BioPHYSICAL chemistry

96 PARTI THERMODYNAMICS AND KINETICS

when XA=0 and XB=1. For intermediate val-

ues, the logarithms are always negative and ΔG

is always negative. Thus, ΔGwill have a para-

bolic shape with a minimum at XA=XB=0.5

(Figure 5.2).

If no other factors are involved, then the dis-

tribution of A and B could change with time,

with the average value being equal amounts,

as this represents the state with the lowest

energy. When enthalpy is involved, the situ-

ation changes, as seen for an ideal gas. Con-

sider the Gibbs energy for the reaction, (ΔG)rec,

which is the difference in the chemical poten-

tials between the reactants and products. For

an ideal gas the chemical potentials can be

written in terms of the total pressure,P, and the

partial pressures,PAandPB:

(db5.2)

(db5.3)

The difference in the standard chemical potentials is usually referred to as the Gibbs energy

of reaction at standard conditions or the standard Gibbs energy of reaction, (ΔG)°rec. Using

the standard Gibbs energy of reaction in eqn db5.3 yields:

(db5.4)

The minimum of the Gibbs energy will occur when it is zero and the reaction will neither

go forwards nor backwards, because the slope is zero. At this equilibrium point:

()()lnΔΔGGRT (db5.5)

P

rec rec P

== 0 ° + B

A

()()lnΔΔGGRT

P

rec rec P

=°+ B

A

lnlnlnln

x

y

z

y

xy

yz

x

z

−= =

0

0.4

0.2

0.6

0.8

0 0.5 1

Gibbs energy of mixing,

ΔG/nRT

Composition, XA

Figure 5.2The Gibbs energy of mixing for

different mole fractions of component A.

()ΔGRTln

P

rec P

=− +μμBA B

A

00

()ΔGRB Tln

P

P

rec=−= +μμμAB^0 B− −μA RTT

P

P

(^0) ln A