Electroquímica y Química Macromolecular: Problemas y Ejercicios, Ejercicios de Electroquímica

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Electroquímica i Química Macromolecular Peroblemes i exercisis Lluís Blancafort, Joan Miró UdG, 20 22 - 2023

Constants principals e 0 - carrega de l'electró: 1.602e-19 C

e 0 - permitivitat del buit: 8.854e-12 C^2 ·s^2 ·kg-^1 ·m-^3

F - constant de Faraday: 9.64 85 e4 C·mol-^1 R - constant de Boltzmann: 8.3145 kg·m^2 ·s-^2 ·mol-^1 ·K-^1 NAv - número d'Avogadro: 6.022e23 mol-^1

Electroquímica i Química Macromolecular - Problemes Capítol 1 - FEM 1.5 Considereu la cel·la electroquímica: Sn(s)|SnO(s)½SnCl 2 /HCl(aq)½H 2 (g)|Pt(s). (a) Escriviu les semirreaccions d'elèctrode i la reacció total, i determineu l'energia lliure de formació de l'òxid d'estany a partir de la FEM estàndard, utilitzant els potencials tabulats. (b) Calculeu l'entropia molar de l'òxid d'estany savent que la FEM a 80 °C augmenta 18. mV respecte al seu valor estàndard a 298 K. Dades: D Gf (H 2 O) = - 285.81 kJ·mol-^1 ; S^0 (H 2 ) = 130.7 J·mol-^1 ·K-^1 ; S^0 (H 2 O) = 70.0 J·mol-^1 ·K-^1 ; S^0 (Sn) = 51.2 J·mol-^1 ·K-^1.

Sol.: (a) D Gf(SnO) = - 305.1 kJ·mol-^1. (b) S^0 (SnO) = 56.1 J·mol-^1 ·K-^1.

1.6 L'entalpia de formació de l'òxid de plata sòlid a 25 °C es - 30.54 kJ·mol-^1. L'entropia de l'Ag 2 O i els seus components és: Ag 2 O(s) Ag(s) O 2 (g) S [J·K·mol-^1 ] 121.59 42.66 204. A més, l'entalpia lliure de formació de l'aigua líquida és - 236.96 kJ·mol-^1 , i el producte iònic de l'aigua, 1.008× 10 -^14. Totes les dades són a 25 °C. a) Calculeu el potencial de reducció de l'elèctrode Ag/Ag 2 O(s) en medi àcid, i compareu-lo amb el valor tabulat. b) Igualeu la reducció amb anions hidroxil en lloc de protons i recalculeu el potencial estàndard. c) Demostreu que els dos resultats són equivalents utilitzant l'equació de Nernst. d) Calculeu el potencial de l'electròlit en condicions de neutralitat. Sol.: a. E = 1.17 V. b. E = 0.343 V. d. E = 0.756 V. 1.7 Calculeu la constant d'equilibri de la reducció de Zn(2+) amb Cu en aigua, savent que la FEM estàndard de la cel·la de Daniell és 1.10 V. Calculeu l'activitat dels ions de coure en la dissolució electrolítica. Sol.: Keq = 1.6e35. 1.8 Per a la bateria següent: Pb|PbCl 2 (s)½KCl(aq)½AgCl(s)|Ag, la FEM estàndard a 25 °C és 0.4902 V, i la variació amb la temperatura és - 1.86e-4 V·K-^1. Escriviu la reacció electroquímica i calculeu les variacions d'energia lliure, entalpia i entropia associades al procés a la temperatura de treball.

Sol.: D G° = - 94.61 kJ·mol-^1 ; D H° = - 105.31 kJ·mol-^1 ; D S° = - 35.90 J·mol-^1 ·K-^1.

1.9 Una bateria Ag|AgCl(s)½HCl(aq)½Hg 2 Cl 2 (s)½Hg a 25 °C es connecta amb una resistència molt alta que s'introdueix dintre del bany d'un calorímetre. Després de que circuli 1 Faraday a través de la resistència, la calor mesurada és 4393.2 J. Si la cel·la també s'introdueix al calorímetre, la calor mesurada augmenta fins a 5313.7 J. Escriviu la reacció electroquímica i calcule: a) la FEM; b) les variacions d'energia lliure, entalpia i entropia associades a la reacció; c) el grau de variació de la FEM amb la temperatura. Nota 1 : Considereu que la calor mesurada a la resistència és igual al treball elèctric extret de la cel·la, i que la calor total emesa per la resistència i la cel·la és igual a l'entalpia de reacció. Perquè és important que la resistència tingui un valor molt elevat? Nota 2 : 1 Faraday º 1 mol of electrons.

