Physical Chemistry from a Different Angle

ThiS is a FM Blank Page

Georg Job • Regina Ruffler

Physical Chemistry froma Different Angle

Introducing Chemical Equilibrium, Kineticsand Electrochemistry by NumerousExperiments

Georg JobJob FoundationHamburgGermany

Regina RufflerJob FoundationHamburgGermany

ISBN 978-3-319-15665-1 ISBN 978-3-319-15666-8 (eBook)DOI 10.1007/978-3-319-15666-8

Library of Congress Control Number: 2015959701

Springer Cham Heidelberg New York Dordrecht London© Springer International Publishing Switzerland 2016This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or partof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformation storage and retrieval, electronic adaptation, computer software, or by similar or dissimilarmethodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in this bookare believed to be true and accurate at the date of publication. Neither the publisher nor the authors or theeditors give a warranty, express or implied, with respect to the material contained herein or for any errorsor omissions that may have been made.

Printed on acid-free paper

Springer International Publishing AG Switzerland is part of Springer Science+Business Media(www.springer.com)

Translated by Robin Fuchs, GETS, Winterthur, Switzerland

Hans U. Fuchs, Zurich University of Applied Sciences at Winterthur, Switzerland

Regina Ruffler, Job Foundation, Hamburg, Germany

Based on German edition “Physikalische Chemie”, ISBN 978-3-8351-0040-4, published by

Springer Vieweg, 2011.

Exercises are made available on the publisher’s web site:

http://extras.springer.com/2015/978-3-319-15665-1

By courtesy of the Eduard-Job-Foundation for Thermo- and Matterdynamics

Preface

Experience has shown that two fundamental thermodynamic quantities are espe-

cially difficult to grasp: entropy and chemical potential—entropy S as quantity

associated with temperature T and chemical potential μ as quantity associated with

the amount of substance n. The pair S and T is responsible for all kinds of heat

effects, whereas the pair μ and n controls all the processes involving substances

such as chemical reactions, phase transitions, or spreading in space. It turns out that

S and μ are compatible with a layperson’s conception.In this book, a simpler approach to these central quantities—in addition to

energy—is proposed for the first-year students. The quantities are characterized

by their typical and easily observable properties, i.e., by creating a kind of “wanted

poster” for them. This phenomenological description is supported by a direct

measuring procedure, a method which has been common practice for the quantifi-

cation of basic concepts such as length, time, or mass for a long time.

The proposed approach leads directly to practical results such as the predic-

tion—based upon the chemical potential—of whether or not a reaction runs spon-

taneously. Moreover, the chemical potential is key in dealing with physicochemical

problems. Based upon this central concept, it is possible to explore many other

fields. The dependence of the chemical potential upon temperature, pressure, and

concentration is the “gateway” to the deduction of the mass action law, the

calculation of equilibrium constants, solubilities, and many other data, the con-

struction of phase diagrams, and so on. It is simple to expand the concept to

colligative phenomena, diffusion processes, surface effects, electrochemical pro-

cesses, etc. Furthermore, the same tools allow us to solve problems even at the

atomic and molecular level, which are usually treated by quantum statistical

methods. This approach allows us to eliminate many thermodynamic quantities

that are traditionally used such as enthalpy H, Gibbs energy G, activity a, etc. Theusage of these quantities is not excluded but superfluous in most cases. An opti-

mized calculus results in short calculations, which are intuitively predictable and

can be easily verified.

v

Because we choose in this book an approach to matter dynamics directly by

using the chemical potential, application of the concept of entropy is limited to the

description of heat effects. Still, entropy retains its fundamental importance for this

subject and is correspondingly discussed in detail.

The book discusses the principles of matter dynamics in three parts,

• Basic concepts and chemical equilibria (statics),

• Progression of transformations of substances in time (kinetics),

• Interaction of chemical phenomena and electric fields (electrochemistry)

and gives at the same time an overview of important areas of physical chemistry.

