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I am a beginning organic chemistry student and trying to reason about something based on information in my book, but seeing that Pubchem gives a different structure than I'd expect.

In considering a disubstituted cyclohexane with hydroxyl groups at 1 and 3, I'd think, ok, there's a competition between steric strain and hydrogen bonding. If hydrogen bonding were the more important force, the molecule would be more stable with the hydroxyl groups in the axial position. If steric strain were more important, the molecule would be more stable with the groups in the equatorial position.

The solution manual for Klein's Organic Chemistry [1, p. 128] says in an answer to the problem 4.75 that the stabilizing effect of intramolecular hydrogen bonding between two hydroxyl groups in a gauche conformation is 20 kJ/mol:

This calculation must be modified when we take into account the effect of two $\ce{OH}$ groups that are gauche to each other, as seen in conformers A and B. We should expect an $\ce{OH-OH}$ gauche interaction to be less than a $\ce{Me-Me}$ gauche interaction (less than 3.8 kJ/mol), because an OH group appears to be less sterically encumbering than a methyl group (compare $\ce{CH3}$ and $\ce{OH}$ in Table 4.8). Therefore, the destabilizing effect associated with an $\ce{OH-OH}$ gauche interaction (less than 3.8 kJ/mol) should be overshadowed by the stabilizing effect that results from the hydrogen bonding interactions between the two $\ce{OH}$ groups, which is expected to be approximately 20 kJ/mol (see section 1.12). As a result, we expect extra stabilization to be associated with any conformer in which two $\ce{OH}$ groups are gauche to each other.

My book also (in the same answer) says the upper bound for the steric strain in an $\ce{OH-OH}$ gauche interaction is 3.8 kJ/mol, i.e., lower than the value for an $\ce{Me-Me}$ interaction. It further tells us that 1,3-diaxial interactions are gauche interactions. Klein's Organic Chemistry [2, p. 166] gives in a different table the value of two $\ce{OH-H}$ 1,3-diaxial interactions in a monosubstituted cycloalkane to be 4.2 kJ/mol.

Table 4.8 1,3-diaxial interactions for several common substituents

It seems to me like the OH's have steric interactions with each other (3.8 kJ/mol), and they each have an interaction with an axial H (4.2 kJ/mol for both of them). So at 8 kJ/mol steric strain, it seems like the hydrogen bonding effect should swamp the steric effects.

But Pubchem shows the hydroxyl groups in the equatorial position. I assume it's showing me the lowest energy conformer. I don't understand what's wrong with my reasoning above.

References

  1. Klein, D. R. Student Study Guide and Solutions Manual, 3e, 3rd ed.; Wiley, 2017. ISBN 978-1-119-37869-3.
  2. Klein, D. R. Organic Chemistry, 3rd ed.; John Wiley & Sons, Inc: Hoboken, 2017. ISBN 978-1-119-31615-2.
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  • $\begingroup$ 1,3-Dihydroxycyclohexane is more stable in the diequatorial conformation than in the diaxial one. Table 4.8 is for monosubstituted cyclohexanes. Do not confuse 1,3-diaxial interactions with 1,3-disubstituted. The groups in the Table have 2 gauche interactions with the ring in the axial conformation. $\endgroup$ – user55119 Nov 4 '19 at 3:14
  • $\begingroup$ I know it's for monosubstituted cyclohexanes. I'm just using it to get a value for what two OH-H gauche interactions add up to. The disubstituted version has an OH-OH gauche interaction, and two OH-H gauche interactions. So that 4.2 kJ/mol value should be equivalent to the two OH-H gauche interactions in the disubstituted version. Then I add the 3.8 kJ/mol for OH-OH to get the 8 kJ/mol total. Maybe this is wrong but I would like to know why. $\endgroup$ – Katie Nov 4 '19 at 3:19
  • $\begingroup$ It is difficult to make this calculation for the diaxial isomer. Diequatorial is taken as 0 kJ/mol. The diaxial diol has not only gauche interactions but also positive hydrogen bonding. The 1,3-trans isomer will work. $\endgroup$ – user55119 Nov 4 '19 at 3:25
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    $\begingroup$ "My book (Wiley, 3rd edition)" isn't a proper reference. There are two distinctive literature sources you are quoting (corrected, please take a note for the future qustions). $\endgroup$ – andselisk Nov 4 '19 at 5:52
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    $\begingroup$ @andselisk thanks for the edit. I didn't even notice that I had put the publisher instead of the author, as well. $\endgroup$ – Katie Nov 4 '19 at 10:28

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