameters
adjusted R-squared, 180
residual degrees of freedom, 179
root mean squared (RMS), 179
R-squared, 180
polynomial regression coefficients, 178
raw data density surface, 182f
residual surface, 183f
temperature and concentration, 176178
variance for each variable, 181f
Dissolved Inorganic carbon (DIC), 193
Dynamic systems
linear time invariant equations, 268271
conservation law equation, 271
examples of, 270271
pure integrator, 270
local stability of nonlinear systems, 272280
asymptotic stability, 272
instability, 273
Oregonator model, 276f
perturbed equation, 273
saddle point, 274
second-order equilibrium points, 274276
stable node, 274
stable spiral, 274275
unstable spiral, 275, 275f
Lyapunov exponents, 276279
BriggsRauscher kinetics, 277f
Jacobian matrix, 277
limit cycle, 279
Oregonator kinetics, 279t
perturbation equations, 272274
second-order systems, 275276
imaginary eigenvalues, 276
322 Indexzero eigenvalues, 275276
singular perturbation, 279280
state space equations, 267268
Dynamic system theory, 46
E
Eigenvalues, 263265
real and complex, 264
Electrochemical cell, 230
Electrochemical series, 231
Electrode potential E0
electrochemical series, 232t
galvanic cell, 230231
half-reaction electrode, 231
oxidation reaction, 231
redox potential, 231
zinc/hydrogen galvanic cell, 230f
Electron activity
redox equilibria, 236
redox intensity, 236
Energy analysis of a galvanic cell, 231234
copper/zinc galvanic cell, 232f, 233234
example, 234
Gibbs free energy, 233
thermodynamics, 233
Equation
balance, 2628
Nernst, 234236
Schroedinger, 312
Van der Waals, 140146
Equations of state, 267
F
First-order irreversible kinetics
Matlab script, 4950, 56f
reactant and product of, 50f
Simulink graphical representation, 4849, 48f
state equation, 4748
First-order reversible reaction
block diagram, 52f
Matlab script, 53
Simulink graphical representation, 52
state equation, 51
Fluegas desulfurization (FDG), 124
Forced equilibrium, 273
Free (or Gibbs) energy, 99100
Freezing point, 173
cryoscopic constant, 174
G
Galvanic cell, 230231
electrode potential, 230231
energy analysis, 231234
standard state, 231234
stanndard hydrogen electrode (SHE), 230
Gas particles
energy distribution, 136137
Gaseous reactions and equilibria
ammonia synthesis, 114116
calcium carbonate (CaCO3), 130132
calcium sulfate (CaSO4) production from lime, 126129
ΔG with the equilibrium constant Kp, 103104
ΔS, ΔH, and ΔG function of temperature, 104105
hydrogen combustion, 110114
hydrogen production, 121124
Matlab scripts, 106110
Methane (CH4) combustion, 117121
NASA CEA thermochemical coefficients, 105106
second law of thermodynamics, 99100
sulfur dioxide (SO2), 124126
sulfur trioxide (SO3), 124126
Gases and vapors
compressibility of a real gas, 137140
condensation, 147149
covolume, 135
at different altitude and humidity, 149152
ideal gas, 135
molecular velocities in the case of oxygen, 136137
real gas, 137140
van der Waals isotherm of real, 140146
water vapor pressure, 147149
Gold in seawater
description, 255
prevalence diagram of, 256f
Graphical plot of a wave function
Cartesian and spherical coordinates, 10f
versus Cartesian axes, 9
radial and angular functions, 9
real and imaginary parts, 9
tangent planes, 10
H
Heun integration method, 298299
Homogeneous system of linear equations
balancing algorithm from chemical formulas, 3031
equation solution, 31
reaction substances, 31
symbols of elements, 30
example, 30
nullspace method, 29
Hopf bifurcation, 89
Hybridization, 17
Hybrid orbitals
d2sp3, 21, 21f
dsp3, 20
sp
3, 19, 19f
Hydrobromic acid
oxidation, 3637
Index 323Hydrogen
Bohr atomic radius, 318319
