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 substances can herewith he predicted by a method that is practical even for species with few or no measured properties. The method is in agreement with this principle from theory: The London forces between molecules and the refraction 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 effects of sufficiently well shielded internal atoms, and we use an objective geometric criterion to exclude them. Addition of the molar refractions (or atomic polarizabilities) of the other atoms, with a n 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 0.05(Rt mol/cm3)~ where the D stands for debye (D1 101sFrcmorD=3.3x1030Cm)andthe Fr for franklin (Fr = 3.3 x 10-lo C). Dipole 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 example of the excluded substances. The low boiling points of the silicon halides have often been noted and explained 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 (identified 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 vapor pressures.) Several values not known at the beginning of this study have since been confirmed.
Table 2. Boillng Points No.
MSj
RdY
Ax
Main Groups, Shielded 1 2 3 4 5 6 7
CF4 IF-, SnFio SbCis
6 9
CH4
1.60 1.89 1.66 1.01 0.33 0.73 0.49
6.40 11.20 16.00 26.55 45.68 24.27 50.68
c3ci8 BBr3
Sni4
145 248 302 413 543 363 621
2.4 -3.7 -0.8 1.6 3.9 4.8 4.8
149 239 300 420 565 360 616
Main-Groups, Intermediate 0.40 0.40
5.83 17.20
C4Hio
7.0 4.5
120 271
112 273
Main Groups, Exposed, General 10 11 12 13 14 15
Ar
16 17 16
F2
4.00 24.68 4.03 13.69 10.80 57.20
AszH4 Hz0 Hi N2F4
P4S3
0.10 1.40 0.11 1.03 0.38
87 373 373 238 200 680
89 353 101 226 202 671
2.2 -5.7 -130.3' -5.0 1.O -1.4
93 444 281
8.9 3.1 0.9
Halogens 3.20 25.34 13.80
12
BrCi
0.09
85 458 278
Aromatics (Exposed) 19 20 21 22 23 24
cs~s
25 26 27 28
CsH5Ci CsHsC2H3 CsH3(N02)3 CsHsCsHs
23.31 63.81 77.31 171.90 33.16 23.14
Ci8Hiz C22H14
Cso C9H8 C4H4S
0.40 0.40 0.40
353 721 793
0.40 0.40
455 357
341 729 843 1524P 445 339
-3.5 1.1 6.1 -2.1 -5.2
Substjtuted Benzenes 28.00 31.08 45.57 44.58
0.73 0.40 1.40 0.40
405 418 529
401 424 63ZP 556
-0.9 1.3 5.0
Name benzene chrysene picene buckminsterfullerene indene thiophene Substituent(s) chloro vinyl 1,3,btrinitro phenyi
Main-Group Organometallics
Refraction The values we use for molar refraction R are mostly by Batsanov (19) 29 and, for electronegativity x, by Allred 30 et al. (20, 21). These sources are valued especially for completeness. 31 32
Electronegativity Our correction is in eq 2. Rt = R&l + f,(Ad2)
Exposed ZnMen TeMen
18.52 22.62
0.84 0.49
319 360
PMe3 AszMe4
18.56 29.12
straightforward, will be shown in e&h subseque& section. -
P
Te -= f(~.(l+ fr(~)2)mol/cm3
Journal of Chemical Education
1.2 1.2
0.44 0.40
314 438
313 439
-0.4 0.1
Shielded
(2)
K
323 364
intermediate
33 BMe3 14.43 0.49 253 where R, is the sum of elemental mo- 34 WMes 28.86 1.10 lar refractions, excluding any shielded e: excluded. elements; f , is the electronegativity p: predicted but not confined. factor, 0.089, and the adjustment for t h i s i s included even when M i s Suwev of Classes shielded.
10
El%
TdK
TdK
(3)
260 466P
2.5
Table 2 includes a few representative halides of maingroup elements, Mixj, whose central atoms Mare shielded. We have, then, simply
R, =jRx
Table 2. Continued No.
