Chapter 2, Problem 2.46P

Interpretation Introduction

Interpretation:

When cyclohexane is substituted by an ethynyl group, the energy difference between axial and equatorial conformations is only $\text{1}\text{.7kJ(0}\text{.41kcal)/mol}$.  The conformational equilibrium for methyl cyclohexane with that of ethynyl cyclohexane has to be compared and the difference between the two structures has to be accounted.

Concept Introduction:

The difference in strain energy between the axial and equatorial conformations can be calculated by the ratio at equilibrium using the equation of the Gibb’s free energy (${\text{ΔG}}^{\text{0}}$).  The equation can be given as

  ${\text{ΔG}}^{\text{0}}{\text{= -RT ln K}}_{\text{eq}}$

The terms in the above equation are explained as

${\text{ΔG}}^{\text{0}}$ = Gibb’s free energy at equilibrium

$\text{R}$ = Universal gas constant

$\text{T}$ = Temperature (in Kelvins)

${\text{K}}_{\text{eq}}$ = Equilibrium constant

The universal gas constant value is $\text{8}\text{.314 J}{\text{.K}}^{\text{-1}}{\text{.mol}}^{\text{-1}}\text{ or 1}\text{.987 cal}{\text{.K}}^{\text{-1}}{\text{.mol}}^{\text{-1}}$.  The value of temperature in kelvin is ${\text{0}}^{\text{0}}\text{C = 273K}$.