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

2. 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

3. §7.1 Electrolyte and its solution

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

5. 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.

6. 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.

7. 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.

8.  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.

9. 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

10. 7.1.2 Solvation (hydration) of ion +

11. 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.

12. 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

13. 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

14. 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.

15. At medium concentration + +  + 
At high concentration
At low concentration
At medium concentration

16. 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.

17. 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

18. 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

19. (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＋;

20. 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- 

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

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

23. (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

24. 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

25. (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 ?

26. 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.

27. 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 = (    1023 ) C·mol-1
= C·mol-1 usually round off as C·mol-1, is the charge carried by 1 mole of electron.
Micheal Faraday
Great Britain
Invent the electric motor and generator, and the principles of electrolysis.

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

29. Application of Faraday’s law
1) Definition of ampere:
IUPAC: constant current that would deposit 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

30. 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+)

31. 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

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

33. 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 exercise 48
Exercise -4
Yin: p. 217 exercise 1.