combustion, 110114
ground atomic state, 318319
production, 121124
radial atomic function, 317319
Hydrogen combustion
description, 110111
Matlab script, 111114
reaction and fumes heat, 111f
linear interpolation, 111
polynomial interpolation, 111
Hydrogen ion in solution, 155156
Hydrogen peroxide
oxidation, 35
Hydrogen production
description and graphical plot, 121122
high-temperature production, 121f
low temperature production, 121124
Matlab script, 122124
I
Ideal gas law, 135
Imbalance concentration in seawater, 193194
Infinite dilution, 169170
Iodine clock reaction
conservation law, 75
Simulink block diagram, 75
state equations, 7477
triiodide steady state, 76f
Ionic product of water, 229
Iron(II) sulfate
oxidation, 42
K
Kinetics
BelousovZhabotinsky, 8596
BriggsRauscher, 8084
calcium carbonate decomposition, 130132
conservation equation, 4748
iodine clock, 7477
irreversible and consecutive, 5860
irreversible and first order, 4750
irreversible reaction with temperature increase, 6566
LotkaVolterra model, 7780
MichaelisMenten, 6874
ozone decomposition, 6364
reversible and first order, 5153
reversible and second order, 5457
state equations, 4748
two stage NO oxidation, 6062
L
Law
Boyle, 135
Proust, 23
Raoult, 173
Lead and lead sulfate
description, 252253
prevalence diagram, 253f
Legendre
associated function, 315
polynomials, 315
Linear algebra
bases of, 259261
Cartesian coordinates, 262f
matrices, 259260
orthogonal matrix, 261263
rank of a matrix, 260261
vectors, 259260
eigenvalues, 263265
eigenvectors, 263265
Linear homogeneous Diophantine equation, 28
Linear regression
and least squares estimation, 284286
adjusted R-squared, 285
Euclidean norms, 284285
explained variance, 285
residual sum of squares (RSS), 285
total sum of squares, 285
model and measurement errors, 283284
parameter vector, 283
predictor variables, 283
model degrees of freedom, 286290
overfitting, 286
poor fitting, 286
test of significance, 286290
F-test, 288289
probability density function, 287f
p-value, 289290
Student’s t-test, 286288
Linear temperature increase, irreversible reaction
energy diagram, 65f
first-order kinetics, 65f
Liquid
evaporation, 147149
LotkaVolterra model
closed orbit, 78
energy conservation, 78
LTI state equations
examples, 270271
Lyapunov exponents, 8384, 276279
M
Magnetic quantum number, 3
Manganese chloride
oxidation, 4243
Manganese oxides and hydroxides
324 Indexdescription, 250251
graphical and numerical results, 250251
Nernst equation, 251252
prevalence diagram of, 251f
Mass
conservation, 27
molar, 23
Matlab script
ammonia synthesis, 115116
BelousovZhabotinsky kinetics, 9396
calcium carbonate decomposition, 130132
calcium sufate production, 127129
carbonatic acidbase equilibria, 166169
density of NaCl solution, 184187
gaseous equilibria, 106110
hydrogen combustion, 111114
hydrogen production, 122124
InitChem, 296
irreversible first order kinetics, 4950
LotkaVolterra model, 7780
methane combustion, 118121
MichaelisMenten kinetics, 6970
monoprotic acid, 157159
ocean chemistry, 202206
phosphate chemistry in seawater, 221223, 225226
prevalence diagram, 240245
pure water electric conductivity, 170171
real gas compressibility, 139140
sulfur trioxide production, 125126
surface seawater equilibrium, 193197
titration of weak biprotic acid, 161163
van der Waals isotherm, 143146
water vapor pressure, 148149
water vapor pressure vs altitude, 150152
wave function, 910
Matlab Simulink
Configuration parameters, 292294, 294f
simulation time unit, 294
3D graphical plot, 297, 297f
initialization script, 296
integrator block, 291292
ODE solvers, 297302
Euler method, 298
