Chapter 7 Electrochemistry Main contents Section 1: Electrolyte and electrolytic solution Section 2: Electrochemical Thermodynamics: Section 3: Irreversible electrochemical system Section 4: Applied electrochemistry

Section 1: Electrolytic solution Part 1 Electrolyte and its solution Main contents: Electrolyte: origin of the concept: van’t Hoff, Arrhenius Existence of ions in the solution: hydration and solvation Hydration theory: Interionic interaction: ionic pair Motion under electric field Conducting mechanism Faraday’s law and its application

§7.1 Electrolyte and its solution

Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002. pp. 294-310 Section 10.6 solutions of electrolytes Section 10.9 ionic association pp. 512-515 Section 16.6 electrical conductivity of electrolyte solutions.

7.1.1 Origin of the concept – electrolyte Electrochemistry A science that studies the relation between electric and chemical phenomena and the disciplines that govern the conversion between electric and chemical energies. 7.1.1 Origin of the concept – electrolyte 1) Definition of electrolyte An electrolyte is a substance that, when dissolved in solvent, produces a solution that will conduct electricity.

2) Dissociation of substance In 1886, Van’t Hoff published his quantitative research on the colligative properties of solution. For sucrose, the osmotic pressure () can be expressed as:  = c R T But for some other kind of solvates such as NaCl, the osmotic pressure had to be expressed as:  = i c R T i , Van’t Hoff factor, is larger than 1. In the paper written in Achieves Neerlandaises (1885) and Transactions of the Swedish. Academy (1886), van't Hoff showed analogy between gases and dilute solutions.

The equation for freezing point depression and boiling point elevation contains the letter i. i stands for the van’t Hoff Factor. ∆T = imKf Since freezing point depression and boiling point elevation depend only on the number of particles ( it does not matter what the particles are), we need only determine the total m of the particles. If a solution is 0.2 m NaCl, the i would be about 2. The true van’t Hoff factor is not exactly 2, but is close enough to call it 2. http://en.wikipedia.org/wiki/Van_'t_Hoff_factor

 3) Dissociation theory for weak electrolytes  + In 1887, Svant August Arrhenius postulated that, when dissolved in adequate solvent, some substances can split into smaller particles, the process was termed as dissociation. +   + AB  A+ + B – molecule cation anion positive ion negative ion The charged chemical species are named as ions and the process is termed as ionization.

Dissociation, ionization Therefore, the number of particles present in solution is actually larger than that predicted by van’t Hoff, which resulted van’t Hoff factor. New definitions: Dissociation, ionization Weak / strong electrolyte? True and potential? Theory of Electrolytic Dissociation Acid-base theory Greenhouse effect Cf. Levine p.295

7.1.2 Solvation (hydration) of ion  +

Solvation shells The interaction between ions and water molecules disturb the structure of liquid water. ion Primary hydration shell secondary hydration shell Disordered layer Bulk solution The water molecules in the hydration sphere and bulk water have different properties which can be distinguished by spectroscopic techniques such as nuclear magnetic resonance (NMR), infrared spectroscopy (IR), and XRD etc.

Hydration of ion Coordination number: Li+: 4, K+: 6 Primary solvation shell: 4-9, 6 is the most common number Secondary slovation shell: 6-8, for Al3+ and Cr3+: 10-20

7.1.3 Hydration Theory / Solvation Theory H / kJ mol-1 4 NaCl(s) Na+(aq) + Cl(aq) Na+(g) + Cl(g) 788 784 1948, Robinson and Storks hydration energy: 784 kJ mol-1

7.1.4 Interaction between cation and anion Long-range forces The interionic distance for NaCl crystal is 200 pm, while for 0.1 moldm-3 solution is 2000 pm. To draw Na+ and Cl apart from 200 nm to 2000 nm, the work is: W (/kJ) = 625 / r for melting: r =1, W = 625 kJ, m.p. = 801 oC。 for dissolution in water: r = 78.5, W = 8 kJ. Therefore, NaCl is difficult to melt by easy to dissolve in water at room temperature.

At medium concentration  + +  +  At high concentration At low concentration At medium concentration

Owing to the strong interaction, ionic pair forms in concentrated solution. +  ionic pair vs free ion In an ionic pair, the cation and anion are close to each other, and few or no solvent molecules are between them. Therefore, HCl does not ionize and NaCl does not dissociate completely in solvents.

