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Solutions Manual for Introduction to Electrochemical Science
and Engineering, 2e by Serguei Lvov (All Chapters)
Keys for Questions and Solutions of Numerical Problems
Appendix A
Quiz 1
1. The absolute value of the chemical potential
(a) is known
(b) is approximately known
(c) is not known
2. In practical calculations, instead of the standard chemical potential, we should use
(a) standard entropy
(b) standard Gibbs energy of formation
(c) standard enthalpy of formation
3. The chemical potential
(a) depends on the concentration scale
(b) does not depend on the concentration scale
(c) slightly depends on the concentration scale
4. The activity coefficient
(a) depends on the concentration scale
(b) does not depend on the concentration scale
(c) none of these
5. The standard chemical potential
(a) depends on the concentration scale
(b) does not depend on the concentration scale
(c) none of these
6. The chemical potential depends on
(a) concentration only
(b) temperature and pressure only
(c) concentration, temperature and pressure
7. In aqueous electrolyte solutions, the standard chemical potential of water is defined when
(a) mole fraction of water ® 0
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(b) mole fraction of electrolyte ® 1
(c) mole fraction of water ® 1
8. In aqueous solutions, the standard chemical potential of electrolyte is defined when
(a) molality of the electrolyte ® 0
(b) molality of the electrolyte ® 1
(c) mole fraction of water ® 0
9. Activity of a component in aqueous solution
(a) is dimensionless
(b) has dimension of molality
(c) has dimension of molarity
10. If molality of CuSO4(aq) is 0.005 mol/kg, the dimensionless ionic strength of the solution, I,
is
(a) 0.005
(b) 0.01
(c) 0.02
11. The ionic strength, Ib, of an aqueous solution which consists of 0.01 mol/kg of HCl and 0.02
mol/kg of CaCl2 is
(a) 0.06 mol/kg
(b) 0.07 mol/kg
(c) 0.08 mol/kg
12. The dissociation constant of the acetic acid can be found in Chapter 10: Data Section.
Calculate the pH of 0.02 mol/kg CH3COOH(aq) solution assuming the activity coefficients
of ions equal 1.
(a) pH=1.23
(b) pH=2.23
(c) pH=3.23
13. For a CaCl2(aq) solution, if the individual ion activity coefficients are equal, then
(a) γ+ = γ±
(b) γ- = γ±
(c) both of these
14. The difference between experimental (Chapter 10: Data Section) and calculated (using
Debye-Huckel limiting law) mean activity coefficient of 0.01 mol/kg NaCl(aq) is about
(a) 0.136
(b) 0.0136
(c) 0.00136
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15. For 0.005 mol/kg CuSO4(aq) solution, the difference between γ± calculated by first and
second approximations of the Debye-Huckel theory is
(a) - 0.0625
(b) - 0.1625
(c) +0.1625
16. The electrolyte activity coefficient can be
(a) <1
(b) >1
(c) both of these
17. If concentrations of acid and salt in the CH3COOH/CH3COONa buffer solution are equal, pH
of the buffer solution is about (use Chapter 10: Data Section)
(a) 2.76
(b) 4.76
(c) 6.76
18. Calculate the dissociation constant of NH4OH(aq) if the degree of dissociation of 0.006
mol/kg solution is 0.053 and the activity coefficients of all species equal 1.
(a) 1.78 × 10-4
(b) 1.78 × 10-5
(c) 1.78 × 10-6
19. If pH of a strong electrolyte aqueous solution of NaOH(aq) at 25 oC is 12, the concentration
of OH-(aq) ions is
(a) exactly 10-2 mol/kg
(b) slightly less than 10-2 mol/kg
(c) slightly larger than 10-2 mol/kg
20. The mole fraction of water in 3 mol/kg KCl(aq) solution is
(a) 0.949
(b) 0.0949
(c) 0.00949
21. In 0.03 mol/kg CaCl2(aq) solution the concentration of Cl-(aq) ions is
(a) 0.03 mol/kg
(b) 0.06 mol kg
(c) 0.09 mol/kg
Key
1. c, 2. b, 3. b, 4. a, 5. a, 6. c, 7. c, 8. a, 9. a, 10. c, 11. b, 12. c, 13. c, 14. b, 15. a, 16. c, 17. b, 18.
b, 19. c, 20. a, 21. b.
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Solutions of Numerical Problems
10.
bCu2+(aq)= 0.005 mol/kg, bSO4--(aq) = 0.005 mol/kg
I = 0.5 Σ [zi2 (bi/b0)] [Eq. (1.14)]
I = 0.5 × [22 × (0.005/1) + (-2)2 × (0.005/1)] = 0.02
11.
