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JOHN J. ALEXANDER University of Cincinnati Cindnnati.OH4~~
exam question exchange Some Questions on Buckminsterfullerene, Cso for General and Inorganic Chemistry Students Charles E. Hecht Hunter College of the City University of New York New York, NY 10021 The molecule CW.now called buckminsterfullerene, was detected in 1985 .I ,.,. and because techniaues for v m d u c i n -~ macmscopic quantities of its solid form were published in 1990 (2). a tremendous amount of research on its properties andderivatives has been undertaken 3 , 4 ) .with this molecule. entirrlv new fields ofchemistrv and material science s e e k to be opening up. Should this fascinating substance be studied in general or inorganic chemistry courses, the following questions and acceptable solutions may be useful. Question 1 The buckminsterfullerene molecule shown in the figure can be described a s a hollow closed cage of equivalent sp2 hybridized carbon atoms arranged on a n approximately spherical soccer-ball-like surface. The surface is made up of 12 pentagons (each surrounded by 5 hexagons) and 20 hexagons (each surrounded by 3 pentagons and 3 hexagons) such that every carbon atom with 3 bonds (one conventionally a double bond) is located a t the common corner of one pentagon and two hexagons. X-ray analysis (5) shows there are two typesoofC-C bonds: conventional double bonds of length 1.39 A being fused hexagon sides and conventional single honds of length 1.43 A being fused hexagon-pentagon sides. (a) Show that the abwe description leads to a count of 60 carbon atoms in the molecule.
(b) What is the total number of bonds? How many single and double bonds are in the molecule? (4The bond energies for conventional C C single and double bonds are 348 and 612 kJImole, respectively Estimate a lower bound in electron volts (eV) per atom for the energy needed to form separated (to infinity) neutral atoms from the solid form of Cso This is called the cohesive energy per atom. Why is your estimate a lower bound? (d)Schulman and Disch (6) have calculated on the basis of self consistent field theory the molar enthalpy of formation of gaseous molecular Cso. Their result is 2.81 x id kJImole. Taking the enthalpy of sublimation of graphite as 716.682 kJ per mole of carbon atoms calculate the effectiveC C bond strength in Csoincluding effects ofthe delocalized n electrons above and below the soccer ball surface implied by the result of Schulman and Diseh. Compare with your result in part c.
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(b) There are (60 --3, - - 90 bonds 2 of which 113 or 30 are double and the remaining 60 are single. (c) If the honds were reallv sinele and double then neglect of further stabilization "because of n electron delocalization and neelect of van der Waals interactions between the molecules o f Csa in the solid give for the estimate of cohesive energy the result:
kJ
60
= 6.78-
eV atom C x kJ 96.49male 1-
1 - [(30)(612)+ (60) (348)l = 654-
eV atom C
This is a lower bound because of the neglect of the two effects mentioned above of which the van der Wads effect is minor on a per atom basis. Indeed, Huffman ( 4 ) reports the cohesive energy per Cso molecule a s 1.5 eV (or only 0.025 eV per atom). However, this value is large enough to give the Csomolecular solid a high melting point. Note also that since every atom of C has an average of 312 = 1.5 bonds our estimate of the effective C-C bond strength in Cso is 65U1.5 = 436 kJ/mole. (d) Since carbon in the form of solid graphite is assigned a zero enthalpy content we have the cycle
AH-
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Cso buckminsterfullerene. Conventional single bonds, light color; conventional double bonds, darkcolor. This image is taken fromcomputer animation studies of CEO by W. G. Harter and D. Weeks, University of Arkansas and is used with their permission.
60 C (solid,graphite) + 60 C (g) 60 C (g)+ Ceo (g)
x
60 C (solid,graphite) -t CeO(g)
2.81 x lo3
(60) (716.682)
This result is only slightly larger than our estimate in c, but it is still too low because Huffman ( 4 )reports the coheVolume 69 Number 8 August 1992
645
sive energy per atom of C in Csoto be 7.4eV corresponding to an effective C-C bond strength of about 480 kJ1mole. Question 2 The X-ray analysis (5) of solid C6o shows it to be a facecentered cubic lattice of Csospheres with a unit cell side of 14.2 and a n average hollow cage diameter of 7.0 for each Csosphere.
tance, a little smaller than the 3.3 A distance between atomic planes in graphite, is needed to accommodate the a-electron clouds on the exterior of both cages. (b) There is a net of four spheres of Cm in each unit cell. Hence, the density is given by
A
(a) Calculate the nearest neighbor distance of Cm spheres in the structure. Why is this distanee larger than the cage diameter? What is the distance between adiacent carbon atom cages? (b) Calculate the density of solid Cm. (c) Compounds between Cs0 and K and between Cso,and Rb have been prepared. Both superconduct with transltlon temperatures of 19 and 28 K, respectively (7, 8)!What is the simplest formula of these wmpounds if the alkali atoms singly occupy all the tetrahedral and octahedral holes in the claaepaeked structure of Csospheres? Solution 2 (a) In an fcc structure the nearest neighbor distance (half a face diagonal) is
where NAis Avogadro's number. This density is considerably less than that of graphite (2.3g/cm3)or diamond (3.5 e/cm3). (c) i n the fee structure, the number of tetrahedral holes is twice the number of fcc sites, and the number of octahedral holes is equal to the number of fcc sites. Hence, in the proposed structure for every single Cm sphere, there are three alkali atom sites, and the formula is M3Cso.
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Literature Cited l.Kmta,H.W.;HesUI,J.R.;O%rien, S. C.;Cud.R.F,:Smallq.,R. E . N a t m 1886.318, 162163. 2. mtsehmer, W.: Lamb, L. D.; Fostimpaulae, K:Huffman, D. R. N o f u n 1980,347,
& 2
where s is the ?it cell side. Hence, the nearest neighbor distance is 10.0Ain this case. The difference between this value and the carbon cage diameter is 3.0 A,which is the distance between adjacent carbon atom cages. This dis-
646
Journal of Chemical Education
6. Schulman, J.M.: Disfh,R. L.JChPm. Sa., Chom. Comm 1981,411412.
7.Hebard.AF;Rosseinsky.M.J.;Haddan,R.C.;Mmphy,D.W:Glarum,S.H.;Palatra, T.T.;Ramirez,A.P.;Rortan,A.R.Notun1981,350.600603. 8. Rosaeinaky. M. J.; &mire%, A. P: Glarum, S. H.; Murphy, D. W.; Haddon, R. C.;
Hebard,A.F.:Palstrs,T.T.;Kortan,A.R.;Zahurah,S.M.;MaWlga,A.v.Phys.Ro".
Left 1981,66,2830-2834.
