of Exposed Atoms Ronald L. ~ i c h ' , ~ Bethel College, North Newton, KS, and Department of Chemical Engineering, North Carolina State University, Raleigh, NC

Boiling points for a n unprecedented variety of sub- stances can herewith he predicted by a method that is practical even for species with few or no measured proper- ties. The method is in agreement with this principle from theory: The London forces between molecules and the re- fraction of light both depend on polarizability and thus mainly on the outer electrons of atoms. The London forces on molecular surfaces, however, should not reflect the ef- fects of sufficiently well shielded internal atoms, and we use an objective geometric criterion to exclude them. Addi- tion of the molar refractions (or atomic polarizabilities) of the other atoms, with an adjustment for electronegativity differences, gives the effective total refraction.

We aim for great generality but emphasize inorganic substances a t present. Boiling points are calculated from a proportionality to the 314 power of the total refractions, with a standard deviation of <4%, up to a t least 800 K. This article is only a brief summary, however, of a study re- cently published in Japan (I).

The old idea of a connection between boihng points and me- lar mass per se still appears in recent writing (2), especially on organic chemistry (3, 4) and chemical education (5-7). However, this connection was disproved long ago (8,9).

We have long had purely empirical predictors of boiling points, especially for certain classes of organic compounds (10-12). The limitations have been

1. application to few types of substances 2. the absence of a reasanahle relation to other properties 3. the implied prediction of negative, imaginav, or complex

absolute boiling points or the absence of any prediction at the bottam of the scale

4. the need for a large number, up to 80 in K+ney9s well- known approach (121, of empirical constants

Many earlier and recent workers (13-17) have shown how to use topological properties to predict some physical characteristics, but limitations 1 and 2 seem self-evident. Concerning the third, i t was well-stated, app,arently with no irony intended, that "There should be no absurdities in the limit of large or small molecules" (13). Some topological indices, however, cannot be applied to CH4 or even up to C4Hla. Granted, we already know their boiling points, but the lack of any basic distinction between these compounds and the other saturated hydrocarbons, plus the arbitrary structures of some of the indices, indicate the inadequacy of topology for real understanding. We should not be sur- prised if topology, whose whole nature is nonmetric, a t least needs supplementing in chemistry by such considera- tions as the sizes of atoms. Accuracy can be improved by restricting scope, as with an analysis of alkyl halides (18), which, in any case, is not directed toward predictions.

'Now at 112 S. Spring St., Bluffton. OH 45817-1112. 2Pallly presented at the 10th Biennial Conference Chemical Edu-

cation. Purdue University, August 1988.

The Present Correlation and the Criteria for Exclusion and Inclusion

The theoretical reason for expecting boiling points to be correlated with refractions was mentioned above. One of the empirical aspects of the present study is the appear- ance of this correlation as a direct proportion between the boiling points and the 314 power of the total, for the ex- posed atoms, of the molar electric polarizability or optical refraction. Equation 1 is the correlation (in dimensionless form) used for actual predictions, as in the figure, which shows 212 substances, which are not all numbered.

where T. is the estimated boiling point, and To (below) in- dicates the observed values. Rt is the total molar refraction for the exposed atoms, including the effect of electronega- tivity differences, as given in eq 2.

Statistical treatment with the SAS package for non- linear relationships shows the factor fr, for conversion to the boiling temperature, to be 31.8 for all substances ex- cept the halogens and organometallics. The exponent p is likewise found to be 0.75 and is now taken as exactly 314 for reasons not discussed here. Tahle 1 lists the major con- stants derived from this study, with standard uncertain- ties. These best, current values differ slightly from those used for the calculations summarized in Tahle 2.

For the statistical analysis and handling of errors we correlate In (To) with In (RJ and define the relative error as

~ s l n h To

which is intermediate between (T. - TJIT. and (T. - TJIT.. . .. " . " . This avoids limiting either the positive or negative error to 100% while the other is unlimited. (The decimal value in El% is sometimes unjustified but always included for con- sistency in presentation.)

Table 1. Some Constants and Statistical Results -

Variable Value Applicability

P 314 all f, 0.0886 f 0.0049 all

fr 31.82f 0.18 general fr 39.17 f 0.54 halogens f r 34.56 f 0.37 organometallics b m d y 2.877 f 0.039 aromatics EM 0 shielded e.4 1 exposed EM 1R htermediate

organometallic EM 0.302 i 0.035 intermediate

transitional The unity. crn31rnal.

