### Conductivity2

```Ion Association
Ion pair formation
Ion Association
Ion pair formation
fully solvated
solvent-shared
or solventseparated
Ion pair
contact ion pair
Ion pairs formed when opposite ions come close
enough to be separated by a distance < r*
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
Electrostatic potential energy for interaction between two univalent ions:
Substitute r = r*
For univalent electrolyte in water at 25oC, IP formation is negligible
r* is only 0.358 nm.
Very difficult to bring the opposite ions so close!
Ionic
Mobilities
Transport Numbers
c=1M
c+= a M
c -= b M
Electroneutrality
condition
c=1M
c+= a M
c -= b M
Let 4F be passed through the cell; t+=3t-
Before electrolysis
On electrolysis
After electrolysis
Let 4F be passed through the cell; t+=3t-
4 Cl- -4e-  2 Cl2
4 H+ +4e-  2 H2
3 mol H+ 1 3 mol H+ 1
mol Cl- 
mol Cl- 
For anodic region:
Cresidual = Cinitial – Creact + C transfer
3 =
6
– 4 + C transfer
t- = 1 / 4 = 0.25
t+ = 3 / 4 = 0.75
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.
Let 1F be passed through the cell;
t 
amount lost in cathode compartmen t
t 
amount lost in anode compartmen t
total amount lost
total amount lost
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 0.793 g.
a. Calculate the transport numbers of Li+ and Cl-.
b. If Lo(LiCl) is 115 W-1cm2mol-1, what are the molar ionic
conductivities and the ionic mobilities?
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.
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
t 
Q
Q

z F c A x
I  t
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
× 96500 C mol-1 / 0.01 A × 200 S
= 0.82
Kohlrausch’s Law of
Independent migration
Valid only at infinite dilution!
Experimentally determined
L o CH 3 COOH
  L o  HCl   L o CH 3 COONa   L o  NaCl 
L o CH 3 COOH
-
-
  L o  HCl   L o CH 3 COONa   L o  NaCl 
Grotthuss Mechanism
Explains the high conductivity of H+ and OH- in water
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
Viscosity of the solvent
acetone
/
0.316
Methyl
alcohol
0.547
mPas
K+
0.0082
0.0054
0.0022
Li+
0.0075
0.0040
0.0015
Walden’s Rule
Ethyl
alcohol
1.200
L. = constant
```