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physical chemistry hmwk3

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Unformatted text preview: ' duws Internet Explorer 5 1 5) as m rseher um/FIIE/‘EIEZE7E/Ehem3322testlsnlnf n @3 There we no Ielfled documents a Ihis lime, Problem 2 — 6 marks The “4n+2 rule” is a well—knewn m e in organic chemistry: the planar, aromatic form of carbocyclic systems of the type (CH)m (cg. benzene in the case of m=fi) are particularly stable for values of in given by m=4n+2 (n=l,2,3,..i) (6) In other words, m=6, 10, 14, If the 11- electrons in these systems are treated as free electrons on a ring, explain how the 4n+2 rule logically follows. Hint: closed-shell systems, that is, in which all energy levels are fully occupied, have enhanced stability in atoms and molecules. Answer: All levels are doubly degenerate except for the ground state. Since two (spin- paired) electrons can fit into each state, the ”closed—shell" configurations have 2, 6, 10, 1.4, .. . electrons, i.e. 4n+2. Information about ‘chem3322_lest1_soln" 3 Type: Notes (hemfiflzz wk In(2[ll] 17 5) duwslnternelEuplnrer m/FIIE/‘E182574/Ehem3322hwkfisulnf There we no relied documents a Ihis lime, Problem 4 — 6 mar-1m The 1r electrons in benzene can be apprmcimated as particles on a ring. Calculate the diameter of this “electron ring" if it is assumed that a. trensitiun occurring at 260.0 nm oorreeponds to an electron going from n = 3 to n = 4. Compare this diameter to the diameter of a benzene molecule, if you approximate the carbon hexagon with a circle. Make sure you EhDW the details of your npprcudmution because there are different Ways to do this. Answer: Using E = Pm and c = Ay‘ the photon of wavelenmh 260 um gives an energy to the molecule of E : 7.64 x 10"“ J. The energy promotes the n : 3 to n : 4 transition. 2 e 2 2 “2:121:12 (5} Using the mean of an electron. since this is what is doing the transition, we get R = 2.36 A. The carbon-carbon bond length in benzene is 1.39 A. Assuming that the Circumference nfthe frielectmn “ring” in benzene is six times this distance, we get a. diameter of 2.65 A. So we see that our simple model of the particle—on»arring estimates the diameter to be about twice as big as it actually is. Information about ‘chem3322_hwk3_snln" ...
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