Volume 72 Number 1 January 1995 9

A strict dichotomy between exposed and shielded atoms wouldbe insupport able. Some must be intermediate and have a fractional exposure of their cen- tral atoms M ( I ) .

Classes Excluded

We could simply exclude all poten- tially polar substances (those of low molecular symmetry) but have chosen to include those with low polarities. Dipole moments, k, of a given magni- tude must be less important for larger molecules (those with larger Rt's), and we exclude those for which

> 0.05(Rt mol/cm3)~

where the D stands for debye (D 1 10- 1sFrcmorD=3.3x1030Cm)andthe Fr for franklin (Fr = 3.3 x 10-lo C). Di- pole moments below this threshold are found to be too small to invalidate our method. No separate treatment of hydrogen bonding is required here. H20 is listed (entry no. 12) as one ex- ample of the excluded substances.

The low boiling points of the silicon halides have often been noted and ex- plained in various ways (I). There are other disturbing factors, such as the quantum influence in helium, but they also will not be examined in this summary.

Predictions Table 2 shows a few of the boiling

points that are predicted here (identi- fied by a raised p) but not known to be confirmed a t this writing; some of these would be accessible only by the extrapolation of vapor pressures from lower temperatures. (Predictions can of course also be used to estimate va- por pressures.) Several values not known at the beginning of this study have since been confirmed.

Refraction

The values we use for molar refrac- tion R are mostly by Batsanov (19) and, for electronegativity x, by Allred et al. (20, 21). These sources are val- ued especially for completeness.

Electronegativity

Our correction is in eq 2.

Rt = R&l + f,(Ad2) (2)

where R, is the sum of elemental mo- lar refractions, excluding any shielded elements; f , is the electronegativity factor, 0.089, and the adjustment for this i s included even when M i s shielded.

Table 2. Boillng Points

No. MSj RdY Ax TdK TdK El%

Main Groups, Shielded

1 CF4 6.40 1.60 145 149 2.4

2 IF-, 11.20 1.89 248 239 -3.7

3 SnFio 16.00 1.66 302 300 -0.8

4 SbCis 26.55 1.01 413 420 1.6

5 c3ci8 45.68 0.33 543 565 3.9

6 BBr3 24.27 0.73 363 360 4 . 8

7 Sni4 50.68 0.49 621 616 4 . 8

Main-Groups, Intermediate

6 CH4 5.83 0.40 112 120 7.0

9 C4Hio 17.20 0.40 273 271 4 . 5

Main Groups, Exposed, General

10 Ar 4.00 87 89 2.2 11 AszH4 24.68 0.10 373 353 -5.7 12 H z 0 4.03 1.40 373 101 -130.3' 13 Hi 13.69 0.11 238 226 -5.0 14 N2F4 10.80 1.03 200 202 1 .O 15 P4S3 57.20 0.38 680 671 -1.4

Halogens

16 F2 3.20 85 93 8.9 17 12 25.34 458 444 3 . 1 16 BrCi 13.80 0.09 278 281 0.9

Aromatics (Exposed) Name

19 c s ~ s 23.31 0.40 353 341 -3.5 benzene 20 Ci8Hiz 63.81 0.40 721 729 1.1 chrysene 21 C22H14 77.31 0.40 793 843 6.1 picene 22 Cso 171 .90 1 524P buckminsterfullerene 23 C9H8 33.16 0.40 455 445 -2.1 indene 24 C4H4S 23.14 0.40 357 339 -5.2 thiophene

Substjtuted Benzenes Substituent(s)

25 CsH5Ci 28.00 0.73 405 401 -0.9 chloro 26 CsHsC2H3 31.08 0.40 418 424 1.3 vinyl 27 CsH3(N02)3 45.57 1.40 63ZP 1,3,btrinitro 28 CsHsCsHs 44.58 0.40 529 556 5.0 phenyi

Main-Group Organometallics

Exposed

29 ZnMen 18.52 0.84 319 323 1.2

30 TeMen 22.62 0.49 360 364 1.2

intermediate

31 PMe3 18.56 0.44 314 313 -0.4

32 AszMe4 29.12 0.40 438 439 0.1

Shielded

33 BMe3 14.43 0.49 253 260 2.5

34 WMes 28.86 1.10 466P

e: excluded. p: predicted but not confined.

