Chemistry - A Molecular Science

process is spontaneous in the reverse direction at standard conditions. Equilibrium in this case is attained when P

PA

, so there is more reactant thB

an product at equilibrium and the

reaction A

→

B is not extensive. We conclude that

GΔ

o gives us the extent of the

reaction

.

-^
ΔG

o << 0: Extensive as much more product

than reactant is present at equilibrium.

-^
ΔG

o >> 0: Not extensive as much more reactant than product is present at equilibrium.

-^
ΔG

o ~ 0: The amounts of reactant and product at equilibrium are comparable.

The temperature dependence of the standard fr

ee energy and, therefore, the extent of

reaction can be determined with Equation 9.6 (

GΔ

o =

HΔ

o – T

SΔ

o), which shows that a

plot of free energy versus temperature is a straight line with an intercept of

HΔ

o and a

slope of -

SΔ

o. At low temperatures, the T

SΔ

o term is negligible, so

ΔG

o has the same sign

as

ΔH

o at low T

, but, at high temperatures, the T

SΔ

o term can dominate if

SΔ

o is not

negligible, so

ΔG

o can have the same sign as -

ΔS

o at high T

. Figure 9.5 treats five

representative reactions, and Table 9.3 summarizes the conclusions.

9.9

ACTIVATION ENERGY

Thermodynamics considers only the reactants and products, while

kinetics

is concerned

with the path used by the reactants to achi

eve the products. The energetics of a reaction are

followed along a

reaction coordinate

, which is a combination of intermolecular distances,

bond angles, and bond lengths that represents th

e molecular course of the reaction. Most

reactions occur as a series of simple steps, which taken together comprise what is known as the

reaction mechanism

. However, we examine the following displacement of iodide

by hydroxide ion, which takes place by a simple, one-step mechanism.

I

H CHH

CO

H^

H HH

+ OH

1-

1- I

+

The reaction involves breaking one C-I bond and forming one C-O bond, so we can estimate

the enthalpy of reaction from tabulated bond energies to be

HΔ

o ~ D

(C-I)

• D

(C-O)

= 234 - 358 or about -120 kJ/mol. The reaction takes place in solution, while bond energies apply to gas phase reactions only, so

our number is not expected to be accurate.

However, the fact that the estimated

HΔ

o is large and negative is important. There are no

gases involved, so

SΔ

o is expected to be small, and we make the approximation that

GΔ

o ~

HΔ

o < 0, so the reaction is expected to be extensive.

The hydroxide ion attacks the carbon by inserting itself into the center of the plane

T

DG

o=-TS

D

o

DH

o

DG

o<0

DG Extensive

o>0

Not extensive

0 0

A

B C

D

E

Figure 9.5 Standard free energy and temperature Reactions in the yellow region ar

e not extensive, but those in the

green region are. A)

ΔH

o > 0 and

ΔS

o > 0. At low T the unfavorable

ΔH

o term

dominates, so

ΔG

o > 0 and the reaction is not extensive. At high

T, the favorable entropy terms dominates, so

ΔG

o < 0 and the

reaction is extensive.

B)

ΔH

o > 0 and

ΔS

o < 0. Both terms are unfavorable, so the reaction

is never extensive.

C)

ΔH

o < 0 and

ΔS

o < 0. At low T, the favorable

ΔH

o term dominates

and

ΔG

o < 0 and the reaction is extensive. At high T, the

unfavorable

ΔS

o term dominates, so

ΔG

o > 0 and the reaction is

not extensive.

D)

ΔH

o < 0 and

ΔS

o > 0. Both terms are favorable, so the reaction is

extensive at all T.

E)

ΔH

o < 0 and

ΔS

o ~ 0.

ΔG

o has the same sign as

ΔH

o at all T.

Table 9.3

Extent of Reaction

ΔH

o^

ΔS

o^

ΔG

o < 0, extensive reaction

A) + + high T, where

⎟ T

ΔS

⎟ >

⎟^ Δ

H⎟

B) + - no T C) - - low T, where

⎟^ Δ

H⎟

>⎟

TΔ

S⎟

D) - + all T E)

• 
  

~0 all T

Chapter 9 Reaction Energetics

© by

North

Carolina

State

University