Because students often regard physical chemistry as very abstract and not useful for

everyday life, theoretical considerations are linked to everyday experience and

numerous demonstration experiments.

We address this book to undergraduate students in courses where physical chem-

istry is required in support but also to beginners inmainstreamcourses.Wehave aimed

to keep the needs of this audience always inmindwith regard to both the selection and

the representation of the materials. Only elementary mathematical knowledge is

necessary for understanding the basic ideas. If more sophisticated mathematical

tools are needed, detailed explanations are incorporated as background information

(characterized by a smaller font size and indentation). The book also presents all the

material required for introductory laboratory courses in physical chemistry.

Exercises are made available on the publisher’s web site. A student manual with

commented solutions is in preparation. Detailed descriptions of a selection of dem-

onstration experiments (partly with corresponding videos clips) can be found on our

web site (www.job-foundation.org; see teaching materials); the collection will be

continuously extended. Further information to the topics of quantum statistics and the

statistical approach to entropy, which would go beyond the scope of this book, can

also be called up on the foundation’s home page.

vi Preface

We would particularly like to thank Eduard J. Job{, the founder of the Job

Foundation, who always supported the goals of the foundation and the writing of

the current book, with great personal commitment. Because efficient application of

thermodynamics played an important role in his work as an internationally suc-

cessful entrepreneur in the field of fire prevention and protection, he was particu-

larly interested in a simplified approach to thermodynamics allowing for faster and

more successful learning.

We gratefully acknowledge the constant support and patience of the board of the

Job foundation. Additionally, we would like to thank the translators of the book,

Robin Fuchs and Prof. Hans U. Fuchs, for their excellent collaboration, and

Dr. Steffen Pauly and Beate Siek at Springer for their advice and assistance. Finally,

we would like to express our gratitude to colleagues who gave their advice on the

German edition and reviewed draft chapters of the English edition: Prof. Friedrich

Herrmann, Prof. Gunter Jakob Lauth, Prof. Friedhelm Radandt, and Dr. Uzodinma

Okoroanyanwu.

We would be very grateful for any contributions or suggestion for corrections by

the readers.

Hamburg, Germany Georg Job

Regina RufflerNovember 2014

Preface vii

ThiS is a FM Blank Page

List of Used Symbols

In the following, the more important of the used symbols are listed. The number

added in parentheses refers to the page where the quantity or term if necessary is

described in detail. Special characters as prefix (j, Δ, ΔR, Δs!l, . . .) were omitted

when ordering the symbols alphabetically.

Greek letters in alphabetical order:

Αα Ββ Γγ Δδ Εε Ζζ Ηη Θθϑ Iι Kκ Λλ Mμ Νv Ξξ Οo Ππ Ρρ Σσς Ττ Υυ Φφ ΧχΨψ Ωω.

Roman

A, B, C, . . . Substance A, B, C, . . .jA, jB, . . . Dissolved in A, in B, . . . (240)Ad Acid (188)

a, ja Amorphous (19) (also subscripted or superscripted)

Bs Base (188)

C Catalyst (462)

c, jc Crystalline (19) (also subscripted or superscripted)

d, jd Dissolved (19) (also subscripted or superscripted)

E Enzyme (466)

e, e� Electron(s) (7, 553) (also subscripted)

e Eutectic (367) (also subscripted or superscripted)

F Foreign substance (320)

g, jg Gaseous (19) (also subscripted or superscripted)

J Ion, unspecific (533)

l, jl Liquid (19) (also subscripted or superscripted)

M Mixture (homogeneous) (346)

M Mixture (heterogeneous) (348)

Me Metal, unspecific (533)

m, jm Metallic (conducting electrons) (553) (also subscripted or

superscripted)

Ox Oxidizing agent (537)

ix

P Products, unspecific (462)

p Proton(s) (187) (also subscripted)