Sol.: a. EMF = 0.0455V. b. dE/dT = - 3.19e-5 V·K-^1. c. D G° = - 4.3932 kJ·eq-^1 ; D H° = - 5.

kJ·eq-^1 ; D S° = - 3. 09 J·eq-^1 ·K-^1.

Electroquímica i Química Macromolecular - Problemes Capítol 1 - FEM 1.10 La FEM a 18 °C de la bateria Pt,H 2 (1 atm)½NaOH(aq)½Bi 2 O 3 (s)|Bi és 0.3846 V. Entre el 10 °C i els 35 °C, la FEM disminueix 0.39 mV per cada grau que augmenta la temperatura. Calculeu l'entalpia de formació de 1 mol de Bi 2 O 3 (s) en aquestes condicions, savent que l'entalpia de formació de 1 mol d'aigua líquida és - 285.81 kJ. Sol.: ΔH = - 569.0 kJ·mol-^1_._

Electrochemistry and Macromolecular Chemistry Chapter 3 – Conductivity and ionic transport

3 CONDUCTIVITY AND IONIC TRANSPORT

Note. Molar conductivities from Vanýsek (Colorado State University), https://sites.chem.colostate.edu/diverdi/all_courses/CRC%20reference%20data/equiva lent%20conductivity%20of%20electrolytes.pdf.

3.1 Conductivity and Kohlrausch’s law

3.1.1 The molar conductivity of the following salts at 10-^5 M is determined at 18 °C with a Kohlrausch bridge: LKCl = 129.7; LNaNO3 = 104.9; LNaCl = 108.6 (units: S·cm^2 ·mol-^1 ). a) Calculate the molar conductivity of a KNO 3 solution with the same concentration. b) Repeat the problem for a 5e-4 M solution of calcium perchlorate, using the following molar conductivities at this concentration: LCaCl2 = 263.7; LKClO4 = 138.7; LKCl = 147.7. Sol.: a. 126.0 S·cm^2 ·mol-^1 ; b. 245.7 S·cm^2 ·mol-^1_._ 3.1.2 At 25 °C, the resistance of a conductivity cell filled with KCl 0.1M is 307.62 Ω, and 362.65 Ω with AgNO 3 0.1M. The specific conductivity of KCl at this temperature is 0. Ω-^1 ·cm-^1. Calculate: a) The cell constant in cm-^1. b) The molar conductivity (S·cm^2 ·mol-^1 ) of the silver nitrate solution, if the conductivity of water is neglected. Sol.: a. 3.938 cm-^1 ; b. Λ = 108.6 S·cm^2 ·mol-^1 3.1.3 Calculate, at 25°C, the specific electrochemical conductivity of a pure water sample after all impurities have been removed. At this temperature, Kw = 1.008× 10 -^14 and the molar conductivity at infinite dilution of HCl, KOH and KCl are, respectively, 426.0 S·cm^2 ·mol-^1 , 271.5 S·cm^2 ·mol-^1 i 149.8 S·cm^2 ·mol-^1. Hint: Consider which species present in the pure water sample are responsible for the conductivity.

Sol.: k = 5.499 × 10 -^8 S·cm-^1.

3.1.4 At 25 oC, the conductivity of a water sample that contains only calcium sulfate and calcium bicarbonate is 1.1815e-3 S·cm-^1. The sample is boiled without loss of volume to induce the precipitation of CaCO 3 , and the conductivity changes to 7.732e-4 S·cm-^1. Suppose that the conductivity relationship L/L 0 for each electrolyte is 0.85 and calculate: a) the CaSO 4 concentration of the sample (permanent hardness); b) the initial CaHCO 3 concentration. Use the limiting equivalent conductivity of the table. ion Λ^0 (S·cm^2 ·eq-^1 ) Ca2+^ 59. SO 42 -^ 80. HCO 3 -^ 44. Sol.: a. 0.00326 mol·l-^1 ; b. 0.00231 mol·l-^1_._