Ib = 0.5 Σ (zi2 bi) [Eq. (1.15)]
Ib = Ib(HCl, 0.01 mol/kg) + Ib(CaCl2, 0.02 mol/kg)
= 0.5 × [12 × 0.01 + (-1)2 × 0.01] + 0.5 × [22 × 0.02 + (-1)2 × 0.04]
= 0.01 + 0.06 = 0.07 mol/kg
12.
Ka ≈ α2 bHA/ [(1-α) b0] [Eq. (1.34)]
pKa = 4.756 (Table 10.15)
-4.756 -5
Ka = 10 = 1.753 10
1.753 × 10 ≈ α2× 0.02 / [(1-α) × 1]
-5
α2 + 9 × 10-4 α - 9 × 10-4 = 0
According to quadratic formula
α = [-8.76 × 10-4 + (3.5 × 10-3)1/2] / 2 = 2.96×10-2 (dimensionless)
Simplified calculation: α ≈ [Ka b0/b] ½ = [1.753 × 10-5/ (2 × 10-2)]½ = 2.96×10-2 (dimensionless)
bH+(aq) = α bHA = 2.96×10-2 × 2 ×10-2 = 5.92 × 10-4 mol/kg
γH+ = 1 (dimensionless)
pH = -log10(aH+(aq)) [Eq. (1.35)]
-4
= -log10[bH+(aq)] = -log [5.92 × 10 ] = 3.23 (dimensionless)
14.
γ± [NaCl(aq), 0.01 mol/kg, exp] = 0.903 (Table 10.17)
γ±[NaCl(aq), 0.01 mol/kg, calc] = exp (- ADH|z+ z-| Ib ½) [Eq. (1.29)]
= exp [-1.172 × |1 × (-1)| × (0.01)1/2 ] = 0.8894
The difference is 0.903 – 0.8894 = 0.0136 (dimensionless)
15.
In the first approximation of the Debye-Huckel theory
ln γ± = - ADH|z+ z-| Ib ½ [Eq. (1.29)]
In the second approximation of the Debye-Huckel theory
ln γ± = - ADH|z+ z-| Ib ½ /(1+ BDHa0Ib ½) [Eq. (1.27)]
Ib = 0.5 × {(22 × 0.005) + [(-2)2 × 0.005]} = 0.02 mol/kg
γ± [CuSO4(aq), 0.005 mol/kg, limiting] = exp [-1.172 × 4 × (0.02)0.5] = 0.5153 (dimensionless)
γ± [CuSO4(aq), 0.005 mol/kg, 2nd approximation]
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Solutions Manual for Introduction to Electrochemical Science
and Engineering, 2e by Serguei Lvov (All Chapters)
Keys for Questions and Solutions of Numerical Problems
Appendix A
Quiz 1
1. The absolute value of the chemical potential
(a) is known
(b) is approximately known
(c) is not known
2. In practical calculations, instead of the standard chemical potential, we should use
(a) standard entropy
(b) standard Gibbs energy of formation
(c) standard enthalpy of formation
3. The chemical potential
(a) depends on the concentration scale
(b) does not depend on the concentration scale
(c) slightly depends on the concentration scale
4. The activity coefficient
(a) depends on the concentration scale
(b) does not depend on the concentration scale
(c) none of these
5. The standard chemical potential
(a) depends on the concentration scale
(b) does not depend on the concentration scale
(c) none of these
6. The chemical potential depends on
(a) concentration only
(b) temperature and pressure only
(c) concentration, temperature and pressure
7. In aqueous electrolyte solutions, the standard chemical potential of water is defined when
(a) mole fraction of water ® 0
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(b) mole fraction of electrolyte ® 1
(c) mole fraction of water ® 1
8. In aqueous solutions, the standard chemical potential of electrolyte is defined when
(a) molality of the electrolyte ® 0
(b) molality of the electrolyte ® 1
(c) mole fraction of water ® 0
9. Activity of a component in aqueous solution
(a) is dimensionless
(b) has dimension of molality
(c) has dimension of molarity
10. If molality of CuSO4(aq) is 0.005 mol/kg, the dimensionless ionic strength of the solution, I,
is
(a) 0.005
(b) 0.01
(c) 0.02
11. The ionic strength, Ib, of an aqueous solution which consists of 0.01 mol/kg of HCl and 0.02
mol/kg of CaCl2 is
(a) 0.06 mol/kg
(b) 0.07 mol/kg
(c) 0.08 mol/kg
12. The dissociation constant of the acetic acid can be found in Chapter 10: Data Section.
Calculate the pH of 0.02 mol/kg CH3COOH(aq) solution assuming the activity coefficients
of ions equal 1.