Rd Reducing agent (537)

S Solvent (97), solution phase (535)

S Substrate (466)

s, js Solid (19) (also subscripted or superscripted)

w, jw Dissolved in water (20) (also subscripted or superscripted)

jα, jβ, jγ, . . . Different modifications of a substance (20)

□, B Adsorption site (“chemical”) empty, occupied (394)

Adsorption site (“physical”) empty, occupied (394)

‡ Transition complex (450) (also subscripted or superscripted)

Italic

A Area, cross section

A Helmholtz (free) energy (only used exceptionally) (595)

A (Chemical) drive, affinity (108)

A� Standard value of the chemical drive (109)

A○

Basic value of the chemical drive (159)

A�

Mass action term of the chemical drive (159)a Acceleration (32)

a Length of box (281)

a (First) van der Waals constant (299)

a Temperature conductivity (491)

a, aB Activity (of a substance B) (only used exceptionally) (604)

B Matter capacity (182)

Bp Buffer capacity (201)

B, Bi Substance in general (with subscript i) (25)b, bB Molality (of a substance B) (18)

b (Second) van der Waals constant (321)

b Matter capacity density (182)

b p Buffer capacity density (212)

C, Cp Heat capacity (global, isobaric) (254, 591)

Cm Heat capacity, molar (isobaric) (254)

CV Heat capacity (global, isochoric) (254, 587)

C;C p Entropy capacity (global, isobaric) (75)

Cm Entropy capacity, molar (isobaric) (75)

CV Entropy capacity (global, isochoriv) (77)

c Speed of light (13)

c, cB Molar concentration (of a substance B) (17)

c, cs Heat capacity, specific (isobaric) (254, 491)

cr Relative concentration c=c� (156)

cξ Density of conversion (163)

x List of Used Symbols

c� Standard concentration (1 kmol m–3) (103, 156)

c{ Arbitrary reference concentration (416)

c Entropy capacity, specific (isobaric) (76, 491)

D Spring stiffness (39)

D, DB Diffusion coefficient (of a substance B) (480)

d Thickness, diameter

E, E!

Electric field (strength) (500)

E Electrode potential, redox potential (558)

ΔE Reversible cell voltage (“zero-current cell voltage”) (568)

e0 Elementary charge, charge quantum (16)

F Force, momentum current (31, 45, 486)

F Faraday constant (504)

f, fB Fugacity (of a substance B) (only used exceptionally) (606)

G Weight (according to everyday language) (9)

G, GQ (Electric) conductance (494, 508)

G Gibbs (free) energy (only used exceptionally) (596)

G Arbitrary quantized quantity (15)

g Gravitational acceleration (46)

gi Content number of the ith basic substance (6)

g Quantum number (15)

H Enthalpy (only used exceptionally) (589)

h Height

h Planck’s constant (451)I (Electric) current (494)

J Current (of a substance-like quantity) (493)

JB Matter flux, current of amount of a substance B (479)

JS Entropy flux, entropy current (490)

j Current density (of a substance-like quantity) (493)

jB Flux density, current density (of matter) (478)

jS Entropy flux (or entropy current) density (490)

K○

Conventional equilibrium constant (167, 176)

K○

Numerical equilibrium constant, equilibrium number (166, 176)KM Michaelis constant (466)

k Rate coefficient (417)

k+1, k�1, . . . Rate coefficient for forward or backward reaction

(No. 1, etc.) (430)

kB Boltzmann constant (280)

k1 Frequency factor (444)

l Length

M Molar mass (16)

m Mass

N Number of particles (15)

NA Avogadro constant (15)

n Amount of substance (15)

List of Used Symbols xi

np Amount of protons (in a reservoir for protons) (203)

P Power

p Pressure (41)

p Probability (291, 307)

p Steric factor (449)

pint Internal pressure (298)

pr Relative pressure p=p� (171)

pσ Capillary pressure (387)

p� Standard pressure (100 kPa) (72, 103)

