6.6 Phase Diagrams of Nonideal Mixtures 291
PROBLEMS
Section 6.6: Phase Diagrams of Nonideal Mixtures
6.50 a.Sketch the temperature–composition phase diagram of
phenol (substance 1) andp-toluidine (substance 2),
usingw 1 (the mass fraction of phenol) as the
independent variable. The melting temperature of
phenol is 40.7◦C and that ofp-toluidine is 43.7◦C. The
molar mass of phenol is 94.11 g mol−^1 , and that of
p-toluidine is 107.16 g mol−^1. There is a single
compound, which has a mass fraction of phenol equal
to 0.4676, and which melts congruently at 30◦C. The
eutectic betweenp-toluidine and the compound is at
145 ◦C and the other eutectic is at 10◦C.b. Redraw the phase diagram using the mole fraction as
the independent variable. What is the formula of the
compound?6.51 Describe what happens if one begins with a vapor phase
containing water and furfural with a water mole fraction
equal to 0.500, and gradually cools this mixture from
150 ◦Cto85◦C. Give the approximate temperatures at
which phase transitions occur.
6.52 Describe what happens if one begins with a small amount
of liquid water at 99.0◦C and gradually adds liquid furfural
to the water at constant temperature until one has a mixture
that has a mole fraction of furfural equal to 0.90. Give the
approximate mole fractions at which phase transitions
occur.
6.53 Draw a sketch of the solid–liquid temperature–
composition phase diagram of sodium and potassium.
There is a single compound, Na 2 K, which melts
incongruently at 6.6◦C to give essentially pure sodium and
a solution with sodium mole fraction equal to 0.42. The
melting temperature of sodium is 97.5◦C, and that of
potassium is 63◦C. There is a eutectic at− 12. 5 ◦C and a
sodium mole fraction equal to 0.15. There is some solid
solubility, which you should indicate qualitatively. Label
each area in the diagram with the number of independent
intensive variables corresponding to that phase.
6.54 Sketch cooling curves for mixtures of phenol (P) and
aniline (A) with aniline mole fractions equal to 0.26 (at the
eutectic between P and the compound AP), 0.35, 0.50, and
0.90. Describe what happens at each break in each curve.
6.55 Sketch the solid–liquid temperature–composition phase
diagram of CuCl (copper(I) chloride) and FeCl 3 (iron(III)
chloride). The melting temperature of CuCl is 430◦C and
that of FeCl 3 is 306◦C. There is a single compound,
CuCl·FeCl 3 , which melts near 320◦C. There is a eutectic
near 300◦C andx 0 .37, wherexis the mole fraction of
FeCl 3. There is a second eutectic near 260◦C and
x 0 .81. Label each area with the phase or phases present
and the number of independent intensive variables.6.56 Sketch the solid–liquid and liquid–vapor
temperature–composition phase diagram of titanium and
uranium. The two substances form a nearly ideal liquid
solution with a uranium boiling temperature of 1133◦C and
a titanium boiling temperature of 1660◦C. The melting
temperature of uranium is 770◦C, and that of titanium is
882 ◦C. There is a compound, TiU 2 , which melts at 890◦C.
The eutectic between the compound and uranium is at
uranium mole fraction 0.95 and 720◦C, and the eutectic
between titanium and the compound is at uranium mole
fraction 0.28 and 655◦C. Label each area with the number
of independent intensive variables.^116.57 From the following information, sketch the
temperature–composition phase diagram of lanthanum
(La) and antimony (Sb) usingxSb(the mole fraction of
antimony) on the horizontal axis.
The melting temperature of pure antimony is 631◦C and
the melting temperature of pure lanthanum is 921◦C. There
are four compounds: La 2 Sb (xSb 0 .333), La 3 Sb 2
(xSb 0 .400), LaSb (xSb 0 .500), and LaSb 2
(xSb 0 .667). La 2 Sb melts incongruently at 1460◦C,
giving La 3 Sb 2 (s) and a solution withxSb 0 .32. La 3 Sb 2
melts congruently at 1690◦C, giving a solution of La and
Sb withxSb 0 .400. LaSb melts incongruently at 1540◦C,
giving La 3 Sb 2 and a solution withxSb 0 .54. LaSb 2
melts incongruently at 1110◦C, giving LaSb and a solution
withxSb 0 .75. There is a eutectic between La and La 2 Sb
at 845◦C withxSb 0 .04. There is a eutectic between
LaSb 2 and Sb at 630◦C withxSb≈ 0 .99. There is no
significant solid solubility between any solid phases.6.58 a.Sketch a cooling curve for a mixture of lanthanum and
copper with a mole fraction of lanthanum equal to 0.30.
Label each break in the curve and say what phase or
phases are freezing out for each portion of the curve.(^11) The actual diagram might be more complicated. See Hansen,The
Constitution of Binary Alloys, McGraw-Hill, New York, 1958, pp. 1238ff.