6.22.In words, explain what slope the Clapeyron equation
can calculate. That is, a plot of what measurement with re-
spect to what other measurement can be calculatedby equa-
tion 6.9?
6.23.Consider the sulfur solid-state phase transition in exer-
cise 6.19. Given that transHfor the rhombic-to-monoclinic
phase transition is 0.368 kJ/mol, use equation 6.12 to estimate
the pressure necessary to make the rhombic phase stable at
100°C. Additional necessary data is given in exercise 6.19.
How does this pressure compare to the answer in 6.19?
6.24.If it takes 1.334 megabars of pressure to change the
melting point of a substance from 222°C to 122°C for a change
in molar volume of 3.22 cm^3 /mol, what is the heat of fusion
of the substance?
6.25.Reusable hot-packs sometimes use the precipitation of
supersaturated sodium acetate or calcium acetate to give off
heat of crystallization to warm a person. Can the conditions of
this phase transition be understood in terms of the Clapeyron
or the Clausius-Clapeyron equation? Why or why not?
6.26.Four alcohols have the formula C 4 H 9 OH: 1-butanol, 2-
butanol (or sec-butanol), isobutanol (or 2-methyl-1-propanol),
and tert-butanol (or 2-methyl-2-propanol). They are examples
of isomers,or compounds that have the same molecular for-
mula but different molecular structures. The following table
gives data on the isomers:
Compound vapH (kJ/mol) Normal boiling point (°C)
1-Butanol 45.90 117.2
2-Butanol 44.82 99.5
Isobutanol 45.76 108.1
tert-Butanol 43.57 82.3
Using the Clausius-Clapeyron equation, rank the isomers of
butanol in order of decreasing vapor pressure at 25°C. Does
the ranking agree with any conventional wisdom based on the
vapHvalues or the normal boiling points?
6.27.What is the rate of change of pressure as temperature
changes (that is, what is dp/dT) for the vapor pressure of naph-
thalene, C 10 H 8 , used in mothballs, at 22.0°C if the vapor pres-
sure at that temperature is 7.9
10 ^5 bar and the heat of va-
porization is 71.40 kJ/mol? Assume that the ideal gas law holds
for the naphthalene vapor at that temperature and pressure.
6.28.Using the data in the previous problem, determine the
vapor pressure of naphthalene at 100°C.
6.29.In high-temperature studies, many compounds are va-
porized from crucibles that are heated to a high temperature.
(Such materials are labeled refractory.) The vapors stream out
of a small hole into an experimental apparatus. Such a crucible
is called a Knudsen cell.If the temperature is increased linearly,
what is the relationship to the change in the pressure of the
vaporized compound? Can you explain why it is important to
be careful when vaporizing materials at high temperatures?
6.30.At what pressure does the boiling point of water be-
come 300°C? If oceanic pressure increases by 1 atm for every
10 m (33 ft), what ocean depth does this pressure correspond
to? Do ocean depths that deep exist on this planet? What is
the potential implication for underwater volcanoes?
6.31.For liquid droplets, the unequal interactions of the liq-
uid molecules with other liquid molecules at a surface give rise
to a surface tension,. This surface tension becomes a com-
ponent of the total Gibbs free energy of the sample. For a
single-component system, the infinitesimal change in Gcan
be written as
dGSdTV dpphasednphasedA
where dArepresents the change in surface area of the droplet.
At constant pressure and temperature, this equation becomes
dGphasednphasedA
For a spherical droplet having radius r, the area Aand vol-
ume Vare 4r^2 and^43 r^3 , respectively. It can therefore be
shown thatdA 2
rdV (6.24)(a)What are the units on surface tension ?
(b)Verify equation 6.24 above by taking the derivative of A
and V.
(c)Derive a new equation in terms of dV, using equation 6.24.
(d)If a spontaneous change in phase were to be accompa-
nied by a positive dGvalue, does a large droplet radius or a
small droplet radius contribute to a large dGvalue?
(e)Which evaporates faster, large droplets or small droplets?
(f)Does this explain the method of delivery of many perfumes
and colognes via so-called atomizers?6.6 & 6.7 Phase Diagrams, Phase Rule, and
Natural Variables
6.32.Explain how glaciers, huge masses of solid ice, move.
Hint:see equation 6.22.
6.33.Show that the units on either side of equations 6.18
and 6.19 are consistent.
6.34.Use a phase diagram to justify the concept that the
liquid phase can be considered a “metastable” phase, de-
pending on the pressure and temperature conditions of the
system.
6.35.Use the phase diagram of water in Figure 6.6 and
count the totalnumber of phase transitions that are repre-
sented.164 Exercises for Chapter 6