þ Momentum (44)

Q (Electric) charge (16)

Q Heat (only used exceptionally) (80)

q Fraction of collisions of particles having minimum energy

wmin (448)

R General gas constant (148, 277)

R, RQ (Electric) resistance (494)

R,R0,R00 Arbitrary reaction (28)

r, rAB, . . . Radius, distance from center, distance between two particles A and B

r Rate density (419)

r+1, r–1, . . . Rate density for forward or backward reaction (No. 1, etc.) (430)

rads, rdes Rate (density) of adsorption or desorption (395)

S Entropy (49)

ΔfusS Molar entropy of fusion (75, 312)

ΔRS Molar reaction entropy (232)

ΔvapS Molar entropy of vaporization (75, 309)

Δ!S (Molar) transformation entropy (234)

Sc Convectively (together with matter) exchanged entropy (65)

Se Exchanged entropy (convectively and/or conductively) (65)

Sg Generated entropy (65)

ΔS‘ Latent entropy (84)

Sm Entropy demand, molar entropy (71, 229)

St Transferred entropy (85)

Sλ Conductively (by conduction) exchanged entropy (65)

s Length of distance traveled

T (Thermodynamic, absolute) temperature (68)

T� Standard temperature (298.15 K) (71, 103)

T , T O Duration of conversion, observation period (404)

t, Δt Time, duration

t1/2 Half-life (420)

t, ti, t+, t– Transport number (of particles of type i, of cations, of anions) (517)U, U1!2 (Electric) voltage (from position 1 to position 2) (502)

U Internal energy (only used exceptionally) (582)

UDiff Diffusion (Galvani) voltage (548)

u, ui Electric mobility (of particles of type i) (503)V Volume

xii List of Used Symbols

ΔRV Molar reaction volume (228)

Δ!V (Molar) transformation volume (228)

Vm Volume demand, molar volume (220)

VW Co-volume (van der Waals volume) (298)

υ, υ!

Velocity (magnitude, vector)

υx, υy, υz Velocity, components in x, y, z direction (281)

W Energy (36)

W Work (only used exceptionally) (581)

WA Molar (Arrhenius) activation energy (581)

WA,W!A Energy expended for a change of surface or interface (385)

WB, Wi, . . . Abbreviation for W!nB, W!ni

, . . . (346)Wb Burnt energy (78)

We Energy transferred together with exchanged entropy (79)

Wf Free energy (only used exceptionally) (592)

Wkin Kinetic energy (43)

Wn, W!n Energy expended for a change of amount of substance (124)

Wpot Potential energy (46)

Wt Energy expended for transfer (of an amount of entropy,

of matter . . .) (85, 235)WS, W!S Energy expended for a change of entropy (“added + generated

heat”) (81)

WV, W!V Energy expended for a change of volume (“pressure–volume

work”) (81)

Wξ, W!ξ Energy expended for a change of conversion (236)

w, wB Mass fraction (of a substance B) (17)

w Energy of a particle (278, 287)

x, xB Mole fraction (of a substance B) (17)

x, y, z Spatial coordinates

ZAB Collision frequency between particles A and B (446)

z, zi, z+, z– Charge number (of a type i of particles, cations, anions) (16, 535)α, αB Temperature coefficient of the chemical potential (of a

substance B) (131)

α, αξ Degree of dissociation, degree of conversion (513, 163)

a Temperature coefficient of the drive (of a transformation of

substance) (131)

β, βB Pressure coefficient of the chemical potential

(of a substance B) (140)

β, βB Mass concentration (of a substance B) (17)

βr Relative pressure coefficient (271)

ß Pressure coefficient of the drive (of a transformation of substance)

(140)

γ Concentration coefficient of the chemical potential (154)

γ Cubic expansion coefficient (256)

