Page 367 - Physical Chemistry

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PROBLEMS

Where appropriate, use the Davies equation to estimate 11.11 A 0.200 mol/kg solution of the acid HX is found to

activity coefficients. have m(H O ) 1.00 10 2 mol/kg. Find K for this acid.
3
a
11.12 Estimate a(H O) in a 0.50 mol/kg aqueous NaCl solu-
2
Section 11.1 tion; take g(H O) 1.
11.1 True or false? (a) Activities are dimensionless. (b) The 2

standard-state activity a° equals 1. 11.13 Find m(H O ) in a 0.10 mol/kg solution of NaC H O 2
3
2
3
i
in water at 25°C, given that K 1.75 10 5 mol/kg for
a
Section 11.3 HC H O at 25°C. (Hint: The acetate ion is a base and reacts
2
3
2

11.2 True or false? (a) The product of H O and OH molal- with water as follows: C H O H O ∆ HC H O OH .)

3
2
2
3
2
3
2
2
2
2
ities in water at 25°C and 1 bar is always 1.0 10 14 mol /kg . Show that the equilibrium constant for this reaction is K
b
(b) For the weak acid HX(aq), g g g . (c) The degree of K /K . Neglect the OH coming from the ionization of water.

ionization of HC H O (aq) is unchanged if some NaCl is w a 7
3
2
2
dissolved in the solution. (d) In a solution prepared by adding 11.14 For H S, the ionization constant is 1.0 10 mol/kg in
2

m moles of HC H O to 1 kg of water, the H molality can water at 25°C. For HS in water at 25°C, the ionization constant
3
2
2
17
never exceed m mol/kg. is 0.8 10 mol/kg (with an uncertainty of a factor of 2) [S.
Licht et al., Anal. Chem., 62, 1356 (1990)]. (a) Ignoring activity
11.3 In the expression (11.15) for the ionization constant K , coefficients, calculate the H O , HS , and S 2 molalities in a

a
3

m(H O ) includes (a) only the hydronium ions that come from 0.100 mol/kg aqueous H S solution at 25°C, making reasonable
3
2
the ionization of HX; (b) all the hydronium ions in the solution, approximations to simplify the calculation. (b) The same as (a),
no matter what their source.
except that activity coefficients are to be included in the calcu-

11.4 For formic acid, HCOOH, K 1.80 10 4 mol/kg in lations. For the ionization of HS , use the form of the Davies
a
water at 25°C and 1 bar. (a) For a solution of 4.603 g of equation that corresponds to (10.57).

HCOOH in 500.0 g of H O at 25°C and 1 bar, find the H mo- 11.15 Given these G° /(kJ/mol) values: 454.8 for
2
f
298
lality as accurately as possible. (b) Repeat the calculation if Mg (aq), 128.0 for IO (aq), and 587.0 for the ion pair
2

0.1000 mol of KCl is added to the solution of (a). (c) Find the 3 2

3
3
H molality in a solution at 25°C and 1 bar prepared by adding MgIO (aq), find K° at 25°C for Mg (aq) IO (aq) ∆

MgIO (aq).
0.1000 mol of formic acid and 0.2000 mol of potassium for- 3
mate to 500.0 g of water. 11.16 For CuSO , the equilibrium constant for association to
4
form CuSO ion pairs has been found from conductivity mea-

4
11.5 (a) Write a computer program to calculate m(H ) in a surements to be 230 kg/mol in aqueous solution at 25°C. Use
solution of the acid HX for a range of stoichiometric molalities the Davies equation (10.68) to calculate the Cu 2 molality, g ,

from m to m in steps of m. The input is K°, m , m , and m. and g [Eq. (10.77)] in a 0.0500 mol/kg aqueous CuSO solu-
a
1
1
2
2
†

4
Use the Davies equation to estimate g . Assume that the H tion at 25°C. (Hint: First estimate g by neglecting ion associ-

from H O ionization is negligible. Test your program by running ation; then use this estimated g to calculate an approximate
2

it for K° 0.01 and compare the results with the Fig. 11.3 value Cu 2 molality; then calculate improved I and g values; and
a

m
m(H ) 0.00173 mol/kg at m 0.00200 mol/kg. (b) Explain then recalculate the Cu 2 molality. Repeat as many times as
why your program will not give accurate results at extremely low necessary to obtain convergence.)
molalities and at high molalities.
11.17 Write a computer program that will calculate the mo-
11.6 Given the following G° /(kJ/mol) values from the z z
f
298
NBS tables (Sec. 5.9): 27.83 for un-ionized H S(aq), 12.08 for lality of MX (aq) ion pairs in a solution of the strong elec-
2
2

HS (aq), and 85.8 for S (aq), calculate the ionization constants trolyte M X n at a given electrolyte stoichiometric molality
n

K°for the acids H S and HS in water at 25°C and 1 bar. Compare using an inputted value of the equilibrium constant for ion-pair
a
2

with the experimental values (Prob. 11.14). If the discrepancy formation. Use the Davies equation to find g and g [see the
surprises you, see Sec. 6.4. sentence after (10.68)]. See Prob. 11.16 for help. Check your
program against a few values in Fig. 10.10.

11.7 Find the H molality in a 1.00 10 5 mol/kg aqueous
HCN solution at 25°C and 1 bar, given that K 6.2 10 10 11.18 Set up a spreadsheet and use the Solver to solve the
a
mol/kg for HCN at 25°C. HOI example (Example 11.3 in Sec. 11.3). Assume activity
coefficients equal 1 but make no other approximations. Avoid

11.8 Calculate m(H O ) in a 0.20 mol/kg aqueous solution of algebraic manipulations. Have the equilibrium-constant
3
NaCl at 25°C. expressions, the electroneutrality condition, and conservation
11.9 The human body is typically at 98.6°F 37.0°C. of matter for the IO group satisfied.
(a) Use the expression given in Prob. 11.38 to calculate 11.19 When two or more simultaneous ionic equilibria occur,

m(H O ) in pure water at 37°C. (b) Using only Appendix data, the following systematic procedure can be used. 1. Write down
3
estimate K° at 37°C and compare with the value found in part the equilibrium-constant expression for each reaction. 2. Write
w
(a). State any approximation made.
down the condition for electrical neutrality of the solution.

11.10 Find m(H O ) in a 1.00 10 8 mol/kg aqueous HCl 3. Write down relations that express the conservation of matter
3
solution at 25°C. for substances added to the solution. 4. Solve the resulting set of