9.7
FREE ENERGY AND REACTION SPONTANEITY
The second law allows us to predict the spontaneity of a reaction from the sign of
SΔ
univ
,
but in order to use this predictive power, we need an expression for
SΔ
univ
that contains
only system quantities. We begin by dividing the entropy change in the universe into its system and surroundings components:
SΔ
univ
=
S + Δ
SΔ
sur
. Δ
S is already a system quantity,
so we need only obtain an expression for
SΔ
in terms of system quantities. We do so by sur
realizing that the entropy of the surroundi
ngs changes because the surroundings exchange
heat with the system, q
sur
= -q.* At constant temperature and pressure, q =
H, so qΔ
= sur
- Δ
H, which can be substituted into Equation 9.5 to yield
SΔ
sur
= -(
ΔH
/T
). Further
substitution of this form of
ΔS
sur
into
ΔS
univ
=
ΔS +
ΔS
sur
yields
ΔS
univ
=
ΔS -
ΔH T
Multiplying both sides by -T and rearranging, we obtain -T
ΔS
univ
=
ΔH - T
ΔS. T
ΔS
univ
is a
function of system quantities alone, so it too
is a system quantity, which is called the
Gibbs free energy change (
ΔG)
. Setting
ΔG
= -T
ΔS
univ
, we obtain Equation 9.6.
G = Δ
H - TΔ
S Eq. Δ
9.6
ΔG is negative when
ΔS
univ
is positive, so we conclude that spontaneous processes at
constant temperature and pressure are those th
at decrease the free energy of the system;
i.e
., those for which
ΔG < 0. Thus, we must modify our initial hypothesis that spontaneous
reactions are those that go downhill in ener
gy to spontaneous reactions at constant
temperature and pressure are those that go do
wnhill in Gibbs free energy. Equation 9.6
indicates that there are two components to the free energy change.
* For example, the heat that is gi
ven off in an exothermic reaction is
absorbed by the surroundings, which causes the entropy of the surroundings to increase by q/T.
Products
Reactants Products
Reactants
energy required
unfavorable
energy liberated
favorable
H > 0, endothermicD
H < 0, exothermicD
potentialenergy
(a)
(b)
Figure 9.3 Enthalpy change (a) Energy is required in an endothermic reaction because the potential energy of the products is gr
eater than that of
the reactants.
(b) Energy is released in an exothermic reaction because the potential energy of the reactants is
greater than that
of the products.
Products
Reactants Products
Reactants
-T S>0Dunfavorable
-T S<0favorable
D
(a)
(b)
Figure 9.4 T
ΔS energy
(a) Reactions that increase constraints require –T
ΔS J of energy.
(b) Reactions that remove constraints release T
ΔS J.
1.
HΔ
is the energy absorbed (-
H is the energy released) when Δ
the potential energy of the
reactants is changed to that of the products. In
Figure 9.4a, the products are at higher potential
energy than the reactants, so
the reaction is endothermic (
H > 0). If this process is to occur Δ
spontaneously, energy must be supplied by the T
S term; Δ
i.e
., Δ
S > 0 for spontaneous
processes in which
H > 0. The process in Figure 9.3b is exothermic (Δ
H < 0). The released Δ
energy can be used to decrease
the entropy of the system if
S < 0, but any released energy Δ
that is not used to decrease entropy can be used to do work.
TΔ
S is the energy required to decrease the entropy (+T
S is the energy released when the Δ
entropy increases). In the reaction shown in Figure 9.4a,
S < 0, so -TΔ
S joules of energy must Δ
be supplied from
H to decrease the entropy if the Δ
process is to be spontaneous (
G < 0). Δ
S Δ
> 0 for the reaction shown in Figure 9.4b, so T
S joules of energy are released. The released Δ
energy can be used to increase the potential
energy of the system
if the process is
endothermic, but any released T
S energy that is not used to do so can be used to do work. Δ
Chapter 9 Reaction Energetics
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Carolina
State
University