Page 259 - Physical Chemistry

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7.18 Use the relation between entropy and disorder to explain 7.27 The vapor pressure of water at 25°C is 23.76 torr.
why the normal-boiling-point S of a hydrogen-bonded Calculate the average value of H of vaporization of water
vap m
m
liquid exceeds the Trouton–Hildebrand–Everett-rule value. over the temperature range 25°C to 100°C.
7.19 Given the normal boiling points 81.7 K for CO, 614 K 7.28 H of vaporization of water is 539.4 cal/g at the normal
for anthracene, 1691 K for MgCl , and 2846 K for Cu, (a) esti- boiling point. (a) Many bacteria can survive at 100°C by form-
2
mate H of each of these substances as accurately as you ing spores. Most bacterial spores die at 120°C. Hence, auto-
vap m,nbp
can; (b) use the end-of-chapter data sources to find the experi- claves used to sterilize medical and laboratory instruments are
mental H values and calculate the percent errors in pressurized to raise the boiling point of water to 120°C. At what
vap m,nbp
your estimates. pressure does water boil at 120°C? (b) What is the boiling point
of water at the top of Pike’s Peak (altitude 14100 ft), where the
7.20 Consider the following reversible isothermal two-step atmospheric pressure is typically 446 torr?
process: vaporization of one mole of liquid i at T nbp,i and 1 atm
to gaseous i with molar volume V m,i ; volume change of gas i 7.29 Some vapor pressures of liquid Hg are:
†
from V m,i to a certain fixed molar volume V . Show that if S m
m
for the two-step process is assumed to be the same for any t 80.0°C 100.0°C 120.0°C 140.0°C
liquid, one obtains the Trouton–Hildebrand–Everett rule P/torr 0.08880 0.2729 0.7457 1.845
vap m,nbp a R ln (T nbp /K), where a is a constant.
S
(a) Find the average H of vaporization over this temperature
m
range from a plot of ln P versus 1/T. (b) Find the vapor pressure
Section 7.3
7.21 True or false? (a) For a reversible phase change at con- at 160°C. (c) Estimate the normal boiling point of Hg. (d) Repeat
stant T and P, S H/T. (b) The relation d ln P/dT (b) using a spreadsheet Solver to minimize the sums of the
2
H /RT should not be applied to solid–liquid transitions. squares of the deviations of the calculated P values from the
m
2
(c) The relation d ln P/dT H /RT should not be applied to observed values.
m
solid–vapor transitions. (d) The relation d ln P/dT H /RT 2 7.30 Some vapor pressures of solid CO are:
m
2
(1/T) dT
T 2
should not be applied near the critical point. (e) T 1
T 2 (1/T) dT (ln T )/(ln T ). t 120.0°C 110.0°C 100.0°C 90.0°C
2
1
ln (T T ). (f) T 1 2 1
7.22 The normal boiling point of diethyl ether (“ether”) is P/torr 9.81 34.63 104.81 279.5
34.5°C, and its H is 6.38 kcal/mol. Find the vapor pres-
vap m,nbp (a) Find the average H of sublimation over this temperature
sure of ether at 25.0°C. State any approximations made. m
range. (b) Find the vapor pressure at 75°C.
7.23 Use the Clapeyron equation and data from Prob. 2.49 to 7.31 Use Trouton’s rule to show that the change T in normal
find the pressure at which water freezes at (a) 1.00°C; boiling point T due to a small change P in pressure is
(b) 10.00°C. (c) The experimental values of these pressures roughly T T nbp P/(10 atm).
1
are 131 atm and 1090 atm. Explain why the value you found in nbp 2
(b) is greatly in error. 7.32 (a) At 0.01°C, vap H m of H O is 45.06 kJ/mol, and
2
H of ice is 6.01 kJ/mol. Find H for sublimation of ice
7.24 The heat of fusion of Hg at its normal melting point, fus m m
at 0.01°C. (b) Compute the slope dP/dT of each of the three
38.9°C, is 2.82 cal/g. The densities of Hg(s) and Hg(l) at lines at the H O triple point. See Prob. 2.49 for further data.
3
38.9°C and 1 atm are 14.193 and 13.690 g/cm , respectively. 2
State any approximations made.
Find the melting point of Hg at (a) 100 atm; (b) 500 atm.
7.33 Vapor-pressure data vs. temperature are often repre-
7.25 (a) Repeat the ethanol example of Sec. 7.3 using the av- sented by the Antoine equation
erage of the 25°C and 78.3°C vap H values instead of the
m
78.3°C value. Compare the result with the experimental 25°C ln 1P>torr2 A B>1T>K C2
vapor pressure. (b) The actual molar volumes of ethanol vapor
in the temperature and pressure ranges of this example are less where A, B, and C are constants chosen to fit the data and K 1
than those predicted by PV RT. Will inclusion of nonideal- kelvin. The Antoine equation is very accurate over a limited
m
ity of the vapor improve or worsen the agreement of the result vapor-pressure range, typically 10 torr to 1500 torr. For H O in
2
of (a) with the experimental 25°C vapor pressure? the temperature range 11°C to 168°C, Antoine constants are A
18.3036, B 3816.44, C 46.13. (a) Use the Antoine equa-
7.26 The average enthalpy of sublimation of C (s) (buckmin-
60 tion to find vapor pressures of H O at 25°C and 150°C and
sterfullerene) over the range 600 to 800 K was determined by 2
compare with the experimental values 23.77 torr and 3569 torr.
allowing the vapor in equilibrium with the solid at a fixed
(b) Use the Antoine equation to calculate H of H O at
temperature to leak into a mass spectrometer and measuring the vap m 2
100°C. State any approximations made. (For more accurate re-
integrated intensity I of the C peaks. The graph of ln (IT/K) ver-
60 sults, see Prob. 8.43.)
4
sus T 1 was found to have an average slope of 2.18 10 K
[C. K. Mathews et al., J. Phys. Chem., 96, 3566 (1992)]. The 7.34 Show that when T 2 T 1 V T 1 , Eq. (7.25) can be re-
solid’s vapor pressure can be shown to be proportional to IT placed with (7.24). Hints: In (7.25), replace T 2 with T 1 ¢T
(see Prob. 14.36). Find H of C (s)in this temperature range. and use (8.36).
sub m 60