Physical Chemistry , 1st ed.

Solution

a.The specific chemical process that is the freezing of mercury is

Hg () →Hg (s)

which occurs at 38.9°C or 234.3 K. When the liquid phase goes to the solid

phase, heat must be lost, so the process is inherently exothermic. Therefore

transHis actually 2.33 kJ/mol, or 2330 J/mol (not the positive 2.33 kJ/mol

given for fusHfor Hg). To determine the entropy change, we have

S

 2

2

3

3

3

4

0

.3

J/

K

mol

9.94

mo

J

lK

The entropy change is negative, meaning the entropy decreases. This is what’s

expected for a liquid-to-solid phase transition.

b.The vaporization of carbon tetrachloride is represented by the reaction

CCl 4 () →CCl 4 (g)

which at normal atmospheric pressure occurs at 77.0°C, or 350.2 K. In order

to go from the liquid phase to the gas phase, energy must be put into the

system, which means that this change is inherently endothermic. Therefore

we can use vapHdirectly. For the entropy change, we have

S ^29

3

,

5

8

0

9

0

2

J

K

/mol85.35

mo

J

lK

It was noted as early as 1884 that many compounds have a vapSof around

85 J/molK. This phenomenon is called Trouton’s rule.Deviations from

Tr o u t o n’s rule are marked for substances that have strong intermolecular in-

teractions, like hydrogen bonding. Table 6.2 gives a list ofvapHand vapS

values for some compounds. Hydrogen and helium have very small entropies

of vaporization. Compounds that have strong hydrogen bonding, like water

(H 2 O) and ethanol (C 2 H 5 OH), have higher entropies of vaporization than ex-

pected. Table 6.2 also lists fusHand fusSvalues for these compounds.

6.4 The Clapeyron Equation

The previous discussion detailed general trends in the behavior of equilibria.

In order to get more quantitative, we need to derive some new expressions.

Equation 6.3, when generalized, states that the chemical potential of two

phases of the same component are equal at equilibrium:

phase1phase2

By analogy to the natural variable expression for G, at a constant total amount

of substance the infinitesimal change in ,d, as pressure and temperature

change infinitesimally is given by the equation

dSdTVdp (6.8)

(Compare this to equation 4.17.) If the multiphase equilibrium experienced an

infinitesimal change in Tor p, the equilibrium would shift infinitesimally but

would still be at equilibrium. This means that the changein phase1would

equal the change in phase2. That is,

dphase1dphase2

148 CHAPTER 6 Equilibria in Single-Component Systems