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thumbnail h e t c h w ed~ted yMARY VIRGINIA RNA,.S UCollege of NewRochelleNew Rochelle NY 10801The Third Law of Thermodynamics and theResidual Entropy of Ice:"Stillwater" or AS''~''~,T=~0

Maureen M. Julian

Frank H. StillingerBell LaboratoriesMurray Hill, NJ 07974Roger R. FestaSchool of Education U-33Universityof ConnecticutStorrs. CT 06268

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The authors have taken a liherty in the title of this article.Indeed , the residual entropy of water, although small, is notzero (8). In 1933, W. F. Giauque and M. F.Ashley a t Berkeley,California, (9) measured the residual entropy of ice. Their datacomhinedwith that of A. R. Gordon (10) gave an experimentalvalue of 0.87 entropy units (eu) which is 3.6 J K-'. Th e first

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major theoretical interpretation is due to Linus Pauling (11)in 1935. His calculations were based on t he interpre tation ofthe randomness of the hydrogen bonds in water. Indeed, manyof the unusual properties of water (12,131 are due to hydrogenbonding: (1) the negative volume of melting; (2) densitymaximum in the normal liauid ranee (at 4C): 131 isothermal. ., . . ~ ~compressibility minimum in the normal liquid range (at46'C): (41 at least nine crvstalline oolvmornhs: (51 hieh d i-. . . . . . , . . "electric constant; (6) anomalously high melting, boiling, andcritical temuera tures for a low-molecular-weight substanceH+ and OH- ions.

If Pauling's argument on residual entropy is to he under-stood, the structure of ice must also he considered. The ar-rangement of the oxygen atoms is known from X-ray dif-fraction (14 ,15). Each oxygen is tetrahedrally surrounded by

in ice: (2) the hvdroeen atoms are directed more closelv to twoof the four neaily teiradedra lly surrounded oxygen atoms; (3)the orientations of adjacent water molecules are such thatexactly one hydrogen atom lies 6n each oxygen-oxygen axis;(4) interactions hevond nearest neighbor interactions mav beneglected.From assumption 2, there are six possible tetrahedralconfigurations of HOH. Now consider the adjacent watermolecule. The probability th at one of the two more closelyhonded sites is occupied is '12, Since each oxygen in water hastwo associated hydrogens, the probability tha t both of the twomore closely bonded sites are occupied is Thus the totalnumber of configurations, W, for Avogadro's numher ofmolecules, N , is W = (6 X %)N= (3/2)N.Substituting in S =RIN In W for one mole, S = (RIN) = R l11(~/2),whichyields SO 0.805 eu (3.37 J K-I) where So is the entropy atabsolute zero.

In 1936, the year following Pauling's calculations, W. F.Giauaue and J. W. Stout (17) im ~r ov edheir calorimetricmeasurement and experimentally found So = 0.82 i .15 eu(3.4 f .6 J K-'1. Thus. the measured and theoretical values

estima te& incredibly accurate due to the fact that a-largenumber of closely lying quantum states are nearly equallypopulated. In 1964,E. A. DiMarzio and F. H. Stillinger (18)calculated that th e Pauling estimate was 1% oo low. Then in1966,J. F. Nagle (19) calculated SO= R In 1.5069 = 0.8151 eu(3.410J K-I). Both Pauling's and Nagle's values lie well withinthe 1936 exner imental limits. Paulinz's calculations are basedon the assumption that all ~ e r n a l- ~ i w l e rce structures havethe same enerev and therefore have eaual a orcon nrobahili-."ties. However, these structures a re not precisely equal in en-erev, hu t suread out over a band of states. Conseauentlv the

the'energy dispersion.A complicating experimental feature is that crystal im -perfections such as vacancies, dislocations, grain houndaries,and impurities would tend to increase So . Their influencewould have to he very carefully assessed. Perhaps this suggestsa series of So determinations on ice samples with differentformation conditions, such as freezing rate, impurity doping,and annealing.Th e last calorimetric measurements of th e entropy of icewere made in 1936. With new theoretical results t he issue isfar from closed. The time is now ripe for a modern experi-mental redetermination of the residual entropy of ice.Acknowledgment

The authors would like to thank Professor BeniaminWidom of Cornell.University for helpful conversatio& andfor his suapestion to MMJ and RRF of collaboration withFHS.Literature Cited(1) Tiernan,N.F., J. CrnM. EDUC. , in press.12) Lewis, G. N., and Randall, M. "Thermodynamics and the Free Energy af ChemicalSubstances? McGraw~Hill. ew York. 1923.(3 ) Nernst. W., Nachr . COPWim Coettingen. Klanno Math. Phys., p. i 11906).(4 ) Rickford, F. R., J. CHEM. EOUC.,59,817 (1982).(5) James. R. W., andFirth,E ..Pmc .Roy. o c London.Al17.62-87 (19271.(6 ) Mendeissohn, K., 'Th e Queat for Absolute Zero,)( McGiaw~Hil l , ew Vork, 1966.(7 ) Planck, M.,'Treatise on Thermodynamics,"3rd ed., trans.Ogg, Longmans,London,1948,p. 270.Eisenberg, D., and Ksurmann. W., "The s,ructure and Properties orwa ter.'University Press, New York. 1969,p. 102.Giauque, W. F.. and Ash1ey.M. F. ,Phys. R r o . , B , 8 1 (1933).Cnrdnn,A.R., J. Chem. Phys. ,2.65 (19%).Pnuling. L. , J, Amen Che m S o c , 57, 26r0 (19361.Stillinger. F. H . , Science, 209,451 (1980).Oma,M. V., J. CHE MEDUC.57.PIS l llX3O).Rragg, W. H.. Pror Roy. Soc.,34,98 (19221.Lonsdale, K . , P m c . Roy. So c London, A247,424 11958).Bernal, J. D., andFow1er.R. H . J . C h e m P h ys .. 1, h i 5 (19:131.~ i a u q u e ,W. F.. and st our,^. W . J . ~ r n whem s o c .& a , 14 4 (19361.DiM anio, E.A. , mdSti l1inger .F. H., J . C h rm Phys, 40 , 1577 11964).Nagle . J .F. , J Mat h . Phys ., ? , 1484-91 (1966).

MisconceptionsWhat misconceptions about science and chemistry do your students have? We all have some that plague us in ourteaching.From the field of physics, for example, it is commonly believed hy beginning students that rockets need somethingto "push" against, that satellites stay aloft because gravity is weak high above the earth, and that a dam's strength musthe in proportion to the size of the lake formed. Biology students believe that Balsa is a softwood.A post-doctoral researcherwa s recently heard to say that asolution whose pH = 2 is twice as acidica s one whose pH = 4! Equilibrium is oftenused when"steadv-state" is meant. or vice-versa.

I to anyone who wants them66 Journal of Chemical Education