Heun’s method, 299
integration rules, 299f
principles of, 298300
Runge-Kutta, 299f, 300
pane and library, 291
integrator block, 293f
script and graphical output, 295
initialization, 295
integration launch, 295
parameter values, 295
solver comparison, 300302
simulation discrepancy, 300, 301f
Matrix
nullspace, 262
orthogonal (basis), 261263
QR factorization, 261
rank, 260261
MaxwellBoltzmann statistics, 135
Maxwell construction, 140141
Mercury
oxidation, 37
Methane (CH4) combustion
combustion, 117f
description and graphical plot, 117
Matlab script, 118121
MichaelisMenten equation, 70
MichaelisMenten kinetics
block diagram and graphical results, 7174
the production rate, 6970
forward rate constant, 69
production rate and the approximation, 70f
state equations, equilibrium, and stability, 6869
Models for regression
introduction, 283
measured variables, 283
measurement error, 283284
model error, 283
parameter vector, 283
predictor (input) variables, 283
Molar conductivity, 169170
Mole, 23
conservation, 27
Molecular velocities in the case of oxygen
description and graphical results, 136
distribution of, 136137
Matlab script, 136137
Monoprotic acid
description and results, 156157
hydrofluoric acid, 156
ionization of weak electrolyte, 156
Matlab script, 157159
N
NaCl solution, 173174
density, 177f
NASA CEA thermochemical coefficients, 103f, 105106
Natural equilibriums, 273
Nernst equation, 234235
copper/zinc cell, 235
half-reaction, 235
thermodynamic equilibrium, 234235
well-known, 234235
Nitric oxide
oxidation, 6062
Nonlinear state equations
Index 325Nonlinear state equations (Continued)
local stability, 272274
Lyapunov exponents, 276279
natural and forced equilibriums, 273
perturbation, 272274
second order equilibriums, 274276
Nonredox reactions, 25
Nullspace algorithm
for balancing chemical reactions, 3234
plug-in code, 34
stoichiometry, 3334
O
Ocean chemistry. See Seawater chemistry
Orthogonal matrix, 262
Oscillating clock, 80
Oscillating kinetics
LotkaVolterra model, 7780, 79f
LV equations, 7778
Osmotic pressure, 173
Oversaturation, 198
Oxidation state method, 26
Ozone decomposition into oxygen
Matlab script, 64
state equations, 6364
P
pH, 155
scales in ocean chemistry, 197
seawater scale, 198
total scale, 197
pH and water ionic product
description, 172
Matlab script, 172
pOH, 155
Phase plane of dynamic systems, 88
Phosphate chemistry in seawater
description and graphical results, 220221
Matlab script, 221223
phosphate ions in, 221f
Point probability, of atomic orbitals, 2
Pourbaix (or prevalence) diagrams
boundary lines in, 237
building prevalence/stability diagrams
first algorithm (pixel by pixel search), 239
second algorithm (explicit search), 239
electrochemical potentials, 238
Fe electrochemical potentials, 237t
Matlab scripts, 236
prevalence, 236239
standard electrode, 237
Precipitation, 191
Prevalence diagrams. See Pourbaix (or prevalence) diagrams
Pure water electric conductivity
description and graphical results, 169170
at different temperatures, 169171
Gibbs equation, 170
Matlab script, 170171
specific conductance, 169170
versus temperature, 170f
Q
Quantum numbers, 1
R
Radial function of hydrogen atom
asymptotic solution, 318
Bohr formula, 318319
dimensionless radius, 318
radial equation, 317
radial probability density, 319
Radial nodes, 14
Radial probability density for s-type orbitals
description, 1415
Matlab script and graphical results, 1516
1s, 2s, and 3s functions, 11
Rate constant in chemical kinetics, 46
Reactants in chemical reactions, 45
Reaction coordinate, 102
Reactions and plug-in codes
bromidric acid by potassium dichromate, 3637
