Quanta, Matter and Change: A Molecular Approach to Physical Chemistry

806 Pages·2009·15.22 MB·English

by  Peter Atkins

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Quanta, Matter, and Change
A molecular approach to physical chemistry
Library of Congress Control Number: 2005936591
Quanta, Matter, and Change: A molecular approach to physical chemistry
© 2009 by Peter Atkins, Julio de Paula, and Ronald Friedman
All rights reserved
ISBN: 0-7167-6117-3
Published in the United States and Canada by W. H. Freeman and Company
This edition has been authorized by Oxford University Press for sale in the
United States and Canada only and not for export therefrom.
First printing 2009
Typeset by Graphicraft Ltd, Hong Kong
Printed and bound in China by C&C Offset Printing Co. Ltd
W. H. Freeman and Company
41 Madison Avenue
New York, NY 10010
www.whfreeman.com
Quanta, Matter,
and Change
A molecular approach to physical chemistry
Peter Atkins
Professor of Chemistry,
University of Oxford,
and Fellow of Lincoln College, Oxford
Julio de Paula
Professor and Dean of the College of Arts and Sciences,
Lewis and Clark College,
Portland, Oregon
Ronald Friedman
Professor and Chair of Chemistry,
Indiana University Purdue University Fort Wayne,
FortWayne, Indiana
W.H. Freeman and Company
New York
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
About the book
Our Physical Chemistryhas always started with thermodynamics, progressed on to quantum
mechanics, and then brought these two great rivers together by considering statistical
thermodynamics. We always took care to enrich the thermodynamics with molecular
understanding, and wrote the text so that it could be used flexibly to suit the pedagogical
inclinations of its users. There are many, though, who consider it more appropriate to build
an understanding of the subject from a firm foundation of quantum theory and then to
show how the concepts of thermodynamics emerge as the microscopic evolves into the
macroscopic. This text is directed at them.
We have taken the cloth of Physical Chemistry, unravelled it, and woven a new cloth that
begins from quantum theory, establishes the link with the macroscopic world by introduc-
ing statistical thermodynamics, and then showshow thermodynamics is used to describe
bulk properties of matter. But this is no mere reordering of topics. As we planned the book
and then progressed through its writing, we realized that we had to confront issues that
required fundamentally new approaches even to very familiar material. In fact, we experi-
enced a kind of intellectual liberation that comes from looking at a familiar subject from a
new perspective. Therefore, although readers will see material that has appeared throughout
the editions of Physical Chemistry, there is an abundance of new material, new approaches
to familiar topics, and—we hope—a refreshing new insight into the familiar.
The text is divided into five parts and preceded by a Fundamentalssection that reviews the
material that we presume is already familiar to readers at this level but about which their
memories might need a gentle prod. In Part 1, Quantum theory, we set out the foundations
of quantum mechanics in terms of its postulates and then show how these principles are
used to describe motion in one and more dimensions. We have acknowledged the present
surge of interest in nanoscience, and have built our presentation around these exciting
systems. In Part 2, Atoms molecules, and assemblies, we turn to the more traditional nano-
systems of chemistry and work progressively through the building blocks of chemistry,
ending with solids. We have paid particular attention to computational chemistry, which is,
of course, of great practical significance throughout chemistry. We have confronted head on
the sheer difficulty of presenting computational chemistry at this level by illustrating all the
major techniques by focusing on an almost trivially simple system. Our aim in this import-
ant chapter was to give a sense of reality to this potentially recondite subject: we develop
understanding and provide a launching platform for those who wish to specialize further.
Part 3, Molecular spectroscopy, brings together all the major spectroscopic techniques, build-
ing on the principles of quantum mechanics introduced in Part 1.
Part 4, Molecular thermodynamics, was for us the most challenging—and therefore the
most exciting—part to write, for here we had to make the awesome passage from the quan-
tum theory of microscopic systems to the thermodynamic properties of bulk matter. The
bridge is provided by that most extraordinary concept, the Boltzmann distribution. Once
that concept has been established, it can be used to develop an understanding of the central
thermodynamic properties of internal energy and entropy. We have trodden carefully
through this material, trying to maintain the sense that thermodynamics is a self-contained
subject dealing with phenomenological relations between properties but, at the same time,
showing the illumination that comes from a molecular perspective. We hope this sensitivity
to the subject is apparent and that the new insights that we ourselves have acquired in the
course of developing this material will be found to be interesting and informative. There are
parts of traditional thermodynamics (phase equilibria, among them), we have to admit, that
are not open to this kind of elucidation or at least would be made unduly complicated, and
vi ABOUT THE BOOK
we have not hesitated where our judgement persuaded us to set the molecular aside and
present the material from a more straightforward classical viewpoint.