Electrochemistry and Macromolecular Chemistry Chapter 3 – Conductivity and ionic transport 3.1.5 The specific conductivity of a series of sodium propionate solutions at 25 °C is: c [mM] k [ μ S·cm-^1 ] 2.18 180 4.18 340 7.87 627 14.27 1112 25.97 1965

(a) Represent the relationship between specific conductivity and concentration ( k vs c )

and show that it does not follow the behaviour of an ideal solution. How would an ideal solution behave? b) Calculate the limiting equivalent conductivity of sodium propionate in S·cm^2 ·mol-^1 amd compare it with the value that appears in the CRC Handbook (85.9 S·cm^2 ·mol-^1 ). How does the real behaviour deviate from Kohlrausch's law at high concentrations? c) Calculate L 0 of propionic acid using the limiting equivalent conductivities of HCl and NaCl, which are 426.2 S·cm^2 ·mol-^1 i 126.5 S·cm^2 ·mol-^1 , respectively, at the working temperature. Sol.: a. Λo(CH 3 CH 2 COONa) = 85.6 S·cm^2 ·mol-^1 ; b. Λo(CH 3 CH 2 COOH) = 385.3 S·cm^2 ·mol-^1_._ 3.1.6 The molar conductivity of a series of KCl solutions at 25 °C is: c [N] Λ [S cm^2 mol-^1 ] 0.100 128. 0.050 133. 0.020 138. 0.010 141. 0.005 143. 0.001 146. Calculate the limiting equivalent conductivity in S·cm^2 ·mol-^1 using Kohlrausch's law.

Sol.: L 0 = 148.0 S·cm^2 ·mol-^1.

3.1.7 A conductivity cell filled with a hydrogen sulfide solution has a resistance of 3736 Ω at 18 °C. 50 mL of this solution bleach 13.75 mL of a 0.1013 M iodine solution. Under the same conditions, the resistance of a 0.02M KCl solution (specific conductivity 0.002397 Ω-^1 cm-^1 ) is 30.08 Ω. The limiting conductivity of the H+^ and HS-^ ions at the working temperature is 318 Ω-^1 ·cm^2 eq-^1 and 62 Ω-^1 ·cm^2 eq-^1. Calculate the ionization constant of H 2 S.

Sol.: Ki = 9.28 × 10 -^8

3.1.8 At 25°C, the specific conductivity of (CH 3 ) 3 Sn+Cl–^ solutions in ethanol at different concentration is: c [mM] k× 107 [S cm-^1 ] 0.1566 17. 0.2600 24. 0.3178 27. 1.0441 53. 3.0545 94.

Electrochemistry and Macromolecular Chemistry Chapter 4 – Electrode kinetics and overpotential

4 ELECTRODE KINETICS AND OVERPOTENTIAL

4.1. In a deposition experiment, a copper layer is grown on a Pt electrode surface at different overpotentials [Choguill, H. S.; Shell, F. J. Trans. Kansas Acad. Sci. 1954 , 57 , 386]. The experiment is carried out at pH 7 on a 0.1 M copper sulfamate solution an oxygen evolution is seen at one of the electrodes. The following intensity values are obtained as a function of the applied voltage: V [V] 0. 2 0.8 1. 0 1. 1 1. 2 1.3 1 .4 1. I [mA] (^0) .00 0.01 0.02 0.04 0.10 0.35 0.78 1. V [V] (^) 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2. I [mA] 2.15 3.15 4.65 6.20 8.00 10.20 11.21 13. (a) Represent the I/ V curve and determine the potential from which there is an efficient deposition. Justify your procedure, considering that the sulfamate starts to decompose approximately over 2 V. (b) This potential is known as static decomposition potential. Determine how much of it corresponds to overpotential and ohmic loss. Sol. Edec = 1.49 V [sum of - EMF, anode and cathode overpotentials and ohmic loss]. EMF:

- 0.51 V. 4.2. Hydrogen gas is produced in the electrolysis of 100 mL of a 0.4 M solution of HCl (ionic activity coefficient 0.645) over a mercury electrode at 298 K and 1 atm. Calculate the total cathode potential if the proton concentration is reduced by 1% after 10 min. Data: exchange current density of hydrogen over mercury in water: 5 e-13 A·cm-^2 ; electrode surface 3 cm^2 ; transmission factor: 0.5. Repeat the problem for a platinum electrode, where the exchange current density is 1e-4 A·cm-^2. Sol. E = 1.292 V; 0.310 V. 4.3. The electrolysis of hydrogen over a mercury cathode in a solution of methanol and 0.1 M hydrochloric acid (1:1 in volume) provides the following current density at different overpotentials:

i [A cm-^2 ] h [V] i [A cm-^2 ] h [V]

1 × 10 -^6 0.665 3 × 10 -^4 0.