carbonic acid with sodium hydroxide, 40
catalog of, 3543
chromium(II) bromide by sodium bromate, 38
hydrogen peroxide by potassium permanganate, 35
insoluble salt (AgCl), 39
iron(II) sulfate by hydrogen peroxide in acid solution, 42
manganese(II) chloride to potassium permanganate, 4243
mercury by nitric and chloridric acid, 37
silver sulfide by aqua regia, 3536
sodium carbonate with nitric acid, 4041
sodium sulfite to sulfate, 41
zinc oxidation by silver arseniate, 3839
Reaction quotient, 102
Real gas
van der Waals isotherm, 140146
Redox potential, 230231
redox reactions, 2526
stoichiometry and, 26
Relaxation times in chemical kinetics, 46
Riccati equation with constant coefficients, 54
S
Schroedinger equation, 267
angular waves, 314317
associated Legendre functions, 316f
azimuth equation, 314315
low-degree Legendre polynomials, 316f
326 Indexpolar angle equation, 315317
variable separation, 314
derivation, 311312
spherical coordinates, 313314
stationary equation, 313314
time-dependent equation, 311
time-independent equation, 312313
Script function
function SeaWNeutr2, 209212, 214
intersection, prev, vert, 245248
NASAdata, 107109
neutrality, 157159
pressure, dPressure, Maxwell, 143146
SeaWNeutr, 193194
ThermoCoef, 110
Seawater chemical equilibria
atmospheric CO2, 189191
hydroxide anion, 191
ionic solutions, 190
methods and techniques, 191192
phosphate chemistry in seawater, 220223
salinity, 223226
spectator and reactive ions in standard, 190t
temperature and pressure, 223226
Seawater chemistry under pressure
bisulfate ion, 197
DIC surface versus temperature and Co2, 220f
dissolved inorganic carbon, 200f
electro-neutrality function, 214
graphical script, 214218
2D graphical representation, 218
surface plot, 216217
variable loading and selection, 215216
homogeneous and heterogeneous reactions in, 198
homogeneous and heterogeneous equilibria, 198200
calcite oversaturation versus pressure and CO2, 199f
calcium carbonate, 198199
seawater equilibria, 199
hydrofluoric acid, 198
Matlab script, 202206
computation, 202
graphical results, 203204
numerical and graphical results, 218219
printing numerical results, 212
symbol, unit, and name of dependent variables, 205t
zero-crossing function, 209212
parameters used in seawater equilibria, 212t
pH scales in, 197198
sea water equilibria computation, 206213
printout of input data, 208
reading the excel spreadsheet, 207208
user data and independent variable range, 206207
seawater pH scale, 198
species involved in seawater equilibria, 209t
Seawater coefficient table
fugacity and H2O vapor pressure, 309
temperature and salinity coefficients, 309
numerical tables, 306309
coefficients of carbonatic species, 307
electrical charge, 306
pressure and temperature coefficients, 307
standard salinity concentrations, 306
temperature and salinity coefficients, 307
other species, 308309
ionic strength coefficients, 308
pressure and temperature coefficients, 308
temperature and salinity coefficients, 308
printout script, 303306
Seawater density, 214
Seawater pH scale, 198
Seawater reaction with atmospheric CO2
current chemical composition, 190
gaseous exchange, 190
hydroxide anion, 191
spectator and reactive ions in standard, 190t
Seawater salinity
density versus hydrostatic pressure, 224f
description, 223225
Matlab script, 224226
temperature and pressure, 223226
temperature and salinity, 224
Seawater surface chemistry
alkalinity, 190
composition (standard), 206213
description and graphical results, 192193
imbalance concentration, 193194
inorganic carbon (DIC) versus temperature, 192f
Matlab script, 193197
dissociation constants, 193t