γ Activity coefficient (only used exceptionally) (604)

η Efficiency (85)

η (Dynamic) viscosity (486)

List of Used Symbols xiii

Θ Degree of filling (degree of protonation, etc.), fractional coverage

(201, 396)

θ Contact angle (387)

ϑ Celsius temperature (70)

κ Dimension factor (167, 173)

ϑF Faraday temperature

Λ, Λi Molar conductivity, (molar) ionic conductivity of ions

of type i (519)λ Thermal conductivity (490)

λ, λ1, λ2, . . . Wave length, wave lengths of fundamental and harmonics (483)

λ, λB Chemical activity (of a substance B) (only used

exceptionally) (605)

μ, μB Chemical potential (of a substance B) (98)

μd Decapotential (abbreviation for RT ln10) (157)

μe, μe(Rd/Ox) Electron potential, of a redox pair Rd/Ox (529, 537)

μp, μp(Ad/Bs) Proton potential, of an acid–base pair Ad/Bs (191)

μ� Standard value of the chemical potential (103, 157)

μ○ Basic value of the chemical potential of a dissolved substance (156)

Δ‡ μ○ Activation threshold (451)

μ○c, μ

○p, μ

○x, . . . Basic value of the chemical potential in the c, p, x, . . . scale (340)

μ� Chemical potential of a substance in its pure state (345)

μ� Mass action term of the chemical potential (157)

μþ Extra potential (extra term of the chemical potential) (345)

eμ, eμi Electrochemical potential (of a substance i) (528)v, vB, vi, . . . Conversion number, stoichiometric coefficient (of a substance B or

i . . .) (26)v Kinematic viscosity (486)

ξ Extent of reaction (26)

ρ, ρB, ρi (Mass) density (of a substance B or i) (9)ρ, ρQ (Electric) resistivity (494, 509)

σ, σg,l, . . . Surface tension, interfacial tension (383, 387)

σ, σQ (Electric) conductivity (493, 509)

σB “Matter conductivity” (for a substance B) (527)

σS Entropy conductivity (490)

τ Elementary amount (of substance), quantum of amount

(of substance) (15, 16)

t1, t2, . . . Decay time of fundamental and harmonic waves, respectively (483)

τ‡ Lifetime of the transition complex (450)

ϕ Fugacity coefficient (only exceptionally used) (612)

φ Electric potential (90, 500)

φ Fluidity (494)

χ Compressibility (268)

ψ “Gravitational potential” (90)

ω, ωB Mechanical mobility (of a substance B) (476)

ω Conversion rate (407)

xiv List of Used Symbols

Subscript

ads Concerning adsorption (396)

c Critical (304)

d!d, dd Transition of a dissolved substance from one phase to another (181)

des Concerning desorption (395)

eq. In equilibrium (166)

g!d, gd Transition from gaseous to dissolved state (180)

l!g, lg Transition from liquid to gaseous state (boiling) (75, 228)

‘ Latent (84, 243)

m Molar

mix Mixing process (351)

osm Osmotic (325)

R Concerning a reaction (228)

r Relative (156)

s!d, sd Transition from solid to dissolved state (176, 228)

s!g, sg Transition from solid to gaseous state (sublimation) (137)

s!l, sl Transition from solid to liquid state (melting) (75, 228)

s!s, ss Transition in the solid state from one structural modification to another

(change of modification) (228)

use Useful (87, 240)

! Concerning a transformation (228)

□ Concerning an adsorption process (396)=0 Value interpolated to vanishingly lowconcentration (477) (also superscript)

+, � Concerning cations, anions (also superscript) (517)

Superscript

� Standard value (71, 103)

• Value for a substance in its pure state (329, 333)~ Characterizes a homogeneous or heterogeneous mixture of

intermediate composition, the “support point” by the application of the

“lever rule” (348)

*, **, . . . Characterizes different substances, phases, areas [e.g., the

surroundings (239)]

