Physical Chemistry , 1st ed.

i

H

ni



S,p,nj(ji)

(4.52)

i

n

A

i



T, V, nj(ji)

(4.53)

However, given the usefulness ofG, the free energy–based definition ofwill

be most useful to us.

Chemical potential is a measure of how much a species wants to undergo a

physical or chemical change. If two or more substances exist in a system and

have different chemical potentials, some process would occur to equalize the

chemical potentials. Thus, chemical potential allows us to begin a considera-

tion of chemical reactions and chemical equilibrium. Although we have con-

sidered chemical reactions in some examples (mostly from a products-minus-

reactants change in energy or entropy), we have not focused on them. This will

change in the next chapter.

4.9 Fugacity

We preface our application of thermodynamics to chemical reactions by defin-

ing fugacity, a measure of the nonideality of real gases. First, let us justify the

need to define such a quantity.

In developing theory, we assume ideal materials, and we have done just

that in thermodynamics. For example, the use of the “ideal gas” is common

throughout these chapters. However, there is no such thing as a truly ideal

gas. Real gases do not obey the ideal gas law and have more complex equa-

tions of state.

As expected, the chemical potential of a gas varies with pressure. By anal-

ogy to equation 4.45:

GnRTln 

p

p

f

i



we might also submit that, because chemical potential is defined in terms of

G, we have a similar equation for the change for an ideal gas:

RTln 

p

p

f

i

 (4.54)

We can write both of these equations in a different fashion, by recognizing

that the signs on Gand represent a change, so we can write Gor as

GfinalGinitialor finalinitial:

GfinalGinitialnRTln 

p

p

f

i



finalinitialRTln p

p

f

i



Suppose that for both equations, the initial state is some standard pressure, like

1 atmosphere or 1 bar. (1 atm 1.01325 bar, so very little error is introduced

by using the non-SI-standard 1 atm.) We will denote the initial conditions with

a ° symbol, and bring the initial energy quantity over to the right side of the

equation. The “final” subscripts are deleted, and the equations are now written

as Gor at any pressure p, calculated with respect to G° and ° at some stan-

dard pressure (that is, 1 atm or 1 bar):

110 CHAPTER 4 Free Energy and Chemical Potential