Chem 351 Fall 2005 MT: Thermodynamics

Part 8: THERMODYNAMICS

This should have been a reasonably straight forward calculation, but care needs to be taken to get the right structures and the right molecular formula, then do the math correctly.

Common stumbling blocks for some students were :

could not draw cis-1,3-dimethylcyclopropane correctly.
could not deduce the correct molecular formula, C₇H₁₄
failed to assign stability order correctly because they did not consider ring strain versus branching issues.

ii All are isomers of C₇H₁₄.
iii Constitutional isomers

b.

c.
i   Remember that the more stable the isomer the more exothermic the heat of formation will be.
    Hence the least stable isomer, IV (1,1,2,2-tetramethylcyclopropane) = -28.6 kcal/mol
    The most stable isomer, III (cis-1,3-dimethylcyclopentane) = -40.2 kcal/mol
    and finally, the intermediate isomer, II (ethylcyclopentane) = -39.1 kcal/mol

ii cis-1,3-dimethylcyclopentane
iii 1,1,2,2-tetramethylcyclopropane

d.
The question asks for the main factors affecting the stability of alkanes and cycloalkanes. The factors are branching and ring strain (which is due mainly to angle and torsional strains), plus other torsional strains and maybe Van der Waals strain. Remember that steric strain is the overall effect of angle, torsional and Van der Waals strain. Note that heats of formation or combustion etc. do not affect stability. They are measures of stability. The stability controls the heat of reaction not the other way around.

Since the ring strain of cyclopentanes and cycloheptanes are about the same the difference in the stability of these structures is controlled by the degree of branching. The methyl groups in cis-1,3-dimethylcyclopentane are too far apart to suffer Van der Waals strain or torsional strain (look at a model of the most stable conformation - the two methyl groups are both in the equatorial type positions). Therefore, this more branched isomer dimethyl isomers is more stable than the ethyl isomer.

In contrast, the 1,1,2,2-tetramethylcyclopropane has a lot of ring strain due to angle strain (bond angle of 60 degrees compared to ideal 109.5) and torsional strain within the ring and between the methyl substituents, hence it is the least stable. Ring strain is small rings like cyclopropane and cyclobutane is very large compared the to the stabilisation given by simple branching.