* Characterizes “transfer quantities” (492)0, 00, 000, . . . Characterizes different substances, phases, areas

List of Used Symbols xv

Character Above a Symbol

! Vector� Mean value� Derivative with respect to time○ Basic term, basic value (156)• Basic value of a quantity for a substance in its pure state (320)

� Quantity caused by mass action (154,157)+ Extra term, extra value (345)* Residual term, residual value (residual without basic term)

General Standard Values (Selection)

b� ¼ 1molkg�1 Standard value of molality

c� ¼ 1, 000molm�3 Standard value of concentration

p� ¼ 100, 000Pa Standard value of pressure

T� ¼ 298:15K Standard value of temperature

w� ¼ 1 Standard value of mass fraction

x� ¼ 1 Standard value of mole fraction

Physical Constants (Selection)

c¼ 2.998� 108 m s�1 Speed of light in vacuum

e0¼ 1.6022� 10–19 C Elementary charge, charge quantum

F ¼ 96, 485Cmol�1 Faraday constant

gn¼ 9.806 m s�2 Conventional standard value of gravitational

acceleration

h¼ 6.626� 10�34 J s Planck constant

kB¼ 1.3807� 10�23 J K�1 Boltzmann constant

NA¼ 6.022� 1023 mol–1 Avogadro constant

R¼ 8.314 G K–1 General gas constant

T0¼ 273.15 K Zero point of the Celsius scale

τ¼ 1.6605� 10�24 mol Elementary amount (of substance), quantum of

amount

xvi List of Used Symbols

Contents

1 Introduction and First Basic Concepts . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Matter Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Substances and Basic Substances . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Measurement and Metricization . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 Amount of Substance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.5 Homogeneous and Heterogeneous Mixtures, and Measures of

Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.6 Physical State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.7 Transformation of Substances . . . . . . . . . . . . . . . . . . . . . . . . . 25

2 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1 Introducing Energy Indirectly . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.2 Direct Metricization of Energy . . . . . . . . . . . . . . . . . . . . . . . . 33

2.3 Energy Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4 Energy of a Stretched Spring . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.5 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6 Energy of a Body in Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.7 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.8 Energy of a Raised Body . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

3 Entropy and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2 Macroscopic Properties of Entropy . . . . . . . . . . . . . . . . . . . . . 51

3.3 Molecular Kinetic Interpretation of Entropy . . . . . . . . . . . . . . . 54

3.4 Conservation and Generation of Entropy . . . . . . . . . . . . . . . . . 55

3.5 Effects of Increasing Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.6 Entropy Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.7 Direct Metricization of Entropy . . . . . . . . . . . . . . . . . . . . . . . . 65

3.8 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

3.9 Applying the Concept of Entropy . . . . . . . . . . . . . . . . . . . . . . 71

3.10 Temperature as “Thermal Tension” . . . . . . . . . . . . . . . . . . . . . 77

xvii

3.11 Energy for Generation or Addition of Entropy . . . . . . . . . . . . . 78

3.12 Determining Energy Calorimetrically . . . . . . . . . . . . . . . . . . . . 84

3.13 Heat Pumps and Heat Engines . . . . . . . . . . . . . . . . . . . . . . . . . 85

3.14 Entropy Generation in Entropy Conduction . . . . . . . . . . . . . . . 89

4 Chemical Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.2 Basic Characteristics of the Chemical Potential . . . . . . . . . . . . 96

4.3 Competition Between Substances . . . . . . . . . . . . . . . . . . . . . . 98

4.4 Reference State and Values of Chemical Potentials . . . . . . . . . . 100

4.5 Sign of the Chemical Potential . . . . . . . . . . . . . . . . . . . . . . . . 105

4.6 Applications in Chemistry and Concept of Chemical Drive . . . . 107

4.7 Direct Measurement of Chemical Drive . . . . . . . . . . . . . . . . . . 117

4.8 Indirect Metricization of Chemical Potential . . . . . . . . . . . . . . 122

5 Influence of Temperature and Pressure on Transformations . . . . . 129

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.2 Temperature Dependence of Chemical Potential and Drive . . . . 130

