Page 41 - Basic physical chemistry for the atmospheric sciences

Chemical thermodynamics 27

listed in chemical tables (a selection of S0 values is given in Appendi x
V) .
The entropy changes associated with the forward reaction of the
general chemical reaction ( . 5) is given by
1
S0
LlS0 = [g S 0 (G) + hS 0 (H) + . . . ] - [a (A) + bS 0 (B) + . . . ] (2.24)
The following exercise illustrates the procedure.
Exercise 2 .5. Calculate the change in entropy LlS0 at 298K associ­
ated with the reaction
2S02(g) + 02(g)� 2S0 (g)
3
Solution. From Appendix V we see that the absolute molar entrop­
ies 5° of S02(g), Oi(g), and S03(g) at 298K are 248. 1 , 205.0, and 256. I
1
J mol- 1 deg.- Therefore, from Eq. (2.24)
LlS0 = {2S [S03(g)] - 2 S0 [S02(g)] - S 0 [02(g)]}
0
= {2(256. l) - 2(248. 1 ) - (205.0)}J deg- I
LlS0 = - 1 8 9.0 J deg- I
Note that the reaction decreases the number of molecules and the
entropy decrease . In general, if a chemical reaction decreases the
s
number of gaseous molecule , it decreases the entropy of a system;
s
conversely, if a chemical reaction increases the number of gaseous
molecules, it increases the entropy of the system.

2.5 Criteria for equilibrium and spontaneous transformation
If a system is in equilibrium with its surroundings, every possible
infinitesimal transformation i s reversible. Hence, a necessary condi­
tion for equilibrium is that Eq. (2. 2 0b) holds for all infinitesimal trans­
formation ; that i s , the sum of the entropy of the system and its
s
surroundings is constant. This is the most general criterion for a sys­
tem to be in equilibrium. Similarly, the most general criterion for
a spontaneous transformation is given by Eq. (2.20c); that is, the
transformation must result in an increase in the sum of the entropy of
the system and its surroundings. However, these criteria are difficult
to apply in practice because they involve the system and its surround­
ings, rather than the system alone.
To develop criteria for equilibrium and spontaneous transformations
that involve only the system, we introduce a new function of state,
called the Gibbs f r ee energy (G, or g for unit mass) which is defined by