Chemistry - A Molecular Science

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.

2. 
   
   
   
   • 
     
   
   
   
   

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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