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7.35 The vapor pressure of SO (s) is 1.00 torr at 177.0 K and 7.43 Explain what is happening in the order–disorder lambda
2
10.0 torr at 195.8 K. The vapor pressure of SO (l) is 33.4 torr transition in HI(s). (Hint: This molecule is polar.)
2
at 209.6 K and 100.0 torr at 225.3 K. (a) Find the temperature 7.44 For T 10 2 K T T 10 9 K, measured C val-
l
P
l
and pressure of the SO triple point. State any approximations ues of liquid He obey the relation [J. A. Lipa et al., Phys. Rev.
2
made. (b) Find H of fusion of SO at the triple point. Lett., 76, 944 (1996)]
2
m
7.36 The normal melting point of Ni is 1452°C. The vapor a 1>2
C P >1J>mol-K2 1A¿>a2t 11 Dt Et2 B
pressure of liquid Ni is 0.100 torr at 1606°C and 1.00 torr at
1805°C. The molar heat of fusion of Ni is 4.2 kcal/mol. where A 5.7015, a 0.01285, D 0.0228, E
5
Making reasonable approximations, estimate the vapor pres- 0.323, B 456.28, and t 1 T/T . For T 10 6 K T
l
l
sure of solid Ni at 1200°C. T 10 8 K, the same equation holds except that A is re-
l
placed by A 6.094 and t is replaced by s T/T 1. (a)
l
Section 7.4 Assume that these expressions hold up to T and find C at T .
l
l
P
3
7.37 At 1000 K and 1 bar, V of graphite is 1.97 cm /mol (b) Find C / T at T . (c) Use a spreadsheet or other program
m P l
greater than that of diamond, and G° 6.07 kJ/mol. Find to graph C versus (T T )/T in the region close to T . (a is
f di P l l l
the pressure of the 1000 K point on the diamond–graphite called a critical exponent. There is a substantial theory de-
phase-transition line. voted to prediction of a and other critical exponents for con-
tinuous phase transitions. See J. J. Binney et al., The Theory of
7.38 The stable form of tin at room temperature and pressure is
white tin, which has a metallic crystal structure. When tin is used Critical Phenomena, Oxford, 1992.)
for construction in cold climates, it may be gradually converted
to the allotropic gray form, whose structure is nonmetallic. Use Section 7.7
Appendix data to find the temperature below which gray tin is 7.45 True or false? (a) Increasing the area of a liquid–vapor
the stable form at 1 bar. State any approximations made. interface increases U of the system. (b) The surface tension of
a liquid goes to zero as the critical temperature is approached.
7.39 In Example 7.7 in Sec. 7.4, we found 15100 bar as the
25°C graphite–diamond transition pressure. At 25°C, graphite 7.46 Verify (7.27) for the units of surface tension.
is more compressible than diamond. If this were taken into ac- 7.47 (a) Calculate the surface area of a 1.0-cm sphere of
3
count, explain why we would get a transition pressure greater gold. (b) Calculate the surface area of a colloidal dispersion of
than 15100 bar. 3
1.0 cm of gold in which each gold particle is a sphere of ra-
7.40 If B and C are two polymorphic forms of a solid and if dius 30 nm.
B is more stable than C at room T and P, prove that C must be
more soluble in water than B at room T and P. 7.48 Calculate the minimum work needed to increase the area
2
2
of the surface of water from 2.0 cm to 5.0 cm at 20°C. The
Section 7.5 surface tension of water is 73 mN/m at 20°C.
7.41 Sketch H versus T for (a) a first-order transition; (b) a 7.49 The surface tension of ethyl acetate at 0°C is 26.5 mN/m,
second-order transition; (c) a lambda transition where C is in- and its critical temperature is 523.2 K. Estimate its surface
P
finite at T . [Hint: Use Eq. (4.30).] Repeat the problem for S tension at 50°C. The experimental value is 20.2 mN/m.
l
versus T.
7.50 J. R. Brock and R. B. Bird [Am. Inst. Chem. Eng. J., 1,
7.42 For b-brass, let the sites occupied by Cu atoms at T 0 174 (1955)] found that for liquids that are not highly polar or
be called the C sites and let the T 0 Zn sites be called Z . At
0 0 hydrogen-bonded the constant g in (7.28) is usually well
0
any temperature T, let r be the number of atoms in right positions approximated by
(a Cu atom on a C site or a Zn on a Z ) and let w be the num-
0 0 2>3 1>3
ber of atoms on wrong positions (Cu on a Z site or Zn on C ). g 0 1P c >atm2 1T c >K2 10.432>Z c 0.9512 dyn>cm
0 0
The long-range-order parameter s is defined as s (r w)/
l l where P , T , and Z are the critical pressure, temperature, and
(r w). (a) What is s at T 0? (b) What is s if all atoms are c c c
l l compressibility factor. For ethyl acetate, P 37.8 atm, T
on wrong sites? Would this situation be highly ordered or highly c c
523.2 K, and Z 0.252. Calculate the percent error of the
c
disordered? (c) What is s at T , where the number of rightly and
l l Brock–Bird predicted value of g for ethyl acetate at 0°C. The
the number of wrongly located atoms are equal? (d) What is s
l experimental value is 26.5 dyn/cm.
in each of the drawings in Fig. 7.12? Let n be the total number
p
of nearest-neighbor pairs of atoms in b-brass and let n be the 7.51 Calculate g/l in Eq. (7.30) for the typical values l 10 cm
rp z z
number of right nearest-neighbor pairs (Cu–Zn or Zn–Cu). The and g 50 dyn/cm; express your answer in atmospheres.
short-range-order parameter s is defined as s 2n /n 1.
s s rp p
(e) What is s at T 0? (f ) What is s in the T → q limit Section 7.8
s s
of complete disorder? (g) What is s in each of the drawings in 7.52 True or false? (a) At equilibrium in a closed system with
s
Fig. 7.12? Note: Count only nearest-neighbor pairs; these no walls between phases, all phases must be at the same tem-
are pairs with one atom at the center of a square and one at the perature and at the same pressure. (b) For a two-phase system
corner of that square. (h) Sketch s and s versus T/T using the with a curved interface, the phase on the concave side is at
l s l
results of this problem and the information in Sec. 7.5. higher pressure than the other phase.