Page 112 - Modern physical chemistry

102 Entropy and the Second Law

and
In Co =ax.
c
But increasing x from 0 to 10.0 cm causes c to drop to 1I2co. We have

a= 1 In~= In2
10.0 cm 1 10.0 cm
-co
2
So for the thermodynamic force, we find

I
alnc (In2)(8.31451 J K- mOI-IX298.15 K)
F=-RT--=aRT= = 1.72 x 10 4 NmOrl.
ax 10.0 x 10- 2 m

Example 5.8
Suppose that the axis of the container in example 5.7 is oriented vertically and deter-
mine the gravitational force acting on the solute if its molar mass is 100 g mol-I.
We have
F = -Mg = -(0.100 kg mOI- I )(9.807 ms-2)= -0.98 N morl.

Note that this is negligible with respect to the thermodynamic force due to any appre-
ciable concentration gradient. In the laboratory, one can generally neglect gravitational
effects on molecules in solution.

5. 14 General Direction for a Process
According to the second law of thermodynamics, spontaneous changes in a system
cause the total entropy of the system and its interacting surroundings to increase. In this
way, the system moves from a less probable to a more probable state. When the total
entropy can no longer increase, a point of equilibrium has been reached. Thus, we have

~totaI ~ 0 [5.114]
on the average. Small deviations from (5.114) arise because of the fluctuations noted in
example 5.4.
For a process occurring at constant temperature and volume, the argument in section
5.9 applies. For the system by itself, we have

[5.115]
on the average. For a process occurring at constant temperature and pressure, the argu-
ment in section 5.10 applies. And for the system by itself, we have

!l.GT,p :s; 0 [5.116]
on the average,
In chapter 6, we will apply the equality in (5.116) to physical equilibria; in chapter 7,
to chemical equilibria.
A qualitative interpretation of condition (5.116) is useful. From definition (5.67), we
have
!l.GT,p = MI - T~. [5.117]