electro-neutrality function SeaWNeutr, 196
graphical tool, 196
reading and printing the excel table, 195
user data, 194
reactive ions, 190
solution molality, 189
spectator ions, 190
Second law of thermodynamics, 99100
Second-order reversible reaction
block diagram of, 55f
Matlab script, 57
reactants and product of, 56f
Riccati equation, 5657
state equations, 5456
Silver sulfide
oxidation, 3536
Simulink block diagram
BelousovZhabotinsky kinetics, 8588
BriggsRauscher reaction, 8182
Index 327Simulink block diagram (Continued)
iodine clock reaction, 7477
irreversible first order kinetics, 48f
MichaelisMenten kinetics, 6869, 7174
reversible first order kinetics, 52f
reversible second order kinetics, 55f
Singular perturbation method, 88
Slaking, 130
Sodium sulfide
oxidation, 41
Spherical harmonics, 317
Square matrix
eigenvalues, eigenvectors, 263264
Stability of dynamic systems, 269
State equations
autonomous, 267
convolution integral, 269
generalities, 267268
linear time invariant (LTI), 268271
LotkaVolterra, 7780
order, 267
singular perturbation, 279280
stability criteria, 269
state matrix eigenvalues, 269
state variables, 267
Statistics
analysis of variance, 181182
Maxwell Boltzmann, 136
Steam-methane reforming, 121
Stoichiometric coefficients, 28
Stoichiometry, 26
Sulfur
description, 253255
numerical and graphical results, 253255
prevalence diagram, 254f
Sulfur trioxide (SO3) production
description and graphical profiles, 124
Matlab script, 125126
from sulfur dioxide (SO2), 124126
Syngas, 122
T
Tangent dynamic system, 277
Tangent planes, 10
Temperature
irreversible reactions, 6566
Test of significance
F-test, 288289
null hypothesis, 288
p-value, 289290
significance threshold, 287
Student’s t-test, 286288
Thermodynamic database
NASA-CEA, 104
Thermodynamics
enthalpy, 99100
entropy, 99100
equilibrium constant and ΔG, 103104
Gibbs energy, 100102
second law, 99100
Time constant, 270
Titrant, 161
Titration
addition of NaOH, 164165, 165f
biprotic acid (weak), 159160
description and graphical results, 164
Matlab script, 165
titration curve, 161
triprotic acid, 163164
addition of, 164165
Matlab script, 165
Triprotic acid
description and results, 163164
Matlab script, 164
phosphoric acid, 163
sodium phosphate, 163
and sodium salt, 163164
Two-stage NO to NO2 oxidation
Matlab script, 62
state equations, 6062
V
Van der Waals isotherm of real gases
algebraic equation, 141
condensation line, 140141
description and graphical results, 140142
energy areas, 141142
Maxwell construction, 140141
real gas pressure versus volume profile, 143f
Vector space
linear independent vectors, 260
matrix of a vector basis, 259
vector basis, 259
Vertical mixing in seawater, 201
W
Water
conductivity of water, 169171
ionic product, 172
prevalence diagram, 248250
Water prevalence diagram
description, 248250
diagram, 249f
gaseous hydrogen, 249
graphical and numerical results, 250
Water vapor pressure
altitude and humidity, 149152
carbon dioxide concentration versus altitude, 150f
328 Indexdescription and graphical results, 149150
dynamic equilibrium, 147
equilibrium constant, 147
hydrostatic pressure, 150
Matlab script, 148152
Wave functions
angular function, 38
Cartesian coordinates, 2f
factorization, 19
generalities, 12
orbital d(z2), 5f
orbital d(xy) and d(x2-y2), 6f
orbital f(xz2) and f(x3-3xy2), 7f
orbitals px and py, 6f
radial function, 8t
real angular function, 4t
spherical coordinates, 2f
table of radial functions, 89
Weak biprotic acid
description and graphical results, 161
Matlab script, 161163
titration curve, 161f
Z
Zinc
oxidation, 3839
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