(a) pH=1.23
(b) pH=2.23
(c) pH=3.23
13. For a CaCl2(aq) solution, if the individual ion activity coefficients are equal, then
(a) γ+ = γ±
(b) γ- = γ±
(c) both of these
14. The difference between experimental (Chapter 10: Data Section) and calculated (using
Debye-Huckel limiting law) mean activity coefficient of 0.01 mol/kg NaCl(aq) is about
(a) 0.136
(b) 0.0136
(c) 0.00136
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15. For 0.005 mol/kg CuSO4(aq) solution, the difference between γ± calculated by first and
second approximations of the Debye-Huckel theory is
(a) - 0.0625
(b) - 0.1625
(c) +0.1625
16. The electrolyte activity coefficient can be
(a) <1
(b) >1
(c) both of these
17. If concentrations of acid and salt in the CH3COOH/CH3COONa buffer solution are equal, pH
of the buffer solution is about (use Chapter 10: Data Section)
(a) 2.76
(b) 4.76
(c) 6.76
18. Calculate the dissociation constant of NH4OH(aq) if the degree of dissociation of 0.006
mol/kg solution is 0.053 and the activity coefficients of all species equal 1.
(a) 1.78 × 10-4
(b) 1.78 × 10-5
(c) 1.78 × 10-6
19. If pH of a strong electrolyte aqueous solution of NaOH(aq) at 25 oC is 12, the concentration
of OH-(aq) ions is
(a) exactly 10-2 mol/kg
(b) slightly less than 10-2 mol/kg
(c) slightly larger than 10-2 mol/kg
20. The mole fraction of water in 3 mol/kg KCl(aq) solution is
(a) 0.949
(b) 0.0949
(c) 0.00949
21. In 0.03 mol/kg CaCl2(aq) solution the concentration of Cl-(aq) ions is
(a) 0.03 mol/kg
(b) 0.06 mol kg
(c) 0.09 mol/kg
Key
1. c, 2. b, 3. b, 4. a, 5. a, 6. c, 7. c, 8. a, 9. a, 10. c, 11. b, 12. c, 13. c, 14. b, 15. a, 16. c, 17. b, 18.
b, 19. c, 20. a, 21. b.
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Solutions of Numerical Problems
10.
bCu2+(aq)= 0.005 mol/kg, bSO4--(aq) = 0.005 mol/kg
I = 0.5 Σ [zi2 (bi/b0)] [Eq. (1.14)]
I = 0.5 × [22 × (0.005/1) + (-2)2 × (0.005/1)] = 0.02
11.
Ib = 0.5 Σ (zi2 bi) [Eq. (1.15)]
Ib = Ib(HCl, 0.01 mol/kg) + Ib(CaCl2, 0.02 mol/kg)
= 0.5 × [12 × 0.01 + (-1)2 × 0.01] + 0.5 × [22 × 0.02 + (-1)2 × 0.04]
= 0.01 + 0.06 = 0.07 mol/kg
12.
Ka ≈ α2 bHA/ [(1-α) b0] [Eq. (1.34)]
pKa = 4.756 (Table 10.15)
-4.756 -5
Ka = 10 = 1.753 10
1.753 × 10 ≈ α2× 0.02 / [(1-α) × 1]
-5
α2 + 9 × 10-4 α - 9 × 10-4 = 0
According to quadratic formula
α = [-8.76 × 10-4 + (3.5 × 10-3)1/2] / 2 = 2.96×10-2 (dimensionless)
Simplified calculation: α ≈ [Ka b0/b] ½ = [1.753 × 10-5/ (2 × 10-2)]½ = 2.96×10-2 (dimensionless)
bH+(aq) = α bHA = 2.96×10-2 × 2 ×10-2 = 5.92 × 10-4 mol/kg
γH+ = 1 (dimensionless)
pH = -log10(aH+(aq)) [Eq. (1.35)]
-4
= -log10[bH+(aq)] = -log [5.92 × 10 ] = 3.23 (dimensionless)
14.
γ± [NaCl(aq), 0.01 mol/kg, exp] = 0.903 (Table 10.17)
γ±[NaCl(aq), 0.01 mol/kg, calc] = exp (- ADH|z+ z-| Ib ½) [Eq. (1.29)]
= exp [-1.172 × |1 × (-1)| × (0.01)1/2 ] = 0.8894
The difference is 0.903 – 0.8894 = 0.0136 (dimensionless)
15.
In the first approximation of the Debye-Huckel theory
ln γ± = - ADH|z+ z-| Ib ½ [Eq. (1.29)]
In the second approximation of the Debye-Huckel theory
ln γ± = - ADH|z+ z-| Ib ½ /(1+ BDHa0Ib ½) [Eq. (1.27)]
Ib = 0.5 × {(22 × 0.005) + [(-2)2 × 0.005]} = 0.02 mol/kg
γ± [CuSO4(aq), 0.005 mol/kg, limiting] = exp [-1.172 × 4 × (0.02)0.5] = 0.5153 (dimensionless)
γ± [CuSO4(aq), 0.005 mol/kg, 2nd approximation]
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