Question

Following are the alternative chair conformations for trans-1,4-dimethylcyclohexane:

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Using the data for ΔG for monosubstituted cyclohexanes at room temperature (25ºC) and the representative value* for the gauche interaction of two equatorially positioned substituents in the 1,2-position:

a) Calculate the difference in the Gibbs free energy between the second and first conformation including the algebraic sign. kJ/mol

b) Given your value in (a), calculate the percent of the chair, indicated as B, presented in an equilibrium mixture of the conformers at 25ºC. %

*The actual value will depend on the substituents.

The values of the gas constant and the temperature for 25ºC are 8.314 JK-1mol-1 and 298 K respectively.

Following are the alternative chair conformations for trans-1,4-dimethylcyclohexane: CH3 • H₃C CH₃ CH3 Using the data for AG for monosubstituted cyclohexanes at room temperature (25°C) and the representative value* for the gauche interaction of two equatorially positioned substituents in the 1,2-position: axial equatorial AGº (kJ/mol) Group -0.8 NH2 -2.4 CH; -3.9 1,2-gauche Group CEN Br OH AGº (kJ/mol) -5.9 -7.3 3.8 a) Calculate the difference in the Gibbs free energy between the second and first conformation including the algebraic sign. kJ/mol b) Given your value in (a), calculate the percent of the chair, indicated as B, presented in an equilibrium mixture of the conformers at 25°C. % *The actual value will depend on the substituents. The values of the gas constant and the temperature for 25°C are 8.314 JK 'moland 298 K respectively.

Answer 1

CH3 - Group CEN Br OH Axial AGO (kylmol) -0.8 -2.4 -309 Equatorial AGroup NH2 CH3 1,2-guache AG° (kJ/mol asig -73 3.8 For these two chair conformation, Difference in Gobb's free energy = AG° Can axial -CH3 + an equatorial cm / And ran axial -Cha tan equatorial) Criz J = -7,3 +(-713) AGO = -14.6 kj/mol / A Gº = - RT in Keq. Geven values, R: 8.314 JK' molt T= 298 K fago we find in @ AGO --14.6 kJ/mol = -14600 J/mol do keq = -AGO RT

Date Jn Req = - = (-146002 L 8:314 x298 14 600 8.314x298 14600 2477, 572 | Un keq = 5,8928 ] Keq = Antiin (5,8928) I keq = 1362:41 . 3:6341 (diequatorial chair conformation) diaxial chair conformation) given instant at room temperature, Thus, at any Approximately Bo 362.4L x 100 363.4) 0.997 x 100 99.72 olo 99,72% The percent of the chair , indicated as B i presented In an equilibrium micture of the conformer at 25°C