Question

Question: a. Which of the monosubstituted cyclohexanes in Table 3.9 on p. 128 has a negative ∆G° for the conversion of an axial-substituted chair conformer to an equatorial-substituted chair conformer?

b.Which monosubstituted cyclohexane has the most negative ∆G° for this conversion?

c. Which monosubstituted cyclohexane has the greatest preference for an equatorial position?

d. Calculate ∆G° for the conversion of “axial” methylcyclohexane to “equatorial” methylcyclohexane at 25 °C.

Short answer

1. All of the equilibria have negative ∆G° values for the conversion of an axial-substituted chair conformer to an equatorial-substituted chair conformer.
2. Tert-butylcyclohexane
3. Tert-butylcyclohexane
4. ∆G°=-1.7 kcal/mol

Step-by-step solution

Step 1

For the conversion of an axial-substituted chair conformer to an equatorial-substituted chair conformer, we must identify the monosubstituted cyclohexanes with a negative ∆G°.

The relationship between the equilibrium constant (K_eq) and the change in free energy (G) is well understood:

G^o = ^_RT ln K_eq

and, Keq=

The Keq value is greater than 1 for all -G^ovalues. The equilibrium constants for all monosubstituted cycloalkanes except H are larger than 1, as seen in the table.

As a result, for the conversion of an axial-substituted chair conformer to an equatorial-substituted chair conformer, all monosubstituted cyclohexanes in the table except H have a negative G^o.

Step 2

b)Tert-butylcyclohexane has the most negative ∆G° for this conversion.

c)Tert-butylcyclohexane has the greatest preference for an equatorial position.

 d) Calculation of ∆G° for the conversion of “axial” methylcyclohexane to “equatorial” methylcyclohexane at 25 °C.

G^o = ^_RT ln K_eq

Keq= 18

-1.986 ×10^-3 kcal/mol ×298 K × ln 18 (T=˚C+273) = G^o

G^o = -0.59× ln 18 kcal/mol

G^o = -0.59×2.89 kcal/mol

G^o = 1.79 kcal/mol