(( Physical Chemistry )) - Question) The -electrons in a linear polyene can be m
ID: 1009036 • Letter: #
Question
(( Physical Chemistry ))
- Question) The -electrons in a linear polyene can be modeled using a particle in a box, but those in a cyclic polyene are better modeled by a particle on a ring. Each energy level (as specified by a unique value of the quantum number m) can hold 2 -electrons. For degenerate states, the electrons singly occupy the energy levels before pairing up. In this problem you will be asked to compare the following two molecules:
C6H6 C8H8
benzene cyclocotatetraene
a. Determine the highest occupied and lowest occupied energy levels in each molecule. If the levels are degenerate, report the level in terms of the absolute value of the level, i.e. |m|?
b. What wavelength of light would be needed to excite an electron from the highest occupied level to the lowest unoccupied level in each molecule?
c. Based on the occupancy of the highest occupied level and your knowledge of general chemistry (“Huh? No one told us we had to know that stuff!”), explain whybenzene is more stable than cyclooctatetraene?
> Book Name: "Quantum Chemistry, 2nd Edition, by Donald McQuarrie"
Explanation / Answer
a)
C6H6
Energy level 1 ----> 2 electrones
Energy level 2 ----> 2 electrones
Energy level 3 ----> 1 electrone
Energy level 4 ----> 1 electrone
Energy level 5 , 6 ----> no electrones
Therefore Highest occupied = Energy level 4
Lowest unoccupied = Energy level 5
C8H8
Energy level 1 ----> 2 electrones
Energy level 2 ----> 2 electrones
Energy level 3 ----> 2 electrones
Energy level 4 ----> 1 electrone
Energy level 5 ----> 1 electrone
Energy level 6,7,8 ----> no electrones
Therefore Highest occupied = Energy level 5
Lowest unoccupied = Energy level 6
b)
wave length = hc/ E
E = E(n2) - E(n1)
En = 1/2m (nh/2d)2
En = n2(4.11×1020 J)
for C6H6
E=E5E4=(5242)×4.11×1020 J= 3.699 x 10-19 J
=hc/E
=6.626×1034 Js×2.998×108 ms1 /3.699 x 10-19 J
= 537 nm
for C8H8
E=E5E4=(6252)×4.11×1020 J= 4.521 x 10-19 J
=hc/E
=6.626×1034 Js×2.998×108 ms1 /4.521 x 10-19 J
= 439 nm
c) benzene is a cyclic molecule in which all of the ring atoms are sp2-hybridized. This allows the pi electrons to be delocalized in molecular orbitals that extend all the way around the ring, above and below the plane. For this to happen, of course, the ring must be planar – otherwise the p orbitals couldn’t overlap properly. Benzene is indeed known to be a flat molecule.The eight-membered cyclooctatetraene ring shown below is not flat, and its bonds react like 'normal' alkenes.Clearly it takes something more to be aromatic, and this can best be explained with molecular orbital theory.
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