(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
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.
Solutions of Numerical Problems 10. bCu2+(aq)= 0.005 mol/kg, bSO4--(aq) = 0.005 mol/kg I = 0.5 Σ [zi2 (bi/b0)] I = 0.5 × [22 × (0.005/1) + (-2)2 × (0.005/1)] = 0.02
[Eq. (1.14)]
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 -5 1.753 × 10 ≈ α2× 0.02 / [(1-α) × 1] 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 γ±[NaCl(aq), 0.01 mol/kg, calc] = exp (- ADH|z+ z-| Ib ½) = exp [-1.172 × |1 × (-1)| × (0.01)1/2 ] = 0.8894 The difference is 0.903 – 0.8894 = 0.0136 (dimensionless)
(Table 10.17) [Eq. (1.29)]
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]
= exp{ [-1.172 × 4 × (0.02)0.5]/[1 + 0.328 × 4.5 × (0.02)0.5] = 0.5778 (dimensionless) The difference is 0.5153 - 0.5778 = - 0.0625 (dimensionless) 17. pH ≈ pKa + log [bsalt γ± /bacid )] bsalt = bacid Assuming γ± = 1 pKa = 4.756 pH ≈ pKa = 4.756 (dimensionless)
[Eq. (1.39)]
(Table 10.15)
18. Ka = α2 bHA/[(1- α) bo] [Eq. (1.34)] α = 0.053 Ka = 0.0532 × 0.006 /[(1 - 0.053) × 1] = 1.78 × 10-5(dimensionless) 19. pOH = pKw – pH = 14 – 12 = 2 aOH-(aq) = 10-2 aOH-(aq) = γOH-(aq) bOH-(aq) / b0 = 10-2 γOH-(aq) ≈ γ± = 0.902 (at bNaOH(aq) ≈ 10-2 mol/kg) bOH-(aq) = 10-2 ×1/0.902 = 0.0111 mol/kg > 0.01 mol/kg 20. xKCl = bi/(bi + 55.51) = 3/(3+ 55.51) = 0.05127 Alternatively, using Table 1.1 xKCl = 3*18.015/(3*18.015+1000) = 0.05127 xH2O = 1 - xKCl = 1 - 0.05127 = 0.949
(Table 10.17)
[Eq. (1.5)]
Quiz 2 1. Electric current density is (a) a core SI unit (b) a derived SI unit (c) not a SI unit 2. The amount of electric charge is (a) current × time (b) potential difference × time (c) resistance × time 3. The electrochemical system that produces electricity by consuming chemicals is (a) an electrolytic (electrolysis) cell
(b) a galvanic cell (c) a chemical cell 4. The electrochemical system that produces chemicals by consuming electricity is (a) an electrolytic (electrolysis) cell (b) a galvanic cell (c) a chemical cell 5. At the anode, a reaction of (a) reduction takes place (b) oxidation takes place (c) neutralization takes place 6. In an electrolytic cell, the cathode is (a) positively charged (b) negatively charged (c) either positively or negatively charged 7. During water electrolysis, if 2 L of hydrogen is produced, then the volume of oxygen produced is (a) 1 L (b) 2 L (c) 3 L 8. What is the internal resistance of a galvanic Daniell cell if the cell potential difference is 0.771 V, the equilibrium potential difference is 1.101 V, and the circuit current is 1.5 mA? (a) 220 Ω (b) 22 Ω (c) 2.2 Ω 9. Cu2+(aq) + 2e- = Cu(s) is (a) an oxidation reaction (b) a reduction reaction (c) a neutralization reaction 10. Zn(s) = Zn2+(aq) + 2e- is (a) an oxidation reaction (b) a reduction reaction (c) a neutralization reaction 11. In a galvanic cell the magnitude of the cell potential is always (a) larger than the magnitude of the equilibrium potential (b) smaller than the magnitude of the equilibrium potential (c) the same as the magnitude of the equilibrium potential