# Stability of geometrical isomers in cycloalkanes

Among the following, which should be the most stable compound? 1)Cis-cyclohexane-1,2-diol 2)Trans-cyclohexane-1,2-diol 3)Cis-cyclohexane-1,3-diol 4)Trans-cyclohexane-1,3-diol

My thought process is-cis isomers with adjacent OH groups lead to Hydrogen bonding so 1) should be the most stable, I'm not sure if repulsion will be the dominating factor and change the answer- what is the correct way to think about this?

• This question seems a little bit invalid since 1,2-diol cannot be directly compared to 1,3-diol counterpart. From hydrogen bonding you can tell that cis- counterpart wins in stability but both are not comparable without actually knowing the values. – Saurabh Singh Apr 19 at 18:25

To answer this question, you needs to know what are the values for each acting forces on the cyclohexane frame work. Without that information, nobody would know if the repulsion forces (steric) would or would not be the dominating factor over hyrdogen bonding (electronic). Once we know the answer for that, you'd be able to calculate and find out the most stable structure. For your convenience, I attached a diagram with the chair conformations of all four structures and their Newman projections to make you understand the hydrogen bonding capabilities:

As you see, if the substitutions are not capable of hydrogen bonding, it is obvious that 1,3-cis structure is the most stable considering only stecic factors (eq-eq conformer). 1,3-trans structure (eq-eq conformer) is also stable relative to others but has an additional gauche interaction of vicinal bulky groups (1,2-substitutions) compared to its 1,3-counterpart.

In your case, however, all four molecules contain hydroxyl groups, so that three of them could be able to have structure stabilizing hydrogen bonding (the exception is trans-cyclohexane-1,3-diol; see Newman projection of IV-eq-ax). Both cis- and trans-cyclohexane-1,2-diols are structurally similar to 1,2-ethanediol, which favors a gauche conformation instead of an anti conformation, because only the gauche conformation allows hydrogen bonding between the two vicinal hydroxyl groups. Thus, both cis- and trans-cyclohexane-1,2-diols would adopt gauche conformations (see Newman projections of I-eq-ax and II-eq-eq) Ref.1. Keep in mind that, for cis-cyclohexane-1,2-diol (I), the anti conformation is impossible because of the restriction of ring structure. In trans-1,2-cyclohexanediol (II), however, the anti conformation is physically possible, but it would require the hydroxyl groups to be in diaxial positions, which is much less less stable than diequatorial due to 1,3-interactions imposed by axial 3,5-hydrogens (ax-ax chair confirmation). According to the literature (Ref.1), cis-cyclohexane-1,2-diol is more acidic than trans-cyclohexane-1,2-diol by about $\pu{1.5 kcal/mol}$, hence 1,2-cis-compound would impose stronger hydrogen bonding than its trans-counterpart.

According to the same study (Ref.1), cis-cyclohexane-1,3-diol is $\pu{10.9 kcal/mol}$ more acidic than trans-cyclohexane-1,3-diol, thus cis-compound is highly stable than its trans-counterpart (also remember, trans-cyclohexane-1,3-diol cannot have hydrogen bonding (vide spupra)). However, between conformers, the diaxial and diequatorial conformations in cis-cyclohexane-1,3-diol are relatively close in energy, so it is not immediately clear which conformation is dominant (Ref.1). Yet, a solution NMR study of this molecule showed that the diequatorial conformer (III-eq-eq) is more stable than diaxial conformar (III-eq-eq) Ref.2, although III-eq-eq is impossible to make hydrogen bonding (see Newman projections of III-eq-eq and III-ax-ax). This shows that hydrogen bonding itself cannot overcome the steric repulsions induced by the 1,3-ax-ax-interactions. My conclusion is without knowing values of these attraction and repulsion interactions, it is impossible to say which of the three structures, I, II, and III), is the most stable.

References

1. X. Chen, D. A. Walthall, and J. I. Brauman, Acidities in Cyclohexanediols Enhanced by Intramolecular Hydrogen Bonds, J. Am. Chem. Soc., 2004, 126(39), pp. 12614–12620.

2. R. J. Abraham, E. J. Chambers, W. A. Thomas, Conformational analysis. Part 21. Conformational isomerism in cis-cyclohexane-1,3-diol, J. Chem. Soc., Perkin Trans. 2, 1993, (6), pp. 1061–1066.

The most stable compound should be cis-cyclohexane-1,3-diol because the formation of the hydrogen bond and less crowding. the less stable is the tran-cyclohexane-1,3-diol there is no way of making hydrogen bond. the second more stable is the cis-cyclohezane-1,2-diol it also has a hydrogen bond and then with little difference the trans-cyclohexane-1,2-diolñ

• How can I tell whether 1,3 is too far to form a hydrogen bond or not? and whether crowding dominates or H-bonding in cis-cyclohexane-1,2-diol? – hiten pandya Sep 6 '18 at 18:39
• if you use any 3D program to write the molecules you can find the data. – Carlos Rius Sep 6 '18 at 19:37
• I'm preparing for an exam where no relevant data, or even calculators are provided. So I can't take the help of models while learning to answer these questions. – hiten pandya Sep 7 '18 at 9:01