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The Elements of Physical Chemistry With Applications in Biology _ Peter Atkins _ Cover design: Patsia MeDeemond CCatalosns-inpublstion dt is viable fom th Library of Cones, © 1905, 1997, amd 2001 by Pee skins Published ia the United Stats of America by W.H.Feeman and Company, 41 Maison Avenue, New York, NY. 10010 Published inthe United Kingda by Oxford Univssy res ‘No pat this Nook may he reproduced by any mechani, photographic, oF electron roves on he fo of pomp eon ora Ee ted i eel sm Printed in the United States of Americ ‘This ton hasbeen authorized by the Oxford Universi Pres fr sale ‘nthe USA and Canada nly al mot Zor export heer. Chapter 16 (NL AE RARE AER TPR 8S Molecular substances Contents ows and molecules with complete valence shells are stil able to interact with one anther: “They attract one anather over the range of several rome diameters and they repel one another when pressed together. These residual forces are highly important. They acccunt, fo instance, for the com. densation of gases to liquids and the structures of molecular solids. All etyanie liquids and soi ranging from small molecules lke benzene 10 vite ‘ually Infinite cellulose snd the polymers from hich fabri are made, are bound together by the forces cf cohesion we exporein this chapter. These ‘orcs are als responsible for the structural organi zation of blowgical macromolecules, fr they twist the log polypeptide chains of proteins into charac teristic shapes and then pin them together ia the arrangement essential to thee function, arcane The origins of cohesion ‘van der Waals force isan interaction between closed-shell molecules, The attractive contrib tions to these forces include the interactions be- ‘rween the parti electric charges of polar molecules and of polar functional groups in macro- ‘molecules, Van der Waal forces also inci the r= plsive interacians that prevent the complete collaase ofmattar to dnsites a high a thotechar- acteristic of atomic nuclei The repulsive interac. ‘ons arse from the exelision of elsctrons from re- sions of space where the orbitals of closed shell species overap. 16.1. Interactions between partial charges Atoms in molecules in general have partial charges “Table 16:1 gives che paral charges typically found in peptides. It these charges were separated by a ‘vacuum, they would atzact or repel each other in Accord with Coulomb's aw and we would write! fns.aa) where and a) are the partial charges and ris their Separation. However, itis more accurate to take into ecount the possibility that other parts ofthe molecule, or other molecules, ie Between the shanges, and decrease the strength ofthe sterae- tion Fig 16-1) We therefore write v= ey asap where cis the permittivity of die msedisua lying be ‘ween the charges. The permittivity is Usually ex pressed asa mulipe o the vacuum permitety by vwmting c= &, where fis the relative permittiv= ty? The eer of the medium can be very lage: for water, = 78, the petential energy of ta charges Table 16:1 Patil chorges in polypeptides Parl chargele 018 3 Distance, F Fig 16.1 the Coulomb potent fort charges ae ce: pendence onthe separa, the we eaves coment erntr2utv perites(Iforavacum, ora fd separated by bulk water i reduced by nearly rw or ders of magnitude compared to the valve f woule hove ifthe charges were separated by a vacium The problem is made worse in calculations oF polypeptices and aucleic acids) by the fac that te Dartial charges may have water and palypentde chain lying between them. Various models hare ‘been proposed fo take this awhward effect into ac ‘count, thesimples being to sete = 3:5 and to hope forthe best. 16.2 Electric dipole moments ‘When the molecules or groups that we ar const ering are widely separated, i€ turns out tobe sn pler to express the principal features of chair interaction in terms of the dipole moments assoc ated withthe charge distibutios rather than with each partial charge, Ae is simplest, an elect die ple consists of wo changes qin -q separated bya Alistance |The product ql sealed the electric d- ie ave peasy sl cd the one ‘pole moment, J. We represent dipole momen: by ‘anarovr with a lenath proportiona’ ta and point- ing fom the negative charge tothe positive charge (1)? Because a dipole moment is the produce of 4 charge in coulomb, Cand length in metres, ‘the Init of dipole moments the coulombmetre (Cin) However it soften mich more convenient two repor:adipole moment in debye, D, where 1p =3335 64x10" Cm ‘because the experimental values for molecules are then close to 1D (Table 16.2). The aipole moraeat lofeharges cand -eseparated by 100 pmis 1.610 ” Gm, comesponcing to 48D. Dipole moments of ‘spall molecules are typically smaller th that, at ge ‘A polar molecule is 2 molecule with a perma: nent electric dipole moment arising from the par tial charges on ite atoms (Section 4171. A nonpolar molecule is 4 molecule tha has no per rmanent electri dipole moment. A heteronuclear diatomic molecules are polar beesuse the difer ‘ence in clectronegativities of their tv atoms re sults i nonzero partial charges, Typical dipole moments are 1.08 