8.5 Nonstandard Potentials and
Equilibrium Constants
8.17.What is the Zn^2 Cu^2 ratio on a Daniell cell that has
a voltage of 1.000 V at 25.0°C? Can you say what the indi-
vidual concentrations of Zn^2 and Cu^2 are? Why or why not?
8.18.The thermite reaction can act as the basis of an elec-
trochemical cell:
2Al (s) Fe 2 O 3 (s) →Al 2 O 3 (s) 2Fe (s)Estimate the electrochemical potential of this reaction at
1700°C if E° is 1.625 V. You will need to look up thermody-
namic data in Appendix 2.
8.19.A concentration cellhas different concentrations of the
same ions, but because of the different concentrations there is
a very small voltage between the cells. This effect is especially
problematic for corrosion. Consider the following overall reac-
tion, which is assumed to occur in the presence of metallic
iron:
Fe^3 (0.08 M) →Fe^3 (0.001 M)(a)What is E°?
(b)What is the expression for Q?
(c)What is Efor the concentration cell?
(d)Should concentration cells be considered another type of
colligative property? Explain your answer.
8.20. (a)What is the equilibrium constant for the following
reaction?
H 2 2D^ D 2 2H^E° for 2D^ 2e^ →D 2 is 0.044 V. (b)Based on your an-
swer, which isotope of hydrogen prefers to be in the 1 state
in aqueous solution?
8.21.Estimate the temperature needed for the reaction in ex-
ercise 8.20 to have an E° of 0.00 V. Assume that S[D^ (aq)] 0.
8.22.Redo Example 8.5 by correcting the entropies for tem-
perature from 298 K to 500 K using the appropriate ther-
modynamic equations. By how much does the final answer
differ?
8.23.Determine an expression for Cp°, the change in the
constant-pressure heat capacity, for an electrochemical
process. Hint:see equation 8.30 and use the definition of heat
capacity.
8.24.Derive equation 8.33.
8.25.Determine Efor the concentration cell whose net reac-
tion is Cu^2 (0.035 m) →Cu^2 (0.0077 m).
8.26.Determine the ratio of molarities necessary to have E
equal to 0.050 V for a concentration cell composed of
(a)Fe^2 ions; (b)Fe^3 ions; (c)Co^2 ions. (d)Compare your
answers and explain the differences or similarities.
8.27.Determine Kspfor AgCl using electrochemical data.
JQPJ8.28.What is the solubility product constant of Hg 2 Cl 2 , which
dissociates into Hg 22 and Cl^ ions?
8.29.What is the pH of a hydrogen ion solution if an H
electrode is connected to a MnO 4
/Mn^2 half cell with
[MnO 4
] 0.034 mand [Mn^2 ] 0.288 m? E1.200 V.
Assume pH 2 1 bar. See Table 8.2 for E° data.
8.30.Using the cell from Example 8.8, determine whether
the oxidation of Fe (the major reaction in the corrosion of
iron) to Fe^2 is promoted by high pH (basic solutions) or low
pH (acidic solutions).
8.31.What is the equilibrium concentration of Cl^ in a stan-
dard calomel electrode? (Hint:you will need to determine the
Kspfor Hg 2 Cl 2 .)8.6 & 8.7 Ions in Solution;
Debye-Hückel Theory
8.32.Show that acan be written as n^ mnn n^ n n^ ,
where mis the original molality of the ionic solution.
8.33.Determine ionic strengths for the following solutions.
Assume that they are 100% ionized. (a)0.0055 molal HCl,
(b)0.075 molal NaHCO 3 , (c)0.0250 molal Fe(NO 3 ) 2 , (d)
0.0250 Fe(NO 3 ) 3
8.34.Although it is not an ionic solute, a 1.00-molal solution
of ammonia, NH 3 , is actually a weak electrolyte and has an
ionic strength of about 1.4 10
5 molal. Explain.
8.35.Calculate the molar enthalpy of formation of I^ (aq) if
that of H 2 (g) I 2 (s) →2H^ (aq) 2I^ (aq) is 110.38 kJ.
8.36.The entropy of formation of Mg^2 (aq) is 138.1 J/molK.
Explain (a)why this value doesn’t violate the third law of ther-
modynamics, and (b)from a molecular level, why the entropy
of formation of anyion might be negative.
8.37.Hydrofluoric acid, HF (aq), is a weak acid that is not
completely dissociated in solution.
(a)Using the thermodynamic data in Appendix 2, determine
H°, S°, and G° for the dissociation process.
(b)Calculate the acid dissociation constant, Ka, for HF (aq) at
25°C. Compare it to a handbook value of 3.5 10
4.
8.38.Determine H°, S°, and G° for the dissolution reac-
tions for NaHCO 3 and Na 2 CO 3. (See Appendix 2 for data.)
8.39.Verify the value and unit for equation 8.54.
8.40.The mean activity coefficient for an aqueous 0.0020-
molal solution of KCl at 25°C is 0.951. How well does the
Debye-Hückel limiting law, equation 8.50, predict this coeffi-
cient? As an additional exercise, calculate using equations
8.52 and 8.53 [where å (K^ ) 3 10
10 m and å (Cl^ )
3 10
10 m] and using equation 8.44.
8.41.Human blood plasma is approximately 0.9% NaCl.
What is the ionic strength of blood plasma?Exercises for Chapter 8 239