7.2 The Gibbs Phase Rule
7.1.Consult Example 7.1 and assume that now your mixed
drink has an olive in it. Now how many degrees of freedom are
there? What might you select as the variables to be specified?
7.2.Referring to Example 7.2, how many degrees of freedom
are specified when there is only Fe 2 (SO 4 ) 3 in the system?
7.3.How many phases are necessary in a three-component
system if you want no degrees of freedom?
7.4.Can there ever be a negative number of degrees of freedom
for any possible one-component physical system at equilibrium?
7.5.For the following chemical equilibrium in an enclosed
system, how many degrees of freedom are there?
2NaHCO 3 (s) Na 2 CO 3 (s) H 2 O () CO 2 (g)7.6.The production of nitrogen gas for automobile airbags
takes advantage of the following chemical reaction:
4NaN 3 (s) O 2 (g) →6N 2 (g) 2Na 2 O (s)If this reaction were in equilibrium, how many degrees of free-
dom would be necessary to describe the system?
7.3 Liquid/Liquid Systems
7.7.Assuming that the vapors act like an ideal gas, what is the
minimum amount of H 2 O needed in a 5.00-L system at 25.0°C
to ensure that there is a liquid phase in equilibrium with a va-
por phase? What is the minimum amount of CH 3 OH needed
to ensure a liquid phase and vapor phase under the same con-
ditions? The equilibrium vapor pressures of H 2 O and CH 3 OH at
this temperature are 23.76 and 125.0 torr, respectively.
7.8.For a solution of H 2 O and CH 3 OH in which xH 2 O0.35,
what are the mole fractions of H 2 O and CH 3 OH in the vapor
phase? Use conditions and data from exercise 7.7.
7.9.What is the activity of liquid H 2 O of a multicomponent
solution in which the vapor pressure of H 2 O is 748.2 mmHg
at 100.0°C?
7.10.Derive equation 7.19.
7.11.Derive equation 7.19 but in terms of y 2 , not y 1.
7.12.Determine the total equilibrium pressure of the vapor
in equilibrium with a 11 molar ratio of hexane (C 6 H 14 ) and
cyclohexane (C 6 H 12 ) if the equilibrium vapor pressures of the
two components are 151.4 and 97.6 torr, respectively.
7.13.Many police departments use breath tests to check for
drunk drivers. What would be the approximate partial pressure
of ethanol in expired breath if the blood alcohol content is ap-
proximately 0.06 mole % (that is, xethanol0.0006)? The
equilibrium vapor pressure of C 2 H 5 OH at 37°C is 115.5 torr.
Use your answer to comment on the necessary sensitivity of
the test.
7.14.A solution of methanol (CH 3 OH) and ethanol (C 2 H 5 OH)
has a vapor pressure of 350.0 mmHg at 50.0°C. If the equi-
librium vapor pressures of methanol and ethanol were 413.5
and 221.6 mmHg, respectively, what is the composition of the
solution?
JQPJ7.15.Derive equation 7.23 from equation 7.19.
7.16.Determine the mole fractions of each component in the
vapor phase of the vapor in equilibrium with a 11 molar
ratio of hexane (C 6 H 14 ) and cyclohexane (C 6 H 12 ) if the equi-
librium vapor pressures of the two components are 151.4 and
97.6 torr, respectively.
7.17.Use equation 7.24 to show that limy 1 0 ptotp 2 * and
ylim 2 0 ptotp^1 *.
7.18.Why could one not use equation 7.24 directly to de-
termine the total pressure of the vapor in Example 7.5?7.19.What are (^) mixG and (^) mixSfor the combination of
1.00 mol of toluene and 1.00 mol of benzene at 20.0°C?
Assume that they mix to make an ideal solution.
7.4 Nonideal Liquid/Liquid Systems
7.20.Why is acetone used to rinse out wet glassware? (Hint:
Water has a boiling point of 100.0°C and acetone has a boil-
ing point of 56.2°C. There is also a low-boiling azeotrope com-
posed of the two molecules.)
7.21.Repeat Example 7.7, but assume that you start with a
solution that has x 1 0.1 using Figure 7.14 as the phase
diagram.
7.22.Repeat Example 7.7, but assume that you start with a
solution that has x 1 0.4 using Figure 7.15 as the phase
diagram.
7.23.How might you be able to distinguish an azeotrope
from a pure compound by purely physical means? (Hint:con-
sider other possible phase changes.)
7.24.Ethanol prepared by distillation is only about 95% pure
because it forms a low-boiling binary azeotrope with water.
“100%” ethanol can be made by adding a specific amount of
benzene to form a ternary azeotrope that boils at 64.9°C.
However, this ethanol should not be ingested! Why?
7.25.Figure 7.31 shows a phase diagram of H 2 O and ethyl-
ene glycol. Explain why this mixture, in an approximately
50 50 mixture, is used as a coolant and antifreeze in auto-
mobile engines.
Exercises for Chapter 7 203
EXERCISES FOR CHAPTER 7
10
60
0
Percent ethylene glycol
100
Temperature (
°C)
80604020
MP (H 2 O) 0 °C
MP (ethylene
glycol) 13 °C
0
10
20
30
40
50
Figure 7.31 A temperature-composition phase diagram of water and
ethylene glycol. Refer to exercise 7.25.
high T