Suwev of Classes

straightforward, will be shown in e&h subseque& section. - Table 2 includes a few representative halides of main- Te - = f(~.(l+ fr(~)2)mol/cm3 P group elements, Mixj, whose central atoms Mare shielded. K (3) We have, then, simply

10 Journal of Chemical Education

Table 2. Continued

No. Mi3 Rdy Ax TdK TdK EISb

Shielded Tlansition-Element Compounds

Halides

35 UFs 13.31 2.88 330 336 1.7 36 Tic14 26.02 1.51 409 422 3.0 37 TaBrs 43.67 1.41 593 613 3.3 38 Zrla 54.81 0.99 704 685 -2.7

rr Bonded

39 Ni(C0)4 16.28 1.75 316 309 -2.3 40a CoCpd 19.42 0.80 CoCpd(CO)z, part a 40b Co(C0)z 8.14 1.80 CoCpd(C0)2, part b 40 CoCpd(C0)2 30.99 - 414 418 1.2 41 FeCpdz 38.85 0.86 522 521 4 . 3 42 WCpdzHz 40.89 1.10 557P

p: predicted but not confirmed.

R, = jRx

The relative error, in the last wlumn, is based on the un- rounded T. and To. Most values ofR, and Az are obtainedvery easily Ib facilitate checking, however, we l is t them here. Boil- i ng points have been taken h m wuntless sources.

Intermediate Main-Group Compounds

Where Mix, = C;H, we calculate

R, = eciRc + jRR

The carbon in C H I and certain derivatives i s found geo- metrical ly (1 ) to be 84.1% exposed, so the exposure factor, eM or ec, i s 0.841.

Exposed Main-Group Substances-General

Here we clearly have

R,(MjXJ = XM + jRx

The "extrapolated bp o f about 100"" reported (22) for en- try no. 11, &HI, was found too late for the general statis-

- 8 ,- Natural log of the observed boiling temperature, TO, vs. natural log of the total exposed refraction, Rt. Left-hand part, using upper abscissa: halooens. oroanometallics. and excluded substances. Rioht-hand oart. usina lower abscissa: others. Rioht-hand ordinate: antiioo of the left. no d spacemeni Upper ine calca for naiogens Secono ink organomela lcs" ~h rd an0 foAh nes (~dehcal 01.1 wltn !he founh sp aced non. zontally to avom crowd ng) others Tne lo1 ow ng symbols and nLmy ca cooes are for the examples Symbols in squares represent exclus~ons for reasons discussed in the text and elsewhere (1). The unity- cmJ/mol

Symbol key €4 30, HnO; 31, Hg; 32, Ns; 33, CO: 34, NO; 35,Os: 36. PHa: 72, SeFs: 73, C&; 74, CFsSFs; 75. SbHa:

+: 1. BMea (Me =CHnl; 2, SMe.; 3, &Men; 4, SbaMer. N o 37, C01: 38, Cdb: 39, BFs: 40, C a d : 41, 76. Ge2Ha: 77, C.&S, thiophene; 76, PCh 79. W: 5, PbMu: 8. AlrMes; 7, SnlEta. AsFs; 43, CsNs; 43, CIFa; 44, XeR; 45, OsOd; 46,

PtFa; 47, CaHsF;46, CsHsN, ~Mdine: 49,AIxCh Ru(C0b: 80, CoCpd(C0h (Cpd r eydopentadi-

A: 10, F2; 11. CI2: l2,BrCI: 13, Bn: 14,ICI: 15, IBr; 18, 50, P,. enyl): 81, CBu; Be, CsFal: 89, Si1Brs; 84, WCla; 18. x:80,Ar;61.O2;82.Oh;68.CH~;64,KT;BS.CF~;66, 86,~CsHdNOsh: 86, GeL; 87, Sa; 66,AsL4; 88,

.: 17, CLF, 18. BrF: 19, CkO. NFa; 67. S-4; 68, Xe; 69, CIIk 70. Baa; 71, CpHx. picene.

Volume 72 Number 1 Janualy 1995 1

tical work but does fit the prediction. (The second signifi- cant figure in E is unjustified but included for consistency.)

Aromatics (Exposed)

In these cases we may have more than two elements in MiXjYk (i.e., CiHjYJ, so

R. = iRM + jRx + kRy

Rc has the aromatic value, as given in Table 1. These hy- drocarbons mostly fit better usingour calculated, rather than the measured, refractions. In general, the calculated values in this work benefit &om the use of atomic refractions, some of which are derived from various measurements whose er- mrs may cancel. Of wurse boiling points are also subject to error but not to such a great degree.

