Page 132 - Essentials of physical chemistry

94 Essentials of Physical Chemistry

ð T 2 3 4
0 0 Da þ DbT þ DcT þ DdT þ DeT
rxn
rxn
T
DS (T) ¼ DS (298) þ dT
298
which is easily integrated:

T Dc Dd
3
0
3
0
DS (T) ¼ DS (298) þ Da ln 2 2 (T (298) )
rxn rxn þ Db(T 298) þ (T (298) ) þ
298 2 3
De 4 4
(T (298) ):
4
þ
The main difference in the entropy integration is in the first natural logarithm term.
TROUTON’S RULE=OBSERVATION
One curiosity of entropy is a relationship between boiling points and heats of vaporization. At an early
age, F.T. Trouton (1863–1922) observed a pattern in boiling points and published two papers on a
trend now known as ‘‘Trouton’s rule.’’ This rule falls within the realm of familiar rules in organic
chemistry, which often have exceptions but are still useful. Basically Trouton’s rule states that

DH vap
10:5 R 88 J= K:

T bp
In use, this rule requires the boiling point in 8K, and it actually works quite well for covalent organic
compounds where there is no H-bonding, so that covers many cases in organic chemistry. It is poor
for water, carboxylic acids, and alcohols due to the complication of H-bonding but overall,
Trouton’s rule is useful to estimate the heat of vaporization if the boiling point is known or to
estimate the boiling point temperature if the heat of vaporization is known.
We can see in Table 5.2 that there is no trend in the entropies of fusion for melting points of a
range of elements or compounds. On the other hand, Table 5.3 shows a near constancy of the
entropy of vaporization with notable exceptions for water and acetic acid, which clearly have strong
internal H-bonding in the liquid phase. Trouton’s rule is more of an ‘‘observation’’ than a derivable
equation but still useful for ‘‘back-of-the-envelope’’ estimation of boiling points or heats of
vaporization.

TABLE 5.2
Entropy of Fusion for Selected Materials

Element=Compound T mp (8C) DH fus (kJ=mol) (DH fus =T mp )(J= K) calc

H 2 O 0.000 6.01 22.002
S monoclinic 115.21 1.721 4.431
Na 97.794 2.60 7.009
K 63.5 2.335 6.936
Mg 650 8.48 9.186
Pb 327.462 4.774 7.949
113.7 15.52 40.119
I 2
5.49 9.87 35.422
C 6 H 6
Acetic acid 16.64 11.73 40.478
Naphthalene 80.26 19.01 53.790