D fer HCl 62 Dfor HU (Table 162). A very approximate relation between the pole moment and the ciference in Paling elec: Uwonegativities Table 24.) ofthe two atoms, 18 HD = ay usa) Mastration 16.1 ‘Theelectronegatvtes ofhydrogen and bromine are 121 ane 2.8 respec. The dference i 0.7, we {edletan eect dlpole moment of about 9.7 for Hes. Theexpeinentavaue 30.800. pec comentin 3 silly adopted "Brenan ter ee bye pee Table 16.2 Dipolemoments(ujandpolaizebilty volumes(2) 10m aa bap Because it atracts the electrons more strongly, the more electronegative atom is usualy the nega tive end of te dipole. However, there are excep- tons, particularly when antibonding ozbitals ate ‘occupied. Thus, the dipale moment of CO is very small (012 Dj but the negative end of the dipole is ‘onthe Catom eventhough the Oatom ismore elec ‘wonegative, This spparent paradox is resolved as soon as we realize tht antibonding orbitals are oc- ‘nied in C0 (se Fig 14.30), and, because electrons in antibonding orbitals tend tobe found closer to the lees electonegative arom, they contelbute negative pana chagge to that atom, If this conti Dution is larger than the opposite contribution from the electons in boading oxbitals, che net effect will be a sina neyative partial charge on Ue Tex electronegative atom. Figure 162 shows a 5 5 Fig 162 The computed cunpedsib.tovina CO males Netti, though ongenemarelecronegetve 0 ce bon trenegethveendefthe pce isoncaben ‘computed electron density disetbution in 80, and ‘he small euarge imbalance can be sen, Molecular symmetry is of the greatest impor tance in deciding whether a polyatomic molec is [Polar or not. indeed, molec symmetry is mare {mpertant than the question of whether or nat the atoms in the melecule belong ta the same element. Homonuclear polyatomic molecules maybe polar they have low symmetry and the atoms ate in i ‘equivalent positiors For instance, the angular mol- ecile ozone, 0; 2), is homonuclear; however ts polar because the centr O atom is different tom, ‘the outer tw fi is bonded fo neo atoms, they are ‘bonded only to onet marenver, the dipole moments associated with each bond make an angle fo each bother and do.a0tczneel Heteronuclear polyatomic ‘molecules may be nonpolar if they have high sy ‘metry, because individ Yond dipoles may the ‘ance. The heteronuclear linear tiaiomie mole ule CO,, for example, Is nonpolar Becase, ak ‘hough there are patil charges on all thee atoms, ‘he dipole momen: assecieted with the OC bond Poluts in the opposite dection to the dipole moment associated with the CO bond, andthe twocan- cel(3 _ 2 orone 3 carbon dose Selftest 16:1 Use the VSEPRmodelt judge whether lfsispolarar onpoa. (nt Predict hestructirefret) [hse ot ‘oa fest approximation, its possible to reso}ve ‘he dipole moment of z polyatemic molecule ito ‘contributions from various groups of atoms in the ‘molecule and the directions in which these individ- usleontibutions eg 163)-Thus pdichlerobenz ene is nonpolar by symmetry on account of the cancellation of two equal but epposing C-Cl mo- _ments (exactly asin carbon dioxide), oDichloroben- ‘zene has a dipole moment which is approximately the resultant of two chlorobenzene dipole mor ‘ments arranged a 0" to each ther. This technique of vector addition’ can be applied with fue success 9 ee cer @hige = 1570 ° =e (higge=220 (ipae= 160 480 Fig 163 “he dpole moment ofthe dlhbenzee bo ints ane etna! appoint by vector wee ‘wochlrobenanecipleremers(1 579). fis 4 tw other series of seated molecules, and the resul- {amt oftwo dipole moments andy, that make anangle 6to each other (4 isapproximately os = ai — nl + 2uycos 163) Abetterapproach tthe calculation of dipole mo- ‘ments isto take nto secon he oetions and mag niludes of the partial charges or. all the atoms, “These paral charges ate included in the aarp of ‘many molecular structure software packages. In- ‘eed, the programs calculate the dipole moments ‘ofthe molecules inthe manner we now deseribe. ‘THE ontcins oF cout Fig 64 the locations ofthe atoms piometres eave to te cane ofthe molec) andthe paral cages (a ral is of@ wed La calle Se pole momen oF > pepe 386 MOLECULAR sunsTANces 16.3 Interactions between dipoles ‘We calculate the pocential energy ofa dipole jain the presence ofa change: by taking into accoun: the interaction of the charge with the two partial ‘charges of the diple ee ao 1 aR 7 3 gt 8 a fg pose, the energy is lowest wher 8 180° {and cos #~~1), because then the patil negative ‘change ofthe dipole ies closer thaa the partial por: itive charge tothe poit charge and ce attraction outweighs the repulsion. This interaction energy creases more rapidly with distance than that be- ween two point changes (at P rather than #) be cause fom the viewpoint ofthe single charge the panial charges ofthe point dipole seem to merge And cancel asthe distance r increases, ‘We can calculate the interaction energy between ‘wodipoles and inthe orientation shown in(9} im a similar way, taking into cccount all four ‘ages f Ue two dipoles, The outcome is ayes S088) 6s) ‘This potential energy decreases even mare rapily ‘thanineqn 16 becmse the charges ofboth dipoles scam 10 merge