A value

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title: "A value" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["isomerism", "physical-organic-chemistry"] description: "Measurements of stable atom orientations" topic_path: "science/chemistry" source: "https://en.wikipedia.org/wiki/A_value" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Measurements of stable atom orientations ::

thumb|400px|right| The A-value for a [[methyl group]] is 1.74 as derived from the [[chemical equilibrium]] above. This means it costs 1.74 kcal/mol of energy to have a methyl group in the axial position compared to the equatorial position.

A-values are numerical values used in the determination of the most stable orientation of atoms in a molecule (conformational analysis), as well as a general representation of steric bulk. A-values are derived from energy measurements of the different cyclohexane conformations of a monosubstituted cyclohexane chemical. Substituents on a cyclohexane ring prefer to reside in the equatorial position to the axial. The difference in Gibbs free energy (ΔG) between the higher energy conformation (axial substitution) and the lower energy conformation (equatorial substitution) is the A-value for that particular substituent.

Utility

A-values help predict the conformation of cyclohexane rings. The most stable conformation will be the one which has the substituent or substituents equatorial. When multiple substituents are taken into consideration, the conformation where the substituent with the largest A-value is equatorial is favored. thumb|600px|center|A methyl substituent has a significantly smaller A-value than a tert-butyl substituent; therefore the most stable conformation has the tert-butyl in the equatorial position. The utility of A-values can be generalized for use outside of cyclohexane conformations. A-values can help predict the steric effect of a substituent. In general, the larger a substituent's A-value, the larger the steric effect of that substituent. A methyl group has an A-value of 1.74 while tert-butyl group has an A-value of ~5. Because the A-value of tert-butyl is higher, tert-butyl has a larger steric effect than methyl. This difference in steric effects can be used to help predict reactivity in chemical reactions.

Free energy considerations

Steric effects play a major role in the assignment of configurations in cyclohexanes. One can use steric hindrances to determine the propensity of a substituent to reside in the axial or equatorial plane. It is known that axial bonds are more hindered than the corresponding equatorial bonds. This is because substituents in the axial position are relatively close to two other axial substituents. This makes it very crowded when bulky substituents are oriented in the axial position. These types of steric interactions are commonly known as 1,3 diaxial interactions. These types of interactions are not present with substituents at the equatorial position.

There are generally considered three principle contributions to the conformational free energy:

1. Baeyer strain, defined as the strain arising from deformation of bond angles.
2. Pitzer strain, defined as the torsional strain arising from 1,2 interactions between groups attached to contiguous carbons,
3. Van der Waals interactions, which are similar to 1,3 diaxial interactions.

Enthalpic components

When comparing relative stability, 6- and 7-atom interactions can be used to approximate differences in enthalpy between conformations. Each 6-atom interaction is worth 0.9 kcal/mol and each 7-atom interaction is worth 4 kcal/mol.

| align = center | image1 = 6atom_int.jpg | width1 = 200 | alt1 = | caption1 = The dashed lines indicate 6-atom interactions found in this conformation of ethyl cyclohexane, which amounts to approximately 2.7 kcal/mol in the enthalpic term of Free Energy. | image2 = 7atom_int_v5.jpg | width2 = 200 | alt2 = | caption2 = The dashed lines here signify the 7 atom interactions, which contribute approximately 8 kcal/mol to the enthalpic term making this conformation unrealistically high in energy. | footer =

Entropic components

References

1. Muller, P. (1994). "Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994)". [[Pure and Applied Chemistry]].
2. (2004). "Organic Chemistry". John Wiley and Sons, Inc..
3. (1974). "Dynamic Chemistry". Springer-Verlag.
4. (2006). "Modern Physical Organic Chemistry". University Science Books.
5. Note: measured under diverse conditions
6. (1994). "Stereochemistry of Organic Compounds". Wiley.
7. (1965). "Conformational Analysis". Interscience Publishers.
8. (1967). "Topics in Stereochemistry". John Wiley & Sons, Inc..
9. (1969). "Topics in Stereochemistry". John Wiley & Sons, Inc..
10. (21 November 2012). "Table of A-Values". University of British Columbia.
11. (1994). "Molecular Recognition of Cyclitols by Neutral Polyaza-Hydrogen-Bonding Receptors: The Strength and Influence of Intramolecular Hydrogen Bonds between Vicinal Alcohols". [[Journal of the American Chemical Society]].

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