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Section 10.10 (a) Use the Lewis–Randall rule and Eq. (10.105) with terms
†
10.60 (a) For a pure gas that obeys the virial equation (8.5), after B P omitted to estimate the fugacity coefficients f chl and
derive (10.105) for ln f. (b) Use (8.6) and (8.9) to show that for f car in the saturated vapor mixture and in the pure saturated
a van der Waals gas vapors. (b) Calculate the activity coefficients g I,chl and g I,car in
the liquid mixture using the fugacity coefficients found in (a).
bRT a 2abRT a 2
ln f P P p (c) Calculate the activity coefficients g I,chl and g I,car assuming
2
4
2
R T 2 2R T 4 the vapor mixture and the pure vapors are ideal.
10.61 (a) For CO , the critical temperature and pressure are
2
304.2 K and 72.8 atm. Assume CO obeys the van der Waals
2 General
equation and use the result from Prob. 10.60b to estimate f for
10.67 Verify that the expressions for the ideal-solution chem-
CO at 1.00 atm and 75°C and at 25.0 atm and 75°C. Compare
2 ical potentials in (9.42) obey the Gibbs–Duhem equation
with the experimental values 0.9969 at 1 atm and 0.92 at
(10.18).
25 atm. (b) Use the Lewis–Randall rule to estimate the fugacity
3
and fugacity coefficient of CO in a mixture of 1.00 mol CO 10.68 For a 1.0 mol/dm NaCl(aq) solution, pretend that the
2 2
and 9.00 mol O at 75°C and 25.0 atm. ions are uniformly distributed in space and calculate the
2
average distance between centers of nearest-neighbor ions.
id
10.62 For a pure gas, show that ln f (G G )/RT, where (See Prob. 2.55.)
m
m
id
G is the molar Gibbs energy of the corresponding ideal gas at
m
the same T and P. 10.69 Suppose that A and B molecules have similar sizes and
shapes and that A-A and B-B intermolecular attractions are
10.63 (a) Calculate G when 1.000 mol of an ideal gas at 0°C
stronger than A-B attractions. State whether each of the fol-
is isothermally compressed from 1.000 to 1000 atm. (b) For N
2 lowing quantities for a solution of A B is likely to be larger
at 0°C, f 1.84 at 1000 atm and f 0.9996 at 1 atm.
or smaller than the corresponding quantity for an ideal solution.
Calculate G when 1.000 mol of N is isothermally com-
2 (a) H; (b) S; (c) G.
pressed from 1.000 to 1000 atm at 0°C. mix mix mix
10.70 Answer the following without looking up any formulas.
10.64 For CH at 50°C, measured V values as a function For a dilute electrolyte solution with g 1, would you expect
m
4

of P are g to increase or to decrease (a) if the ionic charge z increases;

3
V /(cm /mol) 3577 1745 828 365 (b) if the ionic diameter a increases; (c) if the ionic strength I m
m
increases; (d) if the solvent’s dielectric constant increases; (e) if
P/atm 5 10 20 40 the temperature increases. Explain each of your answers.
10.71 (a) Use (10.51) for m to show that for an electrolyte
3
V /(cm /mol) 206 127.0 90.1 75.4 i
m
solute i in a solution in equilibrium with vapor (assumed ideal),
P/atm 60 80 100 120 the equation corresponding to Henry’s law (9.63) is
(a) Use a graph to find the fugacity and fugacity coefficient of P i K i 1n g m i >m°2 n
CH at 50°C and 120 atm. Note from Prob. 8.38 that V
4 m
RT/P does not go to zero as the gas pressure goes to zero. where K is defined as in (9.62) except that m° is replaced by
i
i
(b)Give the value of the second virial coefficient B for CH at m° . Show that for HCl(aq), this equation becomes P
4 m,i i
2
50°C. (c) Instead of using a graph, answer (a) by using the K (g m /m°) . (b) Use data in Table 10.2 and in the Appendix

i
i
†
†
†
Solver to fit the data with Eq. (8.5) and find B , C , and D ; then to find the HCl partial pressure in equilibrium with a 0.10 mol/
use (10.105). kg 25°C HCl(aq) solution.
10.65 (a) Use the law-of-corresponding-states equation in 10.72 For a solution of ethanol (E) in water (W), state
Prob. 8.22 and Table 8.1 to estimate the second virial coeffi- whether each of the following activity coefficients is equal to 1
†
cient B for N at 0°C. (b) Use Eq. (10.105) with terms after B P if water is considered the solvent whenever a solvent is to be
2
omitted to estimate f at 0°C of N for P 1.00 atm and for specified. (a) g , g , g II,W , g , and g m,E , each evaluated in the
II,E
I,E
I,W
2
P 25 atm. Compare with the experimental values 0.99955 at limit x → 1; (b) the activity coefficients of (a) evaluated in the
W
1 atm and 0.9895 at 25 atm. limit x → 1.
E
10.66 A liquid mixture of carbon tetrachloride (car) and chlo- 10.73 True or false? (a) When a solution component is in its
roform (chl) at 40.0°C with x 0.5242 has a vapor pressure standard state, its activity is 1. (b) If a solution component has
chl
of 301.84 torr and has vapor-phase composition x v 0.6456. its activity equal to 1, the component must be in its standard
chl
The pure-liquid 40°C vapor pressures are P 360.51 torr and state. (c) The activity a is never negative. (d) Activity coeffi-
chl i
n
n
P 213.34 torr. The 40°C second virial coefficients of the cients are never negative. (e) g (g ) (g ) . (f ) S° for
car 298
3
3
pure gases are B 1040 cm /mol and B 1464 cm /mol. dissolving a salt in water is always positive.
chl car