每日一句 凡是有大成功的人，都是有绝顶聪明而肯作笨功夫的人。 胡适致白薇

7 4 3 2 1 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84 >85 61.2

§7.1 Electrolyte and electrolytic solution Out-class reading: 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.

Main contents: Electrolyte: origin of the concept Existence of ions in solution Ion-dipole interaction--Hydration theory Interionic interaction Motion under electric field Conducting mechanism Faraday’s law and its application

1) Definition of electrolyte An electrolyte is a substance that, when dissolved in solvent, produces a solution that will conduct electricity. Progress of the definition: (1) molten salt; (2) solid-state electrolyte (3) room-temperature ionic liquids (RTIL).

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 modified 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.

 3) Dissociation theory for weak electrolytes  + In 1887, Svant A. 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.

New definitions: Ion, cation, anion; Dissociation, ionization Weak / strong electrolyte? True / potential electrolyte? Theory of Electrolytic Dissociation Acid-base theory Cf. Levine p.295

2. Ions in solution Solvation shells In what state do ions exist in solution? Solvated (hydrated) ion ion Primary hydration shell secondary hydration shell Disordered layer Bulk solution Solvation shells

Hydration of ion Coordination number: Li+: 4, K+: 6 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. 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

3. Hydration Theory / Solvation Theory Why does NaCl only melt at higher temperature, but dissolve in water at room temperature? H / kJ mol-1 4 NaCl(s) Na+(aq) + Cl(aq) Na+(g) + Cl(g) 788 784 hydration energy: 784 kJ mol-1 1948, Robinson and Storks

4. Interionic interaction 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 In equilibrium -- Bjerrum Cf. Levine, p. 304

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 For concentration-dependence of ion pair, see Levine p. 305, Figure 10.10 Degree of association Activity coefficient is essential for quite dilute solutions

5. Conducting mechanism of electrolyte Electric transfer of ion in solution under electric field +  I E 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: 6. 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) Electrolytic analysis – electroanalysis Q ↔m ↔ n ↔ c

7. Transfer of ion under electric field How do we describe the motion of ions under electric field? 1) Ionic mobility Rate of electric transfer: Ionic velocity Ionic mobility (U) : the ionic velocity per unit electric field, is a constant.

measure ionic mobility using moving boundary method MA, MA’ have an ion in common. The boundary, rather different in color, refractivity, etc. is sharp.

Supporting electrolyte? 8. Transference number Transference number (transfer/ transport number), is the fraction of the current transported by an ion. I = I＋ + I－ Q = Q＋ + Q－ plane A I－ I＋ I t+ + t- = ? Supporting electrolyte?

(1) Principle for measuring transference number For time t: Q+ = A U+t c+ Z+ F Q  = A Ut c Z F Owing to electric migration, on the left side of plane A, there are more anions, while on the right side, more cations. Is this real?

(1) Principle of 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- 

4H+ +4e-  2H2 final result For anodic region: 4Cl- -4e-  2Cl2  4Cl- -4e-  2Cl2 4H+ +4e-  2H2 3 mol H+ 1 mol Cl-  final result anodic region cathodic region bulk solution +  For anodic region:

EXAMPLE What factors will affect the accuracy of the measurement? 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 What factors will affect the accuracy of the measurement? Hittorf’s transference cell

(2) Principle for the moving-boundary method When Q coulomb passes, the boundary moves x, the cross-sectional area of the tube is A, then: xAcZ+F = Q+ = t+Q Why is the moving-boundary method more accurate that the Hittorf method? Are there any other methods for measuring transfer number?

(3) Influential factors (1) Temperature and (2) Concentration Transference number of K+ in KCl solution at different concentration and temperature 0.000 0.005 0.01 0.02 15 0.4928 0.4926 0.4925 0.4924 25 0.4906 0.4903 0.4902 0.4901 35 0.4889 0.4887 0.4886 0.4885 c /mol·dm-3 T /℃

Table transference number on co-existing ions Electrolyte KCl KBr KI KNO3 t+ 0.4902 0.4833 0.4884 0.5084 LiCl NaCl HCl t– 0.6711 0.6080 0.5098 0.1749 Problem: Why does the transference number of certain ion differ a lot in different electrolytes?