Consider the ring-flip equilibrium experienced by trans-1,4-difluorocyclohexane. Write the equilibrium such that the least stable chair...

Consider the ring-flip equilibrium experienced by trans-1,4-difluorocyclohexane. Write the equilibrium such that the least stable chair conformation is the product (this will cause the ΔE to be greater than (or equal to) zero.

T = 298 K
R = 8.315 J/mole-K

H - Substituent Interaction	1,3-Diaxial Strain (kJ/mole)
H ←→ F	0.5
H ←→ OH	2.1
H ←→ CH₃	3.8
H ←→ CH₂CH₃	4.0

ΔE - Enter a number greater than (or equal to) zero     (Tol: ± 0)
Enter the value of k_eq (solve ΔE = -RTlnk_eq)     (Tol: ± 0.01)
Estimate % most stable conformer from graph (page 120)     (Tol: ± 3)
Estimate % least stable conformer from graph (page 120)     (Tol: ± 3)
Calculate % most stable conformer from k_eq     (Tol: ± 1)
Calculate % least stable conformer from k_eq     (Tol: ± 1)

Expert Solution

PART 1: Consider the ring-flip equilibrium experienced by trans-1,4-difluorocyclohexane. Write the equilibrium such that the least stable chair conformation is the product (this will cause the ΔE to be greater than (or equal to) zero.

ANS: Conformation and sterioisomerism of trans-1,4-difluorocyclohexane.

trans-1,4-difluorocyclohexane, the diequatorial is the mosts stable arrangement is the "trans" isomer. Ring flipping of trans-1,4-difluorocyclohexane gives a conformation in which the fluro substituents are anti (dihedral angle of 180) to each other, but this is still trans, and this conformation is less stable because it has two axial substituents.

PART 2: T = 298 K; R = 8.315 J/mole-K

H - Substituent Interaction	1,3-Diaxial Strain (kJ/mole)
H ←→ F	0.5
H ←→ OH	2.1
H ←→ CH3	3.8
H ←→ CH2CH3	4.0

ΔE - Enter a number greater than (or equal to) zero (Tol: ± 0)

Enter the value of keq (solve ΔE = -RTlnkeq) (Tol: ± 0.01)

Estimate % most stable conformer from graph (Tol: ± 3)

Estimate % least stable conformer from graph (Tol: ± 3)

Calculate % most stable conformer from keq (Tol: ± 1)

Calculate % least stable conformer from keq (Tol: ± 1)

ANS:

H - Substituent Interaction	1,3-Diaxial Strain (kJ/mole)	2Diaxial Strain	keq	Axil : equatorial isomer
H ←→ F	0.5	1	- 0.404	1 : 2.5
H ←→ OH	2.1	4.2	- 1.69	1 : 0.6
H ←→ CH3	3.8	7.6	- 3.067	1 : 0.4
H ←→CH2CH3	4.0	8	- 3.229	1 : 0.3

*The axial isomer of isopropylcyclohexane contains two 1,3-diaxial interactions between isopropyl and hydrogen whereas the equatorial isomer of isopropylcyclohexane contains none. Thus, the axial isomer is

(2 x 0.12) kcal/mol = 0.24kcal/mol higher in energy and the equatorial isomer is favored.

ΔE = -RTlnkeq

keq = e(–∆E/ RT)

keq = e (1000)(8.315298) = 0.404

To get to whole number to obtain axil and equatorial ratio,

0.404 1

-------- : --------- = 1 : 2.5

0.404 0.404

Thus, the ratio of axial to equatorial (H ←→ F) that is present at 298k is ~ 1 : 2.5

I need more details to Estimate % most stable conformer from graph (Tol: ± 3)

Estimate % least stable conformer from graph (Tol: ± 3).

queen_honey_blossom answered 1 year ago

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