In Part 5, Chemical dynamics, we turn to another main stream of physical chemistry, the
rates of reactions. Some of this material—the setting up of rate laws, for instance—can be
expressed in a purely traditional manner, but there are aspects of the dynamics of chemical
reactions that draw heavily on what has gone before.
The ‘Using the book’ section that follows gives details of the pedagogical apparatus in the
book, but there is one feature that is so important that it must be mentioned in this Preface.
The principal impediment to the ‘quantum first’ approach adopted by this text is the level of
mathematics required, or at least the perceivedlevel if not the actual level, for we have taken
great pains to step carefully through derivations. The actual level of mathematics needed to
understand the material is not great, but the thought that it exists can be daunting. To help
overcome this barrier to understanding we have included a series of Mathematical back-
groundfeatures between various chapters. These sections (there are eight) give background
support to the mathematics that has been used in the preceding chapter and which will be
drawn on in later chapters. We are aware that many chemists prefer the concrete to the
abstract, and have illustrated the material with numerous examples.
We hope that you will enjoy using the book as much as we have enjoyed—and learned
from—writing it and will appreciate that we have aimed to produce a book that illuminates
physical chemistry from a new direction.
PWA
JdeP
RSF
Using the book
We have paid attention to the needs of the student, and have provided a lot of
pedagogical features to make the learning process more enjoyable and effective. This
section reviews these features. Paramount among them, though, is something that
pervades the entire text: we have tried throughout to interpret the mathematical
expressions, for mathematics is a language, and it is crucially important to be able to
recognize what it is seeking to convey. We have paid particular attention to the level
at which we introduce information, the possibility of progressively deepening one’s
understanding, and providing background information to support the development
in the text. We have also been very alert to the demands associated with problem
solving, and have provided a variety of helpful procedures.
Organizing the information
Checklist of key ideas Notes on good practice
We have summarized the principal concepts introduced in each Science is a precise activity and its language should be used
chapter as a checklist at the end of the chapter. We suggest accurately. We have used this feature to help encourage the use of
checking off the box that precedes each entry when you feel the language and procedures of science in conformity to inter-
confident about the topic. national practice (as specified by IUPAC, the International
Union of Pure and Applied Chemistry) and to help avoid com-
Checklist of key ideas mon mistakes.
1.A van der Waals interaction between closed-shell molecules 8.A hydrogen bond is an interacti
isse pinavreartisoenly. proportional to the sixth power of their 9.Twhhee rLee Ann aanrdd -BJo anree sN (1, O2,6, o) rp Fo.ten 1S0e.l2f- tfeosrt d 1e0t.a4ilsR).epeat the problem for C35ClH3(see Self-test
2.The permittivity is the quantity εin the Coulomb potential is a model of the total intermole [Lines of separation 0.944 cm−1(28.3 GHz)]
energy, V=Q1Q2/4πεr. 10.In real gases, molecular interact
3.A polar molecule is a molecule with a permanent electric state; the true equation of state i
4.Tidpbtsoeirhp potμeword 1opleuμepoec 2mnot/ter r otno3twfimta oitonahne ldfiean e lxttpnh;te aoetdarhrt μtg( eibyna2 meμ loo tc2nwaf/h g-ktearhnTeroeingrtt 6deua m tidaipnoneo lgdoel)e fct – mhuad eldoei pssilpee otpcohluealae rltie an mastt irieooesrm n apfr.creetoneipo tt nooisr rttoihotenatael 11.Tctrbheoyhpee ea rffit evrpsucaaeineren a nedtmqetesdure B atbWet,y irCo a abna, :pl. spoa. efr=. qa:s tmnupaRatVeteTtim eoi/nr(n= V a woRa−hfT nsi aadrmb essayeoss restbees nmebdsy e i b s1a y.cs o atn hmese osrplveiecndu o.l eIf,f t tthhheee angular Aetrthrom anetnai osststsitieoiato itnooneanns la s giqn,n oudt oha sXdnoe mtp←uurpema pYcw ent iiracus y esma tn(abFs tuaeeobr cri sh Jsto, h wraaepssr tdiwbitiotyesenc nhgu, a iwsfivvsihrienos edtgnr.o e toS nhXofee s a aXpvnbe ado→cl uvtYreeo Y) ss.op cifeos c tpiahfinyec
Impact sections
Where appropriate, we have separated the principles from their Justifications
applications: the principles are constant; the applications come
On first reading it might be sufficient simply to appreciate the
and go as the subject progresses. The Impact sections show
‘bottom line’ rather than work through detailed development of
how the principles developed in the chapter are currently being
a mathematical expression. However, mathematical development
applied in a variety of modern contexts, especially biology and
is an intrinsic part of physical chemistry, and to achieve full
materials science.
