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Chapter 4: Problem 77

There are two isomers of decalin. One is of higher energy and the other is more stable. Which is the stabler form? Why?

Short Answer

Expert verified
The more stable isomer of decalin is trans-decalin due to the absence of steric repulsion between the axial hydrogens at the junction of the rings, allowing them to maintain favorable axial positions without any strain. In contrast, cis-decalin experiences unfavorable steric interactions between the axial hydrogens, leading to a higher energy and less stable conformation.

Step by step solution

01

Identify the two isomers of decalin

Decalin (C10H18) has two isomers: cis-decalin and trans-decalin. These isomers differ in the relative orientation of the two cyclohexane rings that form the decalin structure. In cis-decalin, the two hydrogen atoms at the junction of the rings are on the same side, while in trans-decalin, they are on opposite sides.
02

Compare the cyclohexane rings in the isomers

In both cis-decalin and trans-decalin, the cyclohexane rings are in their most stable conformation, which is the chair conformation. However, the relative orientation of the rings in each isomer affects the overall stability of the molecule due to any potential steric strain or torsional strain when different groups on the molecule interact.
03

Analyze the steric interactions in cis-decalin

In cis-decalin, the two cyclohexane rings are on the same side of the molecule, leading to steric repulsion between the two axial hydrogens at the junction of the rings, forcing these hydrogens to adopt an unfavorable equatorial position. This introduces strain in the molecule, making it energetically less stable.
04

Analyze the steric interactions in trans-decalin

In trans-decalin, the two cyclohexane rings are on opposite sides of the molecule, avoiding any steric repulsion between the axial hydrogens at the junction of the rings. Thus, the hydrogens can maintain their favorable axial positions without any strain.
05

Compare the stabilities of the two isomers

Taking into account the steric interactions in both isomers, we can conclude that trans-decalin is more stable than cis-decalin. This is because there are no steric interactions between hydrogens at the junction of the rings in trans-decalin, while there are unfavorable interactions present in cis-decalin. As a result, trans-decalin is the more stable isomer of decalin.

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Most popular questions from this chapter

Write expanded structures showing the \(\mathrm{C}-\mathrm{C}\) bonds for each of the following condensed formulas. Name each substance by an accepted system. a. \(\left(\mathrm{CH}_{2}\right)_{10}\) (saturated compound only) b. \(\left(\mathrm{CH}_{2}\right)_{5} \mathrm{CHCH}_{3}\) (c) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C}\left(\mathrm{CH}_{2}\right)_{6} \mathrm{CHC}_{2} \mathrm{H}_{5}\) d. The isomers of trimethylcyclobutane e. \(\left(\mathrm{CH}_{2}\right)_{6} \mathrm{CHCH}_{2} \mathrm{C}\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}_{2} \mathrm{CI}\) f. \(\left[\left(\mathrm{CH}_{2}\right)_{2} \mathrm{CH}\right]_{2} \mathrm{C}\left(\mathrm{CH}_{3}\right) \mathrm{C}_{2} \mathrm{H}_{5}\)

You have two bottles labeled "1, 2-Cyclopentanediol," one containing a compound of m.p. \(30^{\circ}\), the other a compound of m.p. \(55^{\circ}\); both compounds are optically inactive. How could you decide, beyond any doubt, which bottle should be labeled "cis" and which "trans"?

Which of the following compounds are resolvable, and which are non-resolvable? Which are truly meso compounds? Use models as well as drawings. (d) tran-1, 2-cyclohexanediol (a) cis-1,2-cyclohexanediol (b) trans-1,2-cyclohexanediol (e) cis-1,4-cyclohexanediol (c) cis-1,3-cyclohexanediol (f) trans-1,4-cyclohexanediol

(a) trans-1, 2-Dimethylcyclohexane exists about \(99 \%\) in the diequatorial conformation; trans-1, 2-Dibromocyclohexane on the other hand, exists about equally in diequatorial and diaxial conformations. Furthermore, the fraction of the diaxial conformation decreases with increasing polarity of the solvent. How do you account for the contrast between the dimethyl and dibromo compounds? (b) If trans-3-cis-4-dibromo-tert-butylcyclohexane is subjected to prolonged heating, it is converted into an equilibrium mixture (about \(50: 50\) ) of itself and a diastereomer. What is the diastereomer likely to be? How do you account for the approximately equal stability of these two diastereomers? [Here, and in (c), consider the more stable conformation of each diastereomer to be the one with an equatorial tert-buty1 group]. (c) There, are two more diastereomeric 3,4 -dibromo tert-butylcyclohexanes. What are they? How do you account for the fact that neither is present to an appreciable extent in the equilibrium mixture?

(a) How many pairs of eclipsed hydrogen are present in planar cyclobutane? (b) In puckered cyclobutane ?
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