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simultaneous equations, making judicious approximations 11.26 Find K for BaF in water at 25°C and 1 bar, given
sp
2
2
where possible. For a dilute aqueous solution of the weak acid these G° /(kJ/mol) values: 560.77 for Ba (aq), 278.79
298
f

HX with stoichiometric molality m:(a) perform steps 1 and 2, for F (aq), 1156.8 for BaF (s).
2
assuming that a(H O) 1 and g 1 for each ion (do not 11.27 (a) Use G° data in the Appendix to calculate K for
2
sp
f
neglect the ionization of water); (b) perform step 3 for the X KCl in water at 25°C. (b) A saturated solution of KCl in water

group of atoms (which occurs in HX and in X ); (c) manipulate at 25°C has a molality 4.82 mol/kg. Calculate g of KCl in a
the resulting set of four simultaneous equations in four un- saturated aqueous solution at 25°C.

knowns to eliminate all molalities except m(H O )to show that
3
11.28 For CaSO in water at 25°C, the equilibrium constant
4
2
3
y K a y 1K w mK a 2y K a K w 0
for the formation of ion pairs is 190 kg/mol. The solubility of

where y m(H O ). This is a cubic equation that can be solved CaSO in water at 25°C is 2.08 g per kilogram of water.
3
4

to give m(H O ). Calculate K for CaSO in water at 25°C. (Hint: Get an initial
sp
3
4
estimate of the ion-pair molality and the ion molalities by ig-
11.20 Solve the HOI example (Example 11.3 in Sec. 11.3) by
using the Solver in a spreadsheet to solve the cubic equation in noring activity coefficients. Get an initial estimate of I and use
m
Prob. 11.19. this to get an initial estimate of g . Then recalculate the ionic

molalities. Then calculate an improved g value and recalcu-

11.21 Let K c,a and K m,a be the concentration-scale and the late the ionic molalities. Keep repeating the calculations until
molality-scale equilibrium constants for ionization of the acid convergence is obtained. Then calculate K .)
HX. (a) Use the relation g c r g m (proved in Prob. sp
i
c,i i
A m,i
10.23) to show that K /K m,a r . Since r 0.997 kg/dm 3 11.29 Use data in the Appendix to calculate the equilibrium
c,a
A
A
for water at 25°C, K° and K° have essentially the same nu- pressure of CO above CaCO (calcite) at 25°C.
3
2
c,a
m,a
merical values for aqueous solutions. (b) Show that in a dilute 11.30 The equilibrium constant for the reaction Fe O (s)
3
4
solution, c /m r . Therefore, the molality in mol/kg and the CO(g) ∆ 3FeO(s) CO (g) is 1.15 at 600°C. If a mixture of
A
i
2
i
3
concentration in mol/dm are nearly equal numerically for each 2.00 mol Fe O , 3.00 mol CO, 4.00 mol FeO, and 5.00 mol CO 2
3
4
solute in dilute aqueous solutions. (c) Show that g g m,i in is brought to equilibrium at 600°C, find the equilibrium com-
c,i
dilute aqueous solutions. position. Assume the pressure is low enough for the gases to
behave ideally.
11.22 Fuoss’s theory of ion-pair formation gives the follow-
3
ing expression (in SI units) for the concentration-scale equilib- 11.31 (a) If 5.0 g of CaCO (s) is placed in a 4000-cm con-
3
rium constant for the ion-association reaction M X z ∆ tainer at 1073 K, give the final amounts of CaCO (s), CaO(s),
z
3
MX z z in solution: and CO (g) present. See Prob. 11.37 for K°. (b) The same as
2
4
3
K c pa N A exp b (11.39) (a), except that 0.50 g of CaCO is placed in the container.
3
3
11.32 The reaction CaCO (s) ∆ CaO(s) CO (g) has K°
where N is the Avogadro constant, a is the mean ionic diame- 3 2
A
ter (as in the Debye–Hückel theory), and 0.244 at 800°C. A 4.00-L vessel at 800°C initially contains
only CO (g) at pressure P. If 0.500 g of CaO(s) is added to the
2
2
b z 0z 0e >4pe 0 e r,A akT (11.40) container, find the equilibrium amounts of CaCO (s), CaO(s),
3
where the symbols in (11.40) are defined following (10.59). and CO (g) if the initial CO pressure P is (a) 125 torr; (b) 235
2
2
[For the derivation of (11.39), see R. M. Fuoss, J. Am. Chem. torr; (c) 825 torr.
Soc., 80, 5059 (1958).] For the value a 4.5 Å, use the Fuoss
equation to calculate the ion-association equilibrium constant Section 11.5
K in aqueous solution at 25°C for (a) 1:1 electrolytes; (b) 2:1 11.33 Use Appendix data to find K° for the nonideal-gas re-
298
c
electrolytes; (c) 2:2 electrolytes; (d) 3:2 electrolytes. (Hint: Be action 2HCl(g) ∆ H (g) Cl (g).
2
2
careful with the units of a. Note that the traditional units of K c 11.34 At 450°C and 300 bar, fugacity coefficients estimated
3
are dm /mol.) Conductivity measurements show that in aque- from law-of-corresponding-states graphs are f 1.14, f
N 2 H 2
ous solutions at 25°C, the ion-association equilibrium constant 1.09, and f 0.91. The equilibrium constant for N (g)
NH 3 2
3
is typically of the order of magnitude 0.3 dm /mol for 1:1 elec- 3H (g) ∆ 2NH (g) at 450°C is K° 4.6 10 . Using the
5
2
3
3
3
trolytes, 5 dm /mol for 2:1 electrolytes, 200 dm /mol for 2:2 Lewis–Randall rule to estimate mixture fugacity coefficients,
3
electrolytes, and 4000 dm /mol for 3:2 electrolytes. How well calculate the equilibrium composition of a system that initially
does the Fuoss equation agree with these experimental values? consists of 1.00 mol of N and 3.00 mol of H and that is held
2
2
at 450°C and 300 bar. (Hint: The quartic equation that results
Section 11.4 can be reduced to a quadratic equation by taking the square root
11.23 Calculate the activity at 25°C of NaCl(s)at1, 10, 100, of both sides.)
3
and 1000 bar. The density of NaCl at 25°C and 1 bar is 2.16 g/cm .
11.35 For NH , N , and H , the critical temperatures are
3
2
2
11.24 For AgBrO in water at 25°C and 1 bar, K 5.38 405.6, 126.2, and 33.3 K, respectively, and the critical pressures
sp
3
2
2
10 5 mol /kg . Calculate the solubility of AgBrO in water at are 111.3, 33.5, and 12.8 atm, respectively. G° for NH
3
700
f
25°C. Neglect ion pairing. is 6.49 kcal/mol. Use the Lewis–Randall rule and law-of- 3
11.25 For CaF in water at 25°C and 1 bar, K 3.2 10 11 . corresponding-states graphs of fugacity coefficients (Sec. 10.10)
sp
2
Calculate the solubility of CaF in water at 25°C and 1 bar. In to calculate the equilibrium composition at 700 K of a system
2
this dilute solution, ion pairing can be neglected. that initially consists of 1.00 mol of NH if P is held fixed at
3