IMPACT ON BIOCHEMISTRY ward: we simply replaceg the upper lim Fraotrio h iysd 1r:o2g.en, I=–12, and the ratio is 3:1. For N2, with I=1, the
The hyId13ro.1geTnh beo hnedlsi xb–ectwoiel etnra anmsiitnioon a cinid ps oolfy ap eppotlyidpeesptide give qq =∑nC(n,i)si Justification 10.1The effect of nuclear statistics on rotational
rise to stable helical or sheet structures, which may collapse into 0 i=0 spectra
a random coil when certain conditions are changed. The un- A cooperative transformation is
winding of a helix into a random coil is a cooperative transition, modate, and depends on building a Hspyind roqgueann tunmuc leniu mareb efre;r mini othnes ir( pcaarsteic lIes= w–1i)t,h soh atlfh-ein Pteaguelri
in which the polymer becomes increasingly more susceptible to facilitate each other’s conformational principle requires the overall wavefunction2 to change sign
sat rmuoctduerla bl cahseadn goens othnec ep trhine cpirpolecse sosf h satsa btiesgtiucanl. Wtheer emxaomdyinnea mheirces mceondt etlo, cthoen voenres iuonnd ferrogmoi nhgt oth ce icso anllvo umnodleecr uplea rtthicrloeu ignhte 1rc8h0a°nhgaes. Ha omwoervee rc,o tmhep lricoatatetdio neff oefc ta nth Han2
that accounts for the cooperativity of the helix–coil transition in Thus, the zipper model allows a tran merely relabelling the nuclei, because it interchanges their
polypeptides. ...→...hhhcc..., but not a trans spin states too if the nuclear spins are paired (↑ ↓) but not if
To calculate the fraction of polypeptide molecules present as ...→...hchch....The only except otational wavefunctions (shown they are parallel (↑ ↑).
helix or coil we need to set up the partition function for the vari- the very first conversion from hto dimensional rotor) under a rotation For the overall wavefunction of the molecule to change
swithJevendonotchangesign;
viii USING THE BOOK
understanding it is important to see how a particular expression Synoptic tables and the Resource section
is obtained. The Justifications let you adjust the level of detail
Long tables of data are helpful for assembling and solving exer-
that you require to your current needs, and make it easier to
cises and problems, but can break up the flow of the text. The
review material.
Resource section at the end of the text consists of a Data section
with a lot of useful numerical information and a collection of
interActivities
other useful tables. Short extracts in the Synoptic tables in the
You will find that many of the graphs in the text have an text itself give an idea of the typical values of the physical quan-
interActivity attached: this is a suggestion about how you can tities we are introducing.
use the on-line-resources of the book’s website to explore the
consequences of changing various parameters or of carrying Part 1 Data section
out a more elaborate investigation related to the material in the
illustration. Physical properties of selected materials
r/(g cm−3) Tf/K Tb/K r/(g cm−3) T
at 293K† at 293K†
Elements Inorganic compounds
Aluminium(s) 2.698 933.5 2740 CaCO3(s, calcite) 2.71 1
Intensity,I Intensity,I ABBCorraogrrboomonnin((ngs(e))s(,l )gr) 2123....233168420103 3275208760353s..89 393833711..39 CHHHuBCI(SrlgO(()gg4))·5H2O(s) 2212....7182785874
Carbon(s, d) 3.513 H2O(l) 0.997
Chlorine(g) 1.507 172.2 239.2 D2O(l) 1.104
0 1 (cid:9)~2p 3 4 0 1 (cid:9)~2p Copper(s) 8.960 1357 2840 NH3(g) 0.817
Fluorine(g) 1.108 53.5 85.0 KBr(s) 2.750 1
Fig. 10.25An interferogram produced as the path lengthpis Fig. 10.26An interferogram obtained Gold(s) 19.320 1338 3080 KCl(s) 1.984 1
changed in the interferometer shown in Fig. 10.24. Only a single three) frequencies are present in the r Helium(g) 0.125 4.22 NaCl(s) 2.165 1
fpinrleotqetnu osefin ttych yoe cff outhmnecp trioaodnnie anIt(tipo i)sn =p.rIe0(s1en +t cino st h2eπ #sipg)n, awl,h seor eth Ie0 gisr athpeh is a replaceimdnt obernyA oacc tsihvurimtoym oFavoteirrc a tb hseieag mfinnasli, t cteoh nneu siinms HIIoroyddninr(ose)(gse)n(g) 074...089773140 183108486..07 304225037..35 OHr2SgOan4i(cl )compounds 1.841
iinnt efirnAictteiv ditiystaRnecfeer irnincrge tmo eFnigts. ,1 s0o. 2th4,e tphaet mh dirirffoerr eMn1cem poves tghoi so inn tfoo remxpaltoiorne tthoe d erffaewc ty oouf vr aorwyinn gv e Krypton(g) 2.413 116.6 120.8 Acetaldehyde, CH3CHO(l) 0.788
is also incremented in finite steps. Explore the effect of intensities of the three components o Lead(s) 11.350 600.6 2013 Acetic acid, CH3COOH(l) 1.049
increasing the step size on the shape of the interferogram for a of the interferogram.
