Page 130 - Modern physical chemistry

6.7 The Clapeyron and Ehren/est Equations 121
-------0

II
I I
, I
, I
I
I
I
I

FIGURE 6.16 A unit cell of an ammonium chloride crystal
exhibiting one orientation of the hydrogen atoms in the
OisCI • isN X isH ammonium ion.

I
I
I
I
I
I
I I I I FIGURE 6.17 The other possible orientation of the hydrogen
0-------- atoms in the unit cell. In a completely ordered state, all unit
cells exhibit the same orientation, while in the completely
disordered state, both occur with equal probability through-
o isCI • isN X isH out the crystallite.

Here G(2) and G(l) are the Gibbs free energies of the given amount of substance in phases
(2) and (1), respectively.
Condition (6.26) holds at each point on the boundary between the two phases. So for
an infinitesimal change along the boundary, we have

[6.27J

Since fonnula (5.82) describes how G changes in each phase, equation (6.27) becomes

[6.28J

Here the subscripts identify the phase in which volume V and entropy 8 are deter-
mined. Since pressure P and temperature T are the same in both phases, they do not
need subscripts.
Rearranging (6.28) yields
dP _ 8(2) -8(1) /).8
-- =-, [6.29J
dT ~2) - ~1) ~V

where AS is the change in entropy and ~ V the change in volume for the given amount of
substance undergoing the transition.