Rdy
Mi3
TdK
Ax
TdK
EISb
Shielded Tlansition-ElementCompounds
The relative error, in the last wlumn, i s based on the unrounded T. a n d To.Most values ofR, and Az are obtainedvery easily Ibfacilitate checking, however, we l i s t them here. Boili n g points have been taken h m wuntless sources.
Halides UFs Tic14 TaBrs Zrla
35 36 37 38
13.31 26.02 43.67 54.81
2.88 1.51 1.41 0.99
330 409 593 704
336 422 613 685
1.7 3.0 3.3 -2.7
rr Bonded 39 40a 40b 40 41 42
Ni(C0)4 16.28 CoCpd 19.42 Co(C0)z 8.14 CoCpd(C0)230.99 FeCpdz 38.85 WCpdzHz 40.89 p: predicted but not confirmed.
1.75 0.80 1.80 0.86 1.10
316 309 -2.3 CoCpd(CO)z, part a CoCpd(C0)2, part b 414 418 1.2 522 521 4.3 557P
Intermediate Main-Group Compounds Where Mix, = C;H, we calculate R, = eciRc +jRR The carbon in C H I a n d certain derivatives i s found geometrically ( 1 )t o be 84.1% exposed, so the exposure factor, eM o r ec, i s 0.841. Exposed Main-Group Substances-General Here we clearly have R,(MjXJ
+
= XM jRx
The "extrapolated b p o f about 100"" reported (22) for entry no. 11,&HI, was found too l a t e 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 f o A h nes (~dehcal011. wltn !he founh sp aced non. zontally to avom crowd ng) others Tne lo1ow 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 +: 1.BMea(Me=CHnl;2,SMe.; 3,&Men; 4,SbaMer.
W: 5,PbMu: 8.AlrMes; 7,SnlEta. A:10,F2;11.CI2:l2,BrCI:13,Bn: 14,ICI:15,IBr; 18, 18.
. :17,CLF,18.BrF:19,CkO.
€430,HnO;31,Hg;32,Ns; 33,CO: 34,NO;35,Os: 36. N o 37, C01: 38,Cdb: 39,BFs: 40,C a d : 41,
PHa: 72,SeFs:73,C&; 74,CFsSFs; 75. SbHa: 76. Ge2Ha:77,C.&S, thiophene; 76,P C h 79.
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-
50,P,. x:80,Ar;61.O2;82.Oh;68.CH~;64,KT;BS.CF~;66, NFa; 67. S-4; 68, Xe; 69,CIIk 70. Baa; 71,
enyl): 81,CBu; Be, CsFal: 89, Si1Brs; 84, WCla;
86,~CsHdNOsh:86, GeL;87,Sa; 66,AsL4; 88, CpHx. picene.
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Number 1
Janualy 1995
1
tical work but does fit the prediction. (The second significant 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 + k R y
Rc has the aromatic value, as given in Table 1.These hydrocarbons 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 ermrs 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 sublimationat 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 unshared pairs of outer electrons and thus have a less symmetrical structure than that assumed by our geometric miterion for shielding. We get good results, quite reasonably, by assuming exposure for MX2, intermediate status for (or higher) and and M A ,and shielding for 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 + k R y where e M is 1 for the exposed compounds, and 0 for the shielded ones; l/2is the assigned value for the intermediate compounds. The success of this simple approach in the intermediate group may seem surprising at first for pyramidal molecules like PMea which, however, are exposed on one side but shielded on the other.
12
Journal of Chemical Education
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 transitionelement 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 cyclopentadienyl. The third column finally has Rt in place ofR. (not in parts a and b). This shows how to treat some more complicated compounds generally. Formulas such a s those sometimes written a s W(CPD)ZHZ or W(CP)ZHZ ,for example,can be both shortened and clarified as WCpdzHz or WCpzHz. (Could we construe 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 o1964,174,323. 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 S e e @ : 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. I n h n g d s H o n d ~ . o f C k m L 1 L r y13thed.;Dean, . J.A.Ed.;MeOrawXU: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 . E d m . 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;Consultanb B m a u : 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.
