Organic Chemistry

release more energy than it will consume. It will be an exergonic reaction

(Figure 3.3a). If the products have a higher free energy—are less stable—than the re-

actants, will be positive, and the reaction will consume more energy than it will

release; it will be an endergonic reaction(Figure 3.3b). (Notice that the terms

exergonicand endergonicrefer to whether the reaction has a negative or a posi-

tive respectively. Do not confuse these terms with exothermicand endothermic,

which are defined later.)

Therefore, whether reactants or products are favored at equilibrium can be indicat-

ed either by the equilibrium constant or by the change in free energy

These two quantities are related by the equation

where R is the gas constant or

because and Tis the temperature in degrees Kelvin

therefore,. (By solving Problem 13, you will see

that even a small difference in gives rise to a large difference in the relative con-

centrations of products and reactants.)

PROBLEM 13

a. Which of the monosubstituted cyclohexanes in Table 2.10 has a negative for the

conversion of an axial-substituted chair conformer to an equatorial-substituted chair

conformer?

b. Which monosubstituted cyclohexane has the most negative value of

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

d. Calculate for conversion of “axial”methylcyclohexane to “equatorial”methylcy-

clohexane at 25°C.

PROBLEM 14 SOLVED

a. The for conversion of “axial”fluorocyclohexane to “equatorial”fluorocyclohex-

ane at 25°C is (or Calculate the percentage of fluoro-

cyclohexane molecules that have the fluoro substituent in the equatorial position.

b. Do the same calculation for isopropylcyclohexane (whose at 25 °C is

or

c. Why does isopropylcyclohexane have a greater percentage of the conformer with the

substituent in the equatorial position?

SOLUTION TO 14a

axial equatorial

[fluorocyclohexane]

[fluorocyclohexane]

+

fluorocyclohexane

Now we must determine the percentage of the total that is equatorial:

fluorocyclohexane

=

1.53

1

equatorial

axial

[fluorocyclohexane]

[fluorocyclohexane]

equatorial

equatorial

[fluorocyclohexane]

axial

kcal

mol K

kcal

mol

∆G°−0.25 kcal/mol at 25 °C

∆G°=

=

=

===

1.53

1.53 1

=

+

1.53

2.53

==

−RT ln Keq

0 .422

1 .53

−1.986 298 K

.60

or

60%

−0.25 ×× 10 −^3 × ln Keq

ln Keq

Keq

• 2.1 kcal>mol, -8.8 kJ>mol).

¢G°

• 0.25 kcal>mol -1.05 kJ>mol).

¢G°

¢G°

¢G°?

¢G°

¢G°

(K=°C+273; 25 ° C=298 K)

mol-^1 K-^1 , 1 kcal =4.184 kJ)

(1.986* 10 -^3 kcal mol-^1 K-^1 , 8.314* 10 -^3 kJ

¢G°=-RT ln Keq

1 Keq 2 1 ¢G° 2.

¢G°,

¢G°

¢G°

Section 3.7 Thermodynamics and Kinetics 127

Josiah Willard Gibbs (1839–1903)

was born in New Haven, Connecti-

cut, the son of a Yale professor. In

1863, he obtained the first Ph.D.

awarded by Yale in engineering. After

studying in France and Germany, he

returned to Yale to become a profes-

sor of mathematical physics. His

work on free energy received little at-

tention for more than 20 years be-

cause few chemists could understand

his mathematical treatment and be-

cause Gibbs published it in

Transactions of the Connecticut

Academy of Sciences, a relatively

obscure journal. In 1950, he was

elected to the Hall of Fame for Great

Americans.

When products are favored at equilibri-

um, is negative and is greater

than 1.

≤G° Keq

When reactants are favored at equilibri-

um, is positive and is less

than 1.

≤G° Keq

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