1559T_ch04_55-6910/22/0520:19Pa9e63 EQA Solutions to Problems.63 mize eclipsing interactions of the true boa conformation(Section 4-3). C(CHa (CH3)2C- 31.Models may be helpful here.You should be able to construct structures similar to those pictured below 本B rans-Hexahydmoindane cis-Hexahydroindan roindane and cis to each other envelopes.around the bond away from the give iseto the cyclopentane half-chair conformation,which is similar in energy but harder to draw. 32.In trans-decalin cach of the carbon- al p as A and B,and numbered the four relevant bonds 1-4: ring fusior respect to both rings. In cis-decalin the situation is different.Look at the picture: y).Bondith respect to ring A (rotate the pasecoce this m r bo nds ar to the ring-rusion hydrogens are now equatorial and ax to the we would conclude that the cis isomer is 3.5 keal mol higher in energy dess stable)than the urans.This turns out to be an ove re d has three more than does the trans: cyclohexane in order to minimize eclipsing interactions of the true boat conformation (Section 4-3). (Make a model!) 31. Models may be helpful here. You should be able to construct structures similar to those pictured below. Notice how the ring-fusion hydrogens are trans to each other in trans-hexahydroindane and cis to each other in cis-hexahydroindane. In the drawings, the cyclohexane rings are chairs and the cyclopentane rings are envelopes. A slight twist around the cyclopentane bond away from the envelope “flap” would give rise to the cyclopentane half-chair conformation, which is similar in energy but harder to draw. 32. In trans-decalin each of the carbon–carbon bonds attached to the ring fusion occupy an equatorial po￾sition with respect to the ring on which they are attached. In the illustration below we have labeled the rings as A and B, and numbered the four relevant bonds 1–4: Bonds 1 and 2 (which are part of ring B) are equatorial substituents with respect to ring A. Bonds 3 and 4 (which are part of ring A) are equatorial substituents with respect to ring B. Both hydrogen atoms on the ring fusion carbons are axial with respect to both rings. In cis-decalin the situation is different. Look at the picture: Bond 1 (in ring B) is now axial with respect to ring A (rotate the page clockwise by 60° to see this more clearly). Bond 2 is still equatorial. Also, bond 3 (in ring A) is now axial with respect to ring B (bond 4 is still equatorial). So two of these four bonds are axial with respect to the ring on which they are substituents and, as a result, give rise to 1,3-diaxial interactions that raise the enthalpy of the compound. Notice that the ring-fusion hydrogens are now equatorial with respect to one ring and axial with respect to the other. If we were to assign an energy of about 1.75 kcal mol
1 to each axial bond to a carbon in cis-decalin, we would conclude that the cis isomer is 3.5 kcal mol
1 higher in energy (less stable) than the trans. This turns out to be an overestimate, in part because carbon atoms in rings cannot rotate freely and therefore do not generate as much steric interference as do simple alkyl groups, which can rotate a full 360°. An alterna￾tive way to estimate the energy difference is to search for butane structural fragments that possess gauche conformations. The cis isomer has three more than does the trans; assuming each gauche butane raises the energy content by about 0.9 kcal mol
1 , one arrives at an energy difference of 2.7 kcal mol
1 . H B A 2 3 4 1 H H A B 3 2 4 1 H H H H H trans-Hexahydroindane cis-Hexahydroindane H H C(CH3)3 (CH3)3C Solutions to Problems • 63 1559T_ch04_55-69 10/22/05 20:19 Page 63