We estimate an upper limit of 1.5 kKfor the (extrapolated) boiling point of fully exposed Cm, entry no. 22, even though it is well outside the coniirmed range for our correlation. The molecules' roundness must reduce contact among them and must lower the resultant boiling point. This limit agrees crudely with the report of sublimation at about 600 "C and an enthalpy of sublimation of 39 k d m o l or higher (23). Agood boiling point for Cm should enable estimates for the other fullerenes, including the endohedral compounds.

Main-Group Oganometallics

Many of the central atoms in the compounds retain un- shared pairs of outer electrons and thus have a less sym- metrical structure than that assumed by our geometric mi- terion for shielding. We get good results, quite reasonably, by assuming exposure for MX2, intermediate status for

and MA, and shielding for (or higher) and M 2 X s , unless proved otherwise ( I ) , as with the complete shielding found for the small B atom in BMe3.

Here then we take

R. = eMiRM + jRx + kRy

where e M is 1 for the exposed compounds, and 0 for the shielded ones; l/2 is the assigned value for the intermedi- ate compounds. The success of this simple approach in the intermediate group may seem surprising at first for py- ramidal molecules like PMea which, however, are exposed on one side but shielded on the other.

Shielded Transition-Element Compounds

While the central atoms in silicon halides add less than expected to, or subtract from, the calculated effect of the outer atoms in determining boiling points, the transition- element halides show the opposite effect. Even though shielded, the central atoms appear to project a fraction of their influence (through their d orbitals?) to the outside world. Therefore we again need the factor eM, which is found to be 0.30, to calculate R. as above.

For entry no. 40, CoCpd(CO)z, the Rt is the sum

R,(CoCpd) + Rt(CdCO),)

where cobalt is assumed shielded. Cpd is cyclopentadi- enyl. The third column finally has Rt in place ofR. (not in parts a and b). This shows how to treat some more compli- cated compounds generally.

Formulas such as those sometimes written a s W(CPD)ZHZ or W(CP)ZHZ , for example,can be both short- ened and clarified as WCpdzHz or WCpzHz. (Could we con- strue CPD briefly as carbon phosphide deuteride?)

Literature Cited

b y , CA, 1986; pp 26 and 262. 4. Momieon. R. T; Boyd, R. N. Orgenie CkmlJtry, 5th ed.; AUyn and Bamn: Boston.

MA, 1981; p 170. 5. G i g u h , P.A J. C k m . E d d . 1W, 60.399. 6. Hemmerlin, W. M. J. C h . Educ. 11)8T,M, 533. 7. Beybold, I! G.: May, M.; Bagal, U. A J. Chom. Edue 198T,M,577. 8. Brad1ey.D. C N a f u o 1964,174,323. 9, Rich. R. L. Wit Corrphlions; Benjamin-Cummings: Menlo Pmk. CA, 1965; p 69.

10. Lyrnen, W. J.; Reehl, W F.; RosenbLan, D. H. Handkwh of C h e m i d Prpr*. E& mation Methods; h e r i m Chemical See@: Waehinptan, DC, 1990; Chapter 12.

11. h i d , R. c.; its. J. M . : P O I ~ ~ , B E. m~r~~t&of~-ondwipuids.4th ed.; Mffiraw-EU: New Ymk, 1987.

12. b e y , C.R. InhngdsHond~.ofCkmL1Lry . 13thed.;Dean, J.A.Ed.;MeOraw- XU: New Ymk, 1986: S e h 10.~57: andrefstherein.

13. matt, J. R. J. phys. cham. 196a.56,329. 14. Rammay, D. H. Sci h z 1886.255(9), 40. 15. Hansen, P J.; J-, P C. J C k m . Edm. IW, 65,574. 16. Mihalit, 2.; Mnajatit, N. J C k m . Edm. 199% 69,701. 17. Randif, M. II Chem. Edue. IW2,69,113. 18. Carreia, J. J Chom. Edur I W , 65.62. 19. Bstsanov. S. S.~fmaomrtryondChomievlSVueture; P P Sutton, translator; Con-

sultanb Bmau: New York, 1961; p 29. 20. Al1md.A L.: Rachow, E. G. J. I ~ w . Nuel. C k m . 1868,5,264. 21. Uftle, E. J.; Jones, M. M. J C k m Educ 1960,37,231. 22. Greenwood, N. N.; Eamahaw, A Chemistry of t k Elements; Pergsmon: Oxford,

,a**. " R"c,

23. Chen, H. S.; Kortan, A R.; Haddon, R. C.: Flermng, D. A J Phye Chom. 1983,96, 1018 andrefs therein.

12 Journal of Chemical Education