a the separation of the dipois int creases. The angular factor takes into account how the like of opposite charges come closer to one an other as the telative orientation of the dipoles is changed, The energy is lowest when 8 - © or 180° (when 1 Seos* 9 = -2), because oppunite partial charges then lie closer together chan lke partial ‘charges. The potential energy Is negative [attrac tive} im some orientations when #547 {he angle at which 1 3 cos €= 0) because opposite changes se closer than like charges. Is postive (repulsive) ‘shen @> 54.7" because then lke charges ae closer ‘han unlike charges. he potential enengy is er0on the fine ac 54.7 (and at 180 ~ 54.7 = 1253")because at that angle the two attractions and the two repul Sons cance (10) OY 0 veo husteation 16.2 Tocaldate the molrpotental energy ofthe dipolar Interaction between two peptide links separated by 3.0.nm in diferent regions ofa polypeptide chain sth = 180" we take = 12 14D, corespording e710 Cm andiind = 14010 *cmx6-2) Fer gs Cm) x a0K mF 15610 ‘which caresponds 2-89} mo The average potential energy of interaction be ‘ween polat molecules that are freely zotating ina ‘uid fa g35 or liquid) is zero because the attractions and repuisionseance. However canes the poten til energy ofa dipole near another dipole depends fn their relative orinsatons, the molectles exert forces on each other and therefore de notin fat ro tate completely fey, oven in a gas. Asa result the lower energy orientations are marginally favoured, so there is a nonzero interaction between pola sivlecles (ig 165), The detailed calculation of the average Interaction energy Is quite complicate, but the ina answer is very simple: auth Ba4ney) Kar Te important features of this expression are the dependence of the average interaction enengy on the inverse sixth power ofthe separation end its i verse dependence onthe temperature. The temper aturedependence reflect the way thatthe gretter ‘thermal motion overcomes the mutval eertating effects ofthe dipoles at higher temperatures, 7 06.2) Mustration 16.3 ‘At 25 the average interaction ereray for pas of ‘moleculeswith1=1 Di about—1.44j mol ahenthe ‘Separation 030m. Thiseneray shuld be compared wth the average molar kinetic energy fF = 3.7 ‘Jmol atthe same temperature: the two are not ‘very sa, but they are both uch es than the fenergiesirvolved ia Ee making and breskng of emalbones, -@@ -@@ Fig 165 A docl-dpaleiteseton. When a pa of re ‘lesan ad alreatve rereationswthequl rbsbity ‘re fveurebe rkttons ) andthe narra ones (0) {acd an the argent ao saa ed. retmteacions (a sigh peaimiate 16.4 Induced dipole moments ‘A nonpolar molecule may acquire a temporary in- ‘duced dipole moment, i*, 38 result ofthe inf ence ofan electric fcld generated by aneatby ion ot polar molecule, The field distorts the electron dis tribution of che polarizable molecule and gives rise {oan electric dipole in ft. The magnitude ofthe i duced dipole moment is proportional 0 the strength ofthe field, ¥,and we wnte eat The proportionality constant as the polarizability ‘ofthe molecule. The larger the polarizability of the ‘molecule, the greater the distortion that is caused byagiven lectricfiel. Ifthe molecule has few eiee ‘ons, they are tightly controlled by the nuclear ‘charges and the polarizability of the molecule i low. Ifthe molecule contains lange atoms with eee trons some distance from the nucleus, che miclea controls ess andthe polarizability the moleene is greater The polarizability depends an the ovens tation of the molecule with rexpect fo the field un- less the melecule is tetrahedral (auch 3 CCL), cctahedral (euch 3¢ SE, or icosahedral (Cn, buck: rinsterfllerene Atoms, tetrahedral, octahedral, tnd iecsanedral molecules have iotiop rier tiomindependent) polarizabilities all ether mole cules Ive anisoupic.(erientationsepenent) polarizabilities. The polarzabilties reported in table 162 are sven a polarizability volumes,’ (ss) (69) ‘The polavizabiliy volume has the dimensions ef vole fhence is name) and is eomparsbe in 305 Iltude tothe volume of amolecule” Selftest 16.4 ‘hat strerath of electric fel required induce ectricdipole momentof1.0uD ina molecileof o- lareabity volume 1.110" (ike Cl? ose 2.76 en" A polar motscule with dipole moment uy can n> face 2 dipole moment in a polarizable molecule (which may itself be either pelar oF nonpolar) be «use the partial changes afte polar molecule give ‘se toa electric field that distorts the second mo ‘cule, Tht indueed dipote interes with the per ‘manent dipole ofthe fst molecule, andthe twoare attracted together (Fig 16.6, The formula for the {ipole-Induced-ipole interaction energy is aia, ‘where ois the polarzabilty of molecule 2. The ‘negative sign shows thatthe interaction iy attrac tive Fora molecule with y= 1 rich as 1G) neat molecule of polarizability volume w’ = 1.0% 10" 1m (such as benzene, Table 162) the average inter ‘action energy is about -35 mel "when te separ on is0.3nm. -@2 22 Fig 166 A dool-nduced-diplewterstion The ieeed ‘ple ight aro) fotows the changing eretaon ofthe ferraren ciple rks). v 610) When winger campitinsof ty ea o ‘ing Cee chil uno the aed ves een