1. §7.2 Conductivity and its application
Chapter 7 Electrochemistry
§7.2 Conductivity and its application
0.01
0.02
0.03
0.04
0.00
0.05
0.10
0.15
0.20
m / S·mol-1·m2
HCl
H2SO4
KCl
Na2SO4
HAc

2. Self reading:
Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002. pp
Section 16.5 electrical conductivity
Section 16.6 electrical conductivity of electrolyte solutions

3. Main contents:
7.2.1 some concepts
7.2.2 measurement of electric conductance
7.2.3 factors on conductivity
7.2.4 molar conductivity: Kohlrausch empirical formula and law of independent migration
7.2.5 measurement of limiting molar conductivity of ions
7.2.6 factors on limiting molar conductivity of ions

4. 7.2.1 Some concepts For metals: electric conductance (G) : Ohm’s Law
For electrolyte solution:
electric conductance (G) :
Definition: G = 1/R
Unit: -1, mho, Siemens, S
Ohm’s Law
R: resistance,
Unit: Ohm, 
Reciprocal of resistance
conductivity () or specific conductance:
Definition:  = 1/ 
Unit: S·m-1
resistivity/specific resistance
Unit: Ohm·m, ·m

5. conductance cell
conductance electrode with smooth or platinized platinum foil

6. High-frequency alternative current, ca. 1000 Hertz
7.2.2 Measurement of conductance: ~ G A C B D F R2 R1 R3 R4 I R2
Wheatstone Bridge Circuit
High-frequency alternative current, ca Hertz
R3  R2 = R4  R1
Conductometer

7. Cell constant
EXAMPLE
The conductance of a solution is -1. If the cell constant is cm-1, calculate the specific conductance of the solution.

8. Relative standards are often used in scientific measurement.
The conductance cell is usually calibrated using standard aqueous KCl (potassium chloride ) solution.
11.2
1.289
0.1411
0.0147
/ S m-1
1.00
0.100
0.0100
0.001
c/ mol·dm-3
Relative standards are often used in scientific measurement.

9. EXAMPLE
The conductance of a cell containing an aqueous mol·dm-3 KCl solution whose conductivity is -1·m-1 is -1. When the same cell is filled with an aqueous mol·dm-3 NaCl solution, its conductance is -1. Calculate the conductivity of the NaCl solution.

10. 7.2.3. Influential factors of conductivity
1) concentration – dependence of conductivity
 /S·m-1
H2SO4
KOH
LiCl
MgSO4
HAc 5 10 15
c/mol·dm-3 20 30 40 50 60 70 80

11. 2) Temperature-dependence of conductivity
wt % H2SO4
 / S m-1
50 oC
30 oC
10 oC
-10 oC
-30 oC
Why do we usually used 38 % H2SO4 in acid-lead battery;
Why do we usually conduct electrolysis and electroplating using warm electrolyte?
ice

12. 7.2.4 Molar conductivity Why do we introduce molar conductivity?
1) Definition
degree of dilution
The physical meaning of m:

13. 2) Concentration-dependence of molar conductivity
c / mol·dm-3
m / S·mol-1·m2
HCl
KOH
NaOH
KCl
NaCl
HAc
Why does m decrease with increasing concentration?

14. 3) Kohlrausch’s empirical formula
0.01
0.02
0.03
0.04
0.00
0.05
0.10
0.15
0.20
m / S·mol-1·m2
HCl
H2SO4
KCl
Na2SO4
HAc
Kohlrausch
Why did Kohlrausch plot m against c1/2?
Within what concentration range did the linear relation appear.

15. Kohlrausch empirical formula
limiting molar conductivity
Kohlrausch’s Square Root Law
Within what concentration range is the Kohlrausch law valid?

16. 0.01
0.02
0.03
0.04
0.00
0.05
0.10
0.15
0.20
m / S·mol-1·m2
Problem: Can we obtain the limiting molar conductivity of weak electrolytes just by extrapolating the m ~ c1/2 to infinite dilution?

17. Molar conductivity at infinite dilution for some electrolytes in water at 298 K.
Salts
/S mol-1 cm2
HCl
426.16
LiCl
115.03
NaCl
126.45
KCl
149.85
LiNO3
110.14
KNO3
144.96
NaNO3
121.56

18. 4) Kohlrausch’s law of independent migration
Salts
KCl
NaCl
KNO3
NaNO3
/S mol-1 cm2
149.85
126.45
144.96
121.56
23.4
The difference in of the two electrolytes containing the same cation or anion is the same. The same differences in led Kohlrausch to postulate that molar conductivity at infinite dilution can be broken down into two contributions by the ions.
ionic conductivities at infinite dilution

19. m at infinite dilution is made up of independent contributions from the cationic and anionic species.
Explanation to the same difference

20. How can we determine the limiting molar conductivity of weak electrolyte
Key:
How to measure the ionic conductivity at infinite dilution?

21. 7.2.5 measurement of limiting molar conductivity of ions
1) transference number and molar conductivity
I+ = AU+Z+c+F I = AUZ c F
I = I++ I = Ac+Z+F(U++ U)

22. For uni-univalent electrolyte:
To measure m,+ or m,-, either t+ and t- or U+ and U- must be determined

23. 7.2.6 Influential factors for
1) Nature of ions
ions
r / nm
102 H+ 
3.4982
OH¯
1.98
Li+
0.68
0.387 F¯
1.23
0.554
Na+
0.98
0.501
Cl¯
1.81
0.763 K+
1.37
0.735
Br¯
1.96
0.784
Mg2+
0.74
1.061
CO32
1.66
Ca2+
1.04
1.190
C2O42
1.48
Sr2+
1.189
Fe(CN)63
3.030
Al3+
0.57
1.89
Fe(CN)64
4.420
Fe3+
0.67
2.04
La3+
2.09
Charge; Radius; charge character; transfer mechanism

24. Transport mechanism of hydrogen and hydroxyl ions
Grotthus mechanism (1805)
The ion can move along an extended hydrogen-bond network.
Science, 2002, 297:

25. 2) Temperature
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 /℃

26. 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?

27. Summary
Macroscopic
Microscopic G 
Dynamic  U U t t

28. Exercise-1
The mobility of a chloride ion in water at 25 oC is 7.91  10-4 cm2·s-1·V-1.
Calculate the molar conductivity of the ion at infinite dilution;
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.