CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES
11.7 GIBBSENERGY ANDREACTIONEQUILIBRIUM 348
bc(^0) =n 1
A;0
G
(a)
bc
0 1
=nA;0
G
(b)
bc
0 1
=nA;0
G
(c)
Figure 11.16 Gibbs energy as a function of the advancement of the reaction A!B
in an ideal gas mixture at constantTandp. The initial amount of B is zero. The
equilibrium positions are indicated by open circles.
(a)ÅrG< 0. (b)ÅrGD 0. (c)ÅrG> 0.
The second term on the right side isnÅGmid(mix), the Gibbs energy of mixing pure ideal
gases A and B at constantTandpto form an ideal gas mixture of compositionyAandyB.
Since the curve ofÅGidm(mix) plotted againsthas a minimum (as shown in Fig.11.2on
page 305 ),G./ G.0/also has a minimum.
Figure11.16illustrates how the position of the minimum, which is the position of re-
action equilibrium, depends on the value ofÅrG. The more negative isÅrG, the closer
to the product side of the reaction is the equilibrium position. On the other hand, the more
positive isÅrG, the smaller is the value ofat equilibrium. These statements apply to any
reaction in a homogeneous mixture.
As the reaction A!B proceeds, there is no change in the total number of molecules,
and therefore in an ideal gas mixture at constant temperature and volume there is no pressure
change. The point of reaction equilibrium is at the minimum ofGwhen bothV andpare
constant.
The situation is different when the number of molecules changes during the reaction.
Consider the reaction A!2 B in an ideal gas mixture. As this reaction proceeds to the
right at constantT, the volume increases if the pressure is held constant and the pressure
increases if the volume is held constant. Figure11.17on the next page shows howG
depends on bothpandVfor this reaction. Movement along the horizontal dashed line in
the figure corresponds to reaction at constantTandp. The minimum ofGalong this line is
at the volume indicated by the open circle. At this volume,Ghas an even lower minimum
at the pressure indicated by the filled circle, where the vertical dashed line is tangent to one
of the contours of constantG. The condition needed for reaction equilibrium, however, is
thatÅrGmust be zero. This condition is satisfied along the vertical dashed line only at the
position of the open circle.
This example demonstrates that for a reaction occurring at constant temperature and