3 × 10 -^6 0.716^1 × 10 -^3 0.

1 × 10 -^5 0.791^3 × 10 -^3 1.

3 × 10 -^5 0.834^1 × 10 -^2 1.

1 × 10 -^4 0.893^3 × 10 -^2 1.

Calculate the Tafel constants (intensity in A·cm-^2 ), the exchange current density and the symmetry factor of the system. Note on precision: Compare i 0 calculated using 2 and 4 decimal digits for a and b. Sol. a = 1.29 V; b = 0.10 V; i 0 = 2e-13 A (precision!)

Electrochemistry and Macromolecular Chemistry Chapter 4 – Electrode kinetics and overpotential 4.4. Calculate the minimum electrode potential, in absolute terms, needed to liberate hydrogen gas at 298 K and 1 atm during the electrolysis of a 0.1 M solution of

HCl over a mercury electrode, at a rate of 1e-7 mol·s-^1. Data: Aelect = 8 cm^2 ; g±(HCl) =

0.796; Tafel constants ( i in A·cm-^2 ): a = 1.410, b = 0.116. Sol. V = 1. 14 V. 4.5. The overpotential for the electrolysis of a sulfuric acid solution with a nickel cathode is 0.35 V. It includes an ohmic overpotential of 0.02 V. Calculate the necessary overpotential to increase the intensity current eight times: (a) neglecting the ohmic overpotential and (b) including the ohmic overpotential. Data: Tafel constant: b = 0.12 V (i in A·cm-2).

Sol.: a. h = 0.46 V; b. h = 0.60 V.

4.6. A solution of sulfuric acid of unit activity is electrolyzed at 25°C and 1 atm pressure under continuous stirring. The electrodes are of Pt and have an area of 1 cm^2 , and the intensity is 1 mA. The cell has a resistance of 100 Ω. The overpotentials have the following equations:

h cat = 0.472 + 0.118 log i [A·cm-^2 ]

h an = 1.062 + 0.118 log i [A·cm-^2 ]

Calculate the applied potential. Sol.: E = 2.153 V

Electrochemistry and Macromolecular Chemistry Chapter 6 – Macromolecules

6 MACROMOLECULES

6.1. A way to estimate the induced dipole in an apolar molecule is to calculate the dipole that would have the same interaction energy in a permanent dipole-dipole interaction. (a) Use this idea to estimate the induced dipole moment of benzene in a C 6 H 6 ····HCl complex knowing that the HCl molecule has a permanent dipole moment of 1 D, the distance between the two molecules is 3 Å, and the interaction energy is 0.8 kJ/mol. Assume that the HCl molecule lies parallel to the benzene plane and that the two molecules do not move. (b) Use the same idea to estimate the induced dipole moment in two methane molecules that make a CH 4 ····CH 4 complex with an equilibrium distance of 3 Å and an interaction energy of 2 kJ/mol. Use the Keesom formula for freely rotating molecules and consider a temperature of 298 K. Conversion factor: 1 D [Debye] = 0.2082 eÅ = 3.336e-30 C·m. Sol.: (a) 0.36 D; (b) 1.1 D. 6.2. Three macromolecules have the dispersion radii that are indicated in the table. Classify them as spherical or rod-shaped using their molecular and specific weight ( Mn and V s, respectively). Mn [Dalton] Vs [cm^3 ·g–^1 ] Rdisp [nm] Albumin (^66) × 103 0.752 2. Virus (^) 10.6× 106 0.741 12. DNA 4 × 106 0.556 117. Sol. Spherical, spherical, rod-shaped.