Activity coefficient is essential for quite dilute solutions Some facts about strong electrolytes solution present species 0.52 mol·dm-3 KCl 95% K+ + 5% KCl 0.25 mol·dm-3 Na2SO4 76 % Na+ + 24% NaSO4¯ 0.1 mol·dm-3 CuSO4 44% CuSO4 Activity coefficient is essential for quite dilute solutions

7.1.5 Motion under electric field (1) Ionic mobility Ionic velocity Ionic mobility (U) : the ionic velocity per unit electric field, is a constant. (2) Transference number I = I＋ + I－ Q = Q＋ + Q－ t = t+ + t- = 1 The fraction of the current transported by an ion is its transference number or transport number

(3) Relationship between ionic mobility and transfer number For time t: Q+ = A U+t C+ Z+ F Q  = A Ut C Z F C－, Z－, U－; C＋, Z＋, U＋;

9) Measurement of transference numbers (1) Hittorf method (1853) Example: Electrolysis of HCl solution = 1 F + anodic region cathodic region bulk solution +  When 4 Faraday pass through the electrolytic cell +  4Cl- -4e-  2Cl2 4H+ +4e-  2H2 3 mol H+ 1 mol Cl- 

The final result For anodic region: anodic region cathodic region bulk solution +  For anodic region:

EXAMPLE Hittorf’s transference cell Pt electrode, FeCl3 solution: In cathode compartment: Initial: FeCl3 4.00 mol·dm-3 Final: FeCl3 3.150 mol·dm-3 FeCl2 1.000 mol·dm-3 Calculate the transference number of Fe3+ Anode chamber Cathode chamber Cock stopper Hittorf’s transference cell

(2) The moving-boundary method MA, MA’ have an ion in common. The boundary, rather different in color, refractivity, etc. is sharp. In the steady state, the two ions move with the same velocity. When Q coulomb passes, the boundary moves x, the cross-sectional area of the tube is A, then: xAcZ+F = t+Q

7.1.6 Conducting mechanism of electrolyte (1) Category of conductor: Charge carriers: electron; ion; hole; Cooper electron pair; polaron. PbO2, NiOOH Ion and electron Mixed conductor Superconductors electron pair 5th Conducting polymers polaron 4th Semiconductor Electron and hole 3rd Electrolytic solution, solid-state electrolyte (Al2O3, ZrO2) ion 2nd Metals, carbonous materials, some metal oxides electron 1st samples Charge carrier Conductor

(2) Conducting mechanism When current passes through dilute HCl solution Electric transfer of ion in solution under electric field  + Motion of ions in the solution: 1) diffusion: due to difference in concentration 2) convection: due to the difference in density 3) transfer: due to the effect of electric field How can current cross the electrode / solution interface ?

Conducting mechanism: Cl e At cathode: 2H+ + 2e  H2 H+ At anode: 2Cl  2e  Cl2 Conducting mechanism: Transfer of ion in solution under electric field; electrochemical reaction at electrode/solution interface.

For quantitative electrolysis: 7.1.7 Law of electrolysis For quantitative electrolysis: Faraday’s Law where m is the mass of liberated matter; Q the electric coulomb, z the electrochemical equivalence, F a proportional factor named as Faraday constant, M the molar weight of the matter. Faraday’s constant F = (1.6021917  10-19  6.022169  1023 ) C·mol-1 = 96486.69 C·mol-1 usually round off as 96500 C·mol-1, is the charge carried by 1 mole of electron. Micheal Faraday Great Britain 1791-1867 Invent the electric motor and generator, and the principles of electrolysis.

Current efficiency () Current efficiency is lower than 100% due to side-reactions. For example, evolution of hydrogen occur during electro-deposition of copper.

Application of Faraday’s law 1) Definition of ampere: IUPAC: constant current that would deposit 0.0011180 g of silver per second from AgNO3 solution in one second: 1 ampere. 2) Coulometer: copper / silver / gas (H2, O2) coulometer 3) Electroanalysis, Electrolytic analysis Q ↔m ↔ n ↔ c

Example: Given A=1.05 × 10-5 m2, c(HCl)=10.0 mol·m-3, I = 0.01 A for 200 s, x was measured to be 0.17 m, calculate t (H+)

EXAMPLE The mobility of a chloride ion in water at 25 oC is 7.91  10-4 cm2·s-1·V-1. 1) Calculate the molar conductivity of the ion at infinite dilution; 2) How long will it take for the ion to travel between two electrodes separated by 4.0 cm if the electric field is 20 V·cm-1. Answer

Exercise-1: A 0.100 molality solution of NaCl has a freezing-point depression of -0.348 oC, whereas the expected decrease in the freezing point is -0.186 oC. The van’t Hoff factor in this case is 1.87. if there were no ion pairing, we would expect the van’t Hoff factor for NaCl to be 2.00. similarly, acetic acid in a 0.100 molal solution has a van’t Hoff factor of 1.05. Calculate the concentration of NaCl ion pairs and also the percent ionization of acetic acid form the above information.

Exercise-2: A current of 2.34 A is delivered to an electrolytic cell for 85 min. how many grams of (a) Au from AuCl3, (b) Ag form AgNO3, and (c) Cu from CuCl2 will be plated out? Exercise-3 Levine: p.317 10. exercise 48 Exercise -4 Yin: p. 217 exercise 1.