Page 347 - Physical Chemistry

lev38627_ch10.qxd 3/14/08 1:07 PM Page 328

328
10.37 Use the Davies equation to estimate (a) g for 0.02 Section 10.9

mol/kg CaCl (aq) at 25°C; (b) g for CaCl in an aqueous 25°C 10.48 Use (10.83) and the G° and H° results of the
2
f
f

2

solution that has CaCl molality 0.02 mol/kg, CuSO molality Sec. 10.9 example to find S° 298 (sucrose, aq).
2
4
0.01 mol/kg, and Al(NO ) molality 0.005 mol/kg; (c) g and

3 3
g for the solution of part (a). 10.49 Use data in the Appendix to find G° , H° , and
298
298

2

S° for (a) H (aq) OH (aq) → H O(l); (b) CO (aq)
2
3
298
10.38 (a) For a 0.001 mol/kg 25°C CaCl (aq) solution, what 2H (aq) → H O(l) CO (g).

2
2
2
value of a in the Debye–Hückel equation (10.64) is required to
give agreement with the experimental g of Table 10.2? (b) Use 10.50 (a) Use Appendix data to find G°, H°, and S° at
f
f

the value of a from part (a) and Eq. (10.64) to estimate g of 25°C for Cu(NO ) (aq). (b) Use Appendix data to find H° 298
3 2

0.01 mol/kg 25°C CaCl (aq). for NaCl(s) → NaCl(aq).
2
10.39 Calculate g in a 0.0200 mol/kg HCl solution in 10.51 The NBS tables give G° 298 1010.61 kJ/mol for
f

CH OH at 25°C and 1 atm. For CH OH at 25°C and 1 atm, the NaSO (aq). With the aid of Appendix data, find G° for the
298
4
3
3

2

3
dielectric constant is 32.6 and the density is 0.787 g/cm . ion-pair formation reaction Na (aq) SO (aq) → NaSO (aq).
4
4
Assume a 3 Å.
10.52 The NBS tables (Sec. 5.9) list the following G° 298
f

10.40 For a 25°C aqueous solution of a single strong elec- values: 108.74 kJ/mol for NO (ao) and 111.25 kJ/mol for
3
trolyte, the Meissner equation is HNO (ai). Without looking up any data, explain why at least
3
one of these numbers must be in error.
I 1>2
log 10 g 0.5107z 0z 0
1 cI 1>2 10.53 Find the conventional value of S° i of H O (aq) at
3
25°C. (Hint: Consider the two equivalent ways of writing
q
z 0z 0 log 10 31 b b11 0.1I2 4
the ionization of water: H O ∆ H OH and 2H O ∆
2
2

3
b 0.75 0.065q, c 1 0.055qe 0.023I 3 H O OH .)
10.54 Derive Eqs. (10.92) and (10.93).
where I I /m°. For Na SO (aq), q 0.19. Calculate
4
2
m
the Meissner-predicted g of Na SO (aq) at 0.1 mol/kg and 10.55 (a) The solubility of O (g) in water at 25°C and 1 bar

4
2
2
1 mol/kg and compare with the values in Table 10.2. pressure of O above the solution is 1.26 mmol per kilogram of
2
10.41 For the CaCl (aq) Table 10.2 data: (a) use the 0.1 water. Find G° for O in water. The molality-scale standard
298
2
f
2
mol/kg g and a spreadsheet Solver to find the Meissner q. (q state is used for the solute O . (b) Use a Henry’s law constant
2

can be positive or negative and a reasonable first guess for q is of C H in Sec. 9.8 to find G° for C H (aq).
6
f
2
6
298
2
0.) Then predict g at 5 mol/kg and at 10 mol/kg and compare 10.56 Derive the following equations for partial molar prop-

with the experimental values; (b) find q by fitting the five low- erties of a solute in a nonelectrolyte solution:
est molalities using the Solver and then predict the 5 mol/kg

and 10 mol/kg values. S i S° m,i R ln 1g m,i m i >m°2 RT10 ln g m,i >0T 2 P,n j

Section 10.8 V i V° m,i RT10 ln g m,i >0P2 T,n j

†
2
10.42 Show from (10.77) that g ag if n n . H i H° m,i RT 10 ln g m,i >0T 2 P,n j

†
10.43 Verify Eqs. (10.76) and (10.77) for m and g .
i
10.57 Measurements on electrochemical cells (Sec. 13.9)
†
q n
q n
10.44 Verify that g (m /m ) /n (m /m ) /n g , where give for HCl(aq) that G° 131.23 kJ/mol and H°

298
f
298
f
q
m n m and m n m are the maximum possible molal- 167.16 kJ/mol. Use these data, Appendix entropy data for
q

i
i
ities of the cation and anion and occur in the limit of infinite H (g) and Cl 2 (g), and the H (aq) conventions to find G° ,

dilution, where there is no ion pairing and a 1. (From this 2 of Cl (aq). Start with Eq. (10.91). f 298

f
298
† H° , and S ° 298
result, it follows that g g .)

10.58 At 25°C and 1 bar, the differential heat of solution of
10.45 Starting from G n m n m n m n m , KCl in water at infinite dilution is 17.22 kJ/mol. A saturated

IP IP
A A
derive Eq. (10.54) for an electrolyte solution.
25°C aqueous KCl solution has KCl molality 4.82 mol/kg
10.46 For Pb(NO ) , the fraction of Pb 2 ions that associate and activity coefficient g 0.588. For pure KCl(s) at 25°C,

3 2

with NO ions to form ion pairs is known to be 1 a 0.43 G° 409.14 kJ/mol, H° 436.75 kJ/mol, and S°
f
f

3

in a 0.100-mol/kg aqueous solution at 25°C. (a) Calculate I of 82.59 J/(mol K). Find G° , H° , and S° 298 for K (aq)
298
f
f
298
m

this solution. Note that the ion pair is charged. (b) Use the using these data and the results found for Cl (aq) in Prob. 10.57.
Davies equation to calculate g for this solution. Then calcu-

† † 10.59 For ions in aqueous solution, would you expect S° i to
late g . The experimental g is 0.395.
increase or decrease as the absolute value z of the ionic charge
i
10.47 Use Fig. 13.24 to decide whether ion pairing will increases? Explain your answer. Check your answer by con-
increase or decrease in water as T increases. sulting Appendix data.