5.3 Pressure Dependence of Chemical Potential and Drive . . . . . . . 140

5.4 Simultaneous Temperature and Pressure Dependence . . . . . . . . 144

5.5 Behavior of Gases Under Pressure . . . . . . . . . . . . . . . . . . . . . . 148

6 Mass Action and Concentration Dependence of Chemical Potential . . . 153

6.1 The Concept of Mass Action . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.2 Concentration Dependence of Chemical Potential . . . . . . . . . . . 154

6.3 Concentration Dependence of Chemical Drive . . . . . . . . . . . . . 159

6.4 The Mass Action Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6.5 Special Versions of the Mass Action Equation . . . . . . . . . . . . . 171

6.6 Applications of the Mass Action Law . . . . . . . . . . . . . . . . . . . 172

6.7 Potential Diagrams of Dissolved Substances . . . . . . . . . . . . . . . 183

7 Consequences of Mass Action: Acid–Base Reactions . . . . . . . . . . . . 187

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

7.2 The Acid–Base Concept According to Brønsted and Lowry . . . 188

7.3 Proton Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

7.4 Level Equation and Protonation Equation . . . . . . . . . . . . . . . . . 201

7.5 Acid–Base Titrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

7.6 Buffers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

7.7 Acid–Base Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

8 Side Effects of Transformations of Substances . . . . . . . . . . . . . . . . 219

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

8.2 Volume Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

8.3 Changes of Volume Associated with Transformations . . . . . . . . 226

8.4 Entropy Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

8.5 Changes of Entropy Associated with Transformations . . . . . . . . 231

8.6 Energy Conversion in Transformations of Substances . . . . . . . . 234

8.7 Heat Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

8.8 Calorimetric Measurement of Chemical Drives . . . . . . . . . . . . 245

xviii Contents

9 Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

9.1 Main Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

9.2 Mechanical–Thermal Coupling . . . . . . . . . . . . . . . . . . . . . . . . 255

9.3 Coupling of Chemical Quantities . . . . . . . . . . . . . . . . . . . . . . . 258

9.4 Further Mechanical–Thermal Applications . . . . . . . . . . . . . . . . 266

10 Molecular-Kinetic View of Dilute Gases . . . . . . . . . . . . . . . . . . . . . 271

10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

10.2 General Gas Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

10.3 Molecular-Kinetic Interpretation of the General Gas Law . . . . . 276

10.4 Excitation Equation and Velocity Distribution . . . . . . . . . . . . . 283

10.5 Barometric Formula and Boltzmann Distribution . . . . . . . . . . . 292

11 Substances with Higher Density . . . . . . . . . . . . . . . . . . . . . . . . . . . 295

11.1 The van der Waals Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 295

11.2 Condensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

11.3 Critical Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

11.4 Boiling Pressure Curve (Vapor Pressure Curve) . . . . . . . . . . . . 303

11.5 Complete Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

12 Spreading of Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313

12.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

12.3 Indirect Mass Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

12.4 Osmosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

12.5 Lowering of Vapor Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 326

12.6 Lowering of Freezing Point and Raising of Boiling Point . . . . . 329

12.7 Colligative Properties and Determining Molar Mass . . . . . . . . . 332

13 Homogeneous and Heterogeneous Mixtures . . . . . . . . . . . . . . . . . . 335

13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

13.2 Chemical Potential in Homogeneous Mixtures . . . . . . . . . . . . . 338

13.3 Extra Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

13.4 Chemical Potential of Homogeneous and Heterogeneous

Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344

13.5 Mixing Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348

13.6 More Phase Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

14 Binary Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

14.1 Binary Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357

14.2 Liquid–Liquid Phase Diagrams (Miscibility Diagrams) . . . . . . . 358

14.3 Solid–Liquid Phase Diagrams (Melting Point Diagrams) . . . . . . 362

14.4 Liquid–Gaseous Phase Diagrams (Vapor Pressure and Boiling

Temperature Diagrams) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

Contents xix

