4.2: A-values and Equilibrium Ratios
- Page ID
- 319863
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)So, why do we care about chair conformations? Well, most of the time things aren’t as simple as cyclohexane. Usually, rings have substituents on them. It turns out that as soon as you put a substituent on the cyclohexane ring, you perturb the equilibrium. Consider the following:
The difference in energy between the right- and left-handed chair is 1.7 kcal/mol. This means that the ratio of the chair structures where CH3 is equatorial and axial, respectively, is 19:1 (in other words, favoring the CH3 group in the equatorial position). This happens because a specific type of steric interaction known as a diaxial interaction. Axial substituents that are in a 1,3-relationship on a ring will prefer to be equatorial because they bump into each other when axial (but lie far apart when equatorial).
Can we quantify or predict these ratios? A-values tell you the energetic preference for a substituent in the equatorial position.
| Group | A-value (kcal/mol) |
| Me | 1.7 |
| Et | 1.8 |
| iPr | 2.2 |
| tBu | 5.0 |
| F | 0.24 |
| Cl | 0.53 |
| Br | 0.48 |
| I | 0.47 |
If we take a close look at these numbers, we see a few peculiarities. In the case of the hydrocarbons (Me, Et, iPr, tBu), we see that there is a slight increase in energy as one proceeds from Me to Et to iPr, but then there is a big jump in A-value for tBu. This happens because you can always rotate a Me, Et, or iPr group in a chair conformation so that a H atom points over the middle of the ring. For a tBu substituent, this cannot happen. One of the methyl groups of the tBu substituent will point over the ring and cause a lot of steric strain. This is called a syn-pentane interaction. It’s like trying to fit 7 atoms in a space that geometrically can only fit 6!
The trend in the A-values for the halogens is also counterintuitive. Chlorine is certainly bigger than fluorine, and indeed it has a higher A-value. But this does not hold true for the rest of the series. Br and I are bigger atoms, so one might expect that they have greater A-values. However, since the C-Br and C-I bonds are much longer, this effect is negated, and the A-value goes down.
