1. Ion Association
Ion pair formation

2. solvent-shared or solvent-separated
Ion Association
Ion pair formation
fully solvated
solvent-shared or solvent-separated
Ion pair
contact ion pair
Ion pairs formed when opposite ions come close enough to be separated by a distance < r*

3. Bjerrum As
Charge of ions increases (zi): r* increases, probability of ion pair formation increases.
Temperature increases, r* decreases, probability of IP formation decreases. Kinetic energy acts against attraction.
Polarity of solvent increases (er), attraction decreases, probability of IP formation decreases

4. Very difficult to bring the opposite ions so close!
Electrostatic potential energy for inter- action between two univalent ions:
Substitute r = r*
For univalent electrolyte in water at 25oC, IP formation is negligible
r* is only nm.
Very difficult to bring the opposite ions so close!

6. Ionic Mobilities

11. Transport Numbers
c = 1 M c+= a M c-= b M

12. Electroneutrality condition

14. c = 1 M c+= a M c-= b M

15. Let 4F be passed through the cell; t+=3t-
Before electrolysis
On electrolysis
After electrolysis

16. Let 4F be passed through the cell; t+=3t-
4 Cl- -4e-  2 Cl2
4 H+ +4e-  2 H2
3 mol H+ 1 mol Cl- 
3 mol H+ 1 mol Cl- 

17. For anodic region:
Cresidual = Cinitial – Creact + C transfer
3 = – C transfer
t- = 1 / 4 = 0.25
t+ = 3 / 4 = 0.75

18. measurement of transport numbers by Hittorf method
The method of Hittorf is based on concentration changes in the anodic region and cathodic region in an electrolytic cell, caused by the passage of current through the electrolyte.

19. Let 1F be passed through the cell;

20. A solution of LiCl was electrolyzed in a Hittorf cell
A solution of LiCl was electrolyzed in a Hittorf cell. After a current of 0.79 A had been passed for 2 h, the mass of LiCl in the anode compartment has decreased by g.
Calculate the transport numbers of Li+ and Cl-.
If Lo(LiCl) is 115 W-1cm2mol-1, what are the molar ionic conductivities and the ionic mobilities?

21. 2) The moving-boundary method
MA, MA’ have an ion in common. The boundary, rather difference in color, refractivity, etc. is sharp.
In the steady state, the two ions move with the same velocity.

22. When Q coulomb passes, the boundary moves x, the cross-sectional area of the tube is A:
No. of mole of H+ that passed from AA’ to BB’
n=c.V=c+.A.x
Charge carried by these moles:
Q+=z+ F n+=z+ F c+ A x

23. Sample:
When 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+).
Solution:
t+ = 0.17 m× 1.05 × 10-5 m2 × 10.0 mol m-3 ×1
× C mol-1 / 0.01 A × 200 S
= 0.82

24. Independent migration
Kohlrausch’s Law of
Independent migration
Valid only at infinite dilution!

26. Experimentally determined- - -

27. Grotthuss Mechanism
Explains the high conductivity of H+ and OH- in water

28. Ion Solvation Size  But larger size means slower motion,
the conductivity should drop?!!!!
Smaller size,
larger interaction with water molecule,
hydrate shell larger on Li+,
moving species larger,
Lower conductivity

29. Viscosity of the solvent
acetone
Methyl alcohol
Ethyl alcohol
 / mPas
0.316
0.547
1.200 K+
0.0082
0.0054
0.0022
Li+
0.0075
0.0040
0.0015
Walden’s Rule L.h = constant