+
"t" at 95% confidence level for (nl n? - 2) = 7 is 2.36. The "t" test indicates the mean from either group is acceptable
2) (a) Volume titrant is (50.00ml) X (0.04000 mmole oxalatelml) X (2 mmale Celmmole oralate) + (0.09896 mmole Celml) = 40.42 ml Literature Cited (I1 Ohlwpiier. 0. A , Moditsch, J. 0. and Piatnieki, C. M. (1973).
S.. .4nol.
C h i m A d o . 64. IS9
MO Description of Allene H o w a r d E. Zimmerman Uniuersity of Wisconsin Madison, 53706 This auestion is suitable for senior undereraduates or beginning graduate courses in organic chemistry emphasizing molecular orbital theory. The question tests students' abilities t o distinguish between Hiickel and Mobius systems a s well as to recomize the eauivalence of the traditional model for allene and theone here. Also tested is the ability to employ the well-known circle mnemonic for obtaining MO energies. In terms of the Bloom taxonomy of educational objectives (I), this question affords the opportunity of testing knowledge, comprehension, application and analysis of basic molecular orbital concepts (2). Question T h e following two basis sets are equally acceptable for allene (i.e. set A and set B): these differ in that B has the central pair of p-orbitals twisted 4 5 O from the orientation in A. Without doing the problem explicitly via a secular determinant, obtain the energies of the MO's resulting from mixing the basis orbitals in model B. Do this and show your work. Remembering t h a t overlap varies with the cosine of the dihedral angle, correct the energy units explicitly. Then note if your answer is that expected also from use of model A. (Hint: Use the circle mnemonic.)
Answer Model B for allene is seen to consist of a cyclic array of four atomic p-orbitals. Orbital 1overlaps with 2 at a 45O angleand in aplus-plus and minus-minus fashion. Similarly,orbital 2 overlaps with 3 in the same way, as doesorbital 3 with orbital 4. However,orbital 4 overlaps with orbital 1with plus-minus overlap. With one plus-minus overlap (an odd number) in this cyclic array, this isa "MBbius type" system. This contrasts with the H"ekel type array which would have zero or an even number of overlaps. Since this is a Mobius type system, we use the circle mnemonic with a square inscribed (i.e., 4 orbitals) and one side down. For a Hiickel system, s vertex would be put at the bottom. The radius of the circle is 2e = 2cos R where R is the 45' dihedral angle (i.e., e = cos 8). We find energy levels at the four intersection points: i.e., at - f i e , - f i t , + f i r , and +&; note the circle drawn below. Although these energy levels look different than the standard plus and minus one levels f& the two sets of ethylenic bonding and &tibonding MO's of the traditional allene model A, when we substitute in the value for 8 = 1 1 ~- ,4we . find that the MO'sderived from Model Bare also at *I. The energy units here are 101 = 18 kcallmole.
i
plus-minus ovedap
energy
Literature Cited i l l Bloum.S. R.. "Texonomy ofEducationa1 Ohjectivos". York. 1956. (2, Zimmeman. H. E.;'Qusntum York, 1975.
Machenin fc,r
Longmans,Green end Co.. New
oreenic Chemists':
Acsdemic Press, New
Volume 54, Number 10, October 1977 1 609
