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