Physical Chemistry Third Edition

4.1 Criteria for Spontaneous Processes and for Equilibrium: The Gibbs and Helmholtz Energies 157

In the case of constant temperature and constant pressure withPequal toP(trans-

mitted), Eq. (4.1-24) is

dU−TdS+PdV−dwnetdG−dwnet≤0(TandPconstant)

dG≤dwnet (TandPconstant) (4.1-31)

For a finite process

∆G≤wnet (TandPconstant) (4.1-32)

It is possible to increase the Gibbs energy of a nonsimple system at constantTandP

by doing net work on the system, but the increase in the Gibbs energy cannot be greater

than the net work done on the system. In electrolysis or charging a battery, a chemical

reaction is caused to proceed in the nonspontaneous direction (the direction of increase

of the Gibbs energy) by passing an electric current through an electrochemical cell,

performing net work.

A nonsimple system can do work on the surroundings by lowering its Gibbs energy,

but Eq. (4.1-31) provides a limit to the net work that can be done on the surroundings:

dwnet,surr≤−dG (TandPconstant) (4.1-33)

For a finite process,

wnet,surr≤−∆G (TandPconstant) (4.1-34)

To do net work on the surroundings at constantTandP, a process with a negative

value of∆Gmust be found.

Equilibrium Criteria for Nonsimple Systems

If a system at equilibrium undergoes an infinitesimal change at constantTandV,

dA−dwnet 0

(equilibrium,

constantTandV)

(4.1-35)

In the case of constantTandP,

dG−dwnet 0

(equilibrium,

constantTandP)

(4.1-36)

The equilibrium state of a nonsimple system is affected by the agent that can do net

work on it. For example, a galvanic cell such as a lead storage battery has an equilibrium

state that depends on the external voltage applied to it. With an external voltage you

can charge a lead storage battery to an equilibrium state with large amounts of reactants

(Pb, PbO 2 , and H 2 SO 4 ). If you remove the external voltage and attach a short circuit,

the battery will tend toward an equilibrium state in which the battery is fully discharged

and the reactants are depleted, leaving a large amount of products (PbSO 4 ).