Table 4.7 Relationship Between Free-energy Difference and
Isomer Percentages for Isomers at Equilibrium at 25 °C
Free-energy Difference
∆G° (kJ mol–1) KMore Stable
Isomer (%)Less Stable
Isomer (%) M/L
0 (0)b 1.00 50 50 1.00
1.7 (0.41)b 1.99 67 33 2.03
2.7 (0.65)b 2.97 75 25 3.00
3.4 (0.81)b 3.95 80 20 4.00
4 (0.96)b 5.03 83 17 4.88
5.9 (1.41)b 10.83 91 9 10.11
7.5 (1.79)b 20.65 95 5 19.00
11 (2.63)b 84.86 99 1 99.00
13 (3.11)b 190.27 99.5 0.5 199.00
17 (4.06)b 956.56 99.9 0.1 999.00
23 (5.50)b 10782.67 99.99 0.01 9999.00
a. ∆G° = −2.303 RT log K. ⇒ K = e–∆G°/RT b. In Kcal mol–1.Table 4-2 The relationship between stability and isomer percentages at equilibriuma
More stable isomer
(%)Less stable isomer
(%)Energy difference (25 °C)
(kcal/mol) (kJ/mol)
50 50 0 0
75 25 0.651 2.72
90 10 1.302 5.45
95 5 1.744 7.29
99 1 2.722 11.38
99.9 0.1 4.092 17.11
aThe values in this table are calculated from the equation K = e–∆E/RT, where K is the equilibrium
constant between isomers; e ≈ 2.718 (the base of natural logarithms); ∆E = energy difference between
isomers; T = absolute temperature (in kelvins); and R = 1.986 cal/mol×K (the gas constant).
3) In the equilibrium mixture, the conformation of methylcyclohexane with an
equatorial methyl group is the predominant one (~95%).
4) 1,3-Diaxial interaction: the axial methyl group is so close to the two axial