15 Interfacial Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

15.1 Surface Tension, Surface Energy . . . . . . . . . . . . . . . . . . . . . . . 381

15.2 Surface Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

15.3 Adsorption on Liquid Surfaces . . . . . . . . . . . . . . . . . . . . . . . . 390

15.4 Adsorption on Solid Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . 392

15.5 Applying Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

16 Basic Principles of Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

16.2 Conversion Rate of a Chemical Reaction . . . . . . . . . . . . . . . . . 405

16.3 Rate Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

16.4 Measuring Rate Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

16.5 Rate Laws of Single-Step Reactions . . . . . . . . . . . . . . . . . . . . 413

17 Composite Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

17.2 Opposing Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

17.3 Parallel Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

17.4 Consecutive Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

18 Theory of Rate of Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439

18.1 Temperature Dependence of Reaction Rate . . . . . . . . . . . . . . . 439

18.2 Collision Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

18.3 Transition State Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

18.4 Molecular Interpretation of the Transition State . . . . . . . . . . . . 450

19 Catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455

19.2 How a Catalyst Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

19.3 Enzyme Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

19.4 Heterogeneous Catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467

20 Transport Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

20.1 Diffusion-Controlled Reactions . . . . . . . . . . . . . . . . . . . . . . . . 471

20.2 Rate of Spreading of Substances . . . . . . . . . . . . . . . . . . . . . . . 472

20.3 Fluidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

20.4 Entropy Conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

20.5 Comparative Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

21 Electrolyte Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

21.1 Electrolytic Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

21.2 Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

21.3 Ion Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

21.4 Conductivity of Electrolyte Solutions . . . . . . . . . . . . . . . . . . . . 503

21.5 Concentration Dependence of Conductivity . . . . . . . . . . . . . . . 507

21.6 Transport Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

21.7 Conductivity Measurement and Its Applications . . . . . . . . . . . . 518

xx Contents

22 Electrode Reactions and Galvani Potential Differences . . . . . . . . . . 521

22.1 Galvani Potential Difference and Electrochemical Potential . . . 522

22.2 Electron Potential in Metals and Contact Potential Difference . . . 524

22.3 Galvani Potential Difference Between Metal and Solution . . . . 527

22.4 Redox Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531

22.5 Galvani Potential Difference of Half-Cells . . . . . . . . . . . . . . . . 534

22.6 Galvani Potential Difference Across Liquid–Liquid Interfaces . . . 542

22.7 Galvani Potential Difference Across Membranes . . . . . . . . . . . 544

23 Redox Potentials and Galvanic Cells . . . . . . . . . . . . . . . . . . . . . . . . 549

23.1 Measuring Redox Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . 549

23.2 Cell Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

23.3 Technically Important Galvanic Cells . . . . . . . . . . . . . . . . . . . 565

23.4 Cell Voltage Measurement and Its Application . . . . . . . . . . . . . 570

24 Thermodynamic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573

24.2 Heat Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574

24.3 Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

24.4 Partial Molar Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

24.5 Activities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607

A.1 Foundations of Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607

A.1.1 Linear, Logarithmic, and Exponential Functions . . . . . . . . . . 607

A.1.2 Dealing with Differentials . . . . . . . . . . . . . . . . . . . . . . . . . . 610

A.1.3 Antiderivatives and Integration . . . . . . . . . . . . . . . . . . . . . . . 614

A.1.4 Short Detour into Statistics and Probability Calculation . . . . . . 619

A.2 Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621

A.2.1 Table of Chemical Potentials . . . . . . . . . . . . . . . . . . . . . . . . 621

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

Contents xxi