dmroawno pclhortos mofa It(icp )b/eI0amag aoifn wsta #vpen, euamchb ewri #tha an dd iiffnetreennstit ny uI0m. Tbehra ot fis,
dmaotav apbolien mts isrproanr nMin1.g the same total distance path taken by the cwahrerireed I(o0u)t isn ugimveenri cbayl leyqinn 1a0c.2o3m wpiu Mathematics support
A brief comment
Further information A topic often needs to draw on a mathematical procedure or a
concept of physics;A brief commentis a quick reminder of the
In some cases, we have judged that a derivation is too long, too
procedure or concept.
detailed, or too different in level for it to be included in the text.
In these cases, the derivations will be found less obtrusively at
the end of the chapter. A brief commentA symmetry operation is an action (such
as a rotation, reflection, or inversion) that leaves an object
looking the same after it has been carried out. There is a
corresponding symmetry elementfor each symmetry opera-
Further information 13.2The partition functions of polyatomic rotors Now we assume that the temperature is so
tion, which is the point, line, or plane with respect to which
occupied and that the sums may be appro
The energies of a symmetric rotor are the symmetry operation is performed. For instance, an n-fold
wofi tchEo JnJ,Ks=,iMd0Je,= r1ih,n 2cgè, t.Jh(.eJ.s+e,K 1ra)= n+gJh,e Jsc,(− éw1e−, c.èa.)n.K ,c 2−ovJ,e arn thde M saJm=eJ, vJa−lu1e,s. b.y. a, l−loJ.w Iinnsgte Kad q=(cid:2)−∞∞e−{hc(é−è)/kT}K2(cid:2)|∞K|(2J+1)e−hcè nhssi ltdaheteido e (nnbstu i(rtne no cotr try esnflteaeclc eststisroaunrcistl,yu rroet actaino nbse, rstiyoomtnamt itoehntrroy(ut(hgtehh e s 3ycm6o0rm°r/enestp.r oyS neodep ineCrgha tsaiypomtnem)r ae7bt rofyou ert leaamn m enno-tfr)oe li dsd aea txraioislt eaod-f
to range from −∞to ∞, with Jconfined to |K|, |K|+1,..., ∞for each As before, the integral over Jcan be recog discussion of symmetry.
fctvohaalenld urq beed = eaoe rgwf∑Je e∞K=r n20itJe(Kt∑Fre+=aJin−gt1 Je.e M.v1q Ia∑3JutlJ=. uif2−voee3Jals−)ll eoE.o nJBwf,K teM,slMcy tJaJ h/aukfasTostre t ehthaece ph ea nvraetilrtugieoy nois ff iuJn,n decaetcpiohen nvdaelunet ooff JMisJ ,( a2nJd+1)- der (cid:2)iv|∞aKt|(iv2eJ o+f 1a) efu−hncècJt(iJo+n1),/ kwThdJic h== (cid:2)i⎛⎝⎜⎜s− |∞tKhh|k⎛⎝⎜⎜ecT −èfu⎞⎠⎟⎟hknceTcè−
q=K∑=∞−∞J∑=∞|K(|2J+1)e−EJ,K,MJ/kT =⎛⎝⎜⎜hkcTè⎞⎠⎟⎟e−h
=K∑∑=∞−∞J∑=∞|K(|2J+1)e−hc{èJ(J+1)+(é−è)K2}/kT (13.59) ≈⎛⎝⎜⎜hkcTè⎞⎠⎟⎟e−hc