Electrochemistry and Macromolecular Chemistry Chapter 6 – Macromolecules 6.3. Two PVC polymer samples have the following molecular weight (MW, Dalton) distribution, where xi represents the fraction of molecules with a given MW. MW 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 xPVC,1 0.009 0.017 0.034 0.069 0.138 0.121 0.103 0.086 0.078 0. xPVC,2 0.009 0.018 0.036 0.071 0.107 0.036 0.018 0.018 0.036 0. MW 32000 34000 36000 38000 40000 42000 44000 46000 48000 xPVC,1 0.060 0.052 0.043 0.034 0.026 0.022 0.017 0.013 0. xPVC,2 0.036 0.054 0.071 0.089 0.107 0.107 0.089 0.054 0. In turn, a dextran sample has the following distribution: log(MW) 3.950 4.025 4.100 4.175 4.250 4.325 4.400 4.475 4.550 4.625 4.700 4.775 4.850 4.925 5.000 5.075 5.150 5.225 5.300 5.375 5. x_i 4e- 4 0.001 0.001 0.001 0.002 0.003 0.004 0.005 0.007 0.010 0.012 0.016 0.019 0.023 0.027 0.032 0.036 0.041 0.044 0.048 0. log(MW) 5.525 5.600 5.675 5.750 5.825 5.900 5.975 6.050 6.125 6.200 6.275 6.350 6.425 6.500 6.575 6.650 6.725 6.800 6.875 6. x_i 0.052 0.052 0.052 0.050 0.048 0.046 0.044 0.041 0.039 0.036 0.033 0.030 0.025 0.021 0.016 0.012 0.008 0.006 0.004 0. Data for dextran adapted from: Gaube, J. et al. J. Chem. Eng. Data 1993 , 38 , 207. (a) Do a graphical representation of the three distributions. (b) Calculate the number-average, weight-average and Z molar mass of the polymers ( Mn , Mw and Mz , respectively). (c) Order the polymers according to their dispersity Đ. Sol. , 1.08, 1.12, 2.8. 6.4. A series of experimental measures of the osmotic pressure of polyacrylonitrile solutions in dimethylformamide at 25°C gives the following values: (P) [mm Hg] conc. [g·l–^1 ] 0.47 1 1.04 2 1.69 3 2.43 4 Calculate the molecular weight of the polymer using the lineal van't Hoff formula and the virial form. Sol.: M = 28.5 and 43.6 kDalton

Electrochemistry and Macromolecular Chemistry Chapter 6 – Macromolecules 4 MACROMOLÈCULES

4.1 Tres macromolècules tenen els radis de dispersió que s'indiquen a la taula.

Classifiqueu-les segons els models de l'esfera o del bastó utilitzant el seu

pes molecular i el volum específic.

Mn Vs [cm^3 ·g–^1 ] Rdisp [nm] albúmina (^66) × 103 0.752 2. virus 10.6× 106 0.741 12. ADN 4 × 106 0.556 117. Sol.: esfera, esfera, bastó.

4.2 Tres polímers A i B iC presenten la distribució següent de pesos

moleculars, segons la fracció de molècules amb el pes molecular indicat.

(a) Representeu gràficament les tres distribucions. (b) Calculeu la massa molecular mitjana numèrica ( Mn ) i per pes ( Mw ) per als tres polímers i representeu-les al gràfic. (c) Determineu l'índex d'heterogeneïtat per als tres polímers ==> Ordeneu!! PM

x_ A 0.007 0.022 0.037 0.051 0.059 0.066 0.070 0.074 0.075 0. x_ B 0.003 0.005 0.010 0.020 0.030 0.051 0.076 0.102 0.127 0. x_ C 0.009 0.017 0.034 0.069 0.138 0.121 0.103 0.086 0.078 0. PM 32000 34000 36000 38000 40000 42000 44000 46000 48000 x_A 0.075 0.074 0.070 0.066 0.059 0.051 0.037 0.022 0. x_B 0.127 0.102 0.076 0.051 0.030 0.020 0.010 0.005 0. x_C 0.060 0.052 0.043 0.034 0.026 0.022 0.017 0.013 0. Sol. : 1.08, 1.04 i 1.08.

4.3 En el curs d'un experiment de determinació de pressions osmòtiques de

dissolucions de polacrilonitril en dimetilformamida a 25oC, s'han obtingut

els valors següents:

(P) [mm Hg] conc. [g·l–^1 ] 0.47 1 1.04 2 1.69 3 2.43 4

Electrochemistry and Macromolecular Chemistry Chapter 6 – Macromolecules Calculeu el pes molecular de poliacrilonitril amb la fórmula de van't Hoff lineal i amb la seva forma virial. Sol.: M = 28.5 i 43 .6·10^3 g·mol–^1