Chapter 7 Electrochemistry
m / S·mol-1·m2
§7.2 Conductivity and its application
0.04
HCl
0.03
H2SO4
0.02
KCl
0.01
0.00
0.05
HAc
0.15
0.10
Na2SO4
0.20
c / mol  dm3
Self reading:
Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002.
pp. 506-521
Section 16.5 electrical conductivity
Section 16.6 electrical conductivity of electrolyte solutions
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
7.2.1 Some concepts
For metals:
Ohm’s Law
U
R
I
R: resistance,
Unit: Ohm, 
l
R
A
resistivity/specific
resistance
Unit: Ohm·m, ·m
For electrolyte solution:
electric conductance (G) :
Definition: G = 1/R
Unit: -1, mho, Siemens, S
Reciprocal of resistance
conductivity () or specific
conductance:
Definition:  = 1/ 
Unit:
S·m-1
A
G 
l
conductance cell
conductance electrode
with smooth or
platinized platinum foil
7.2.2 Measurement of conductance:
Wheatstone Bridge Circuit
High-frequency alternative
current, ca. 1000 Hertz
D
F
R1
R2
A
R2
R4
G
R3
C
I
~
R3  R2 = R4  R1
R2 R3
R1 
R4
1
G
R1
Conductometer
A
G 
l
B
Cell constant
l 
  G   K cellG
 A
K cell  R
EXAMPLE
The conductance of a solution is 0.689 -1. If the cell constant
is 0.255 cm-1, calculate the specific conductance of the solution.
K cell  R
 s Rs   x Rx
Rs
x  s
Rx
The conductance cell is usually calibrated using standard
aqueous KCl (potassium chloride ) solution.
c/ mol·dm-3
0
0.001
0.0100
0.100
1.00
/ S m-1
0
0.0147
0.1411
1.289
11.2
Relative standards are often used in scientific measurement.
EXAMPLE
The conductance of a cell containing an aqueous
0.0560 mol·dm-3 KCl solution whose conductivity is
0.753 -1·m-1 is 0.0239 -1. When the same cell is filled
with an aqueous 0.0836 mol·dm-3 NaCl solution, its
conductance is 0.0285 -1. Calculate the conductivity of
the NaCl solution.
7.2.3. Influential factors of conductivity
 /S·m-1
1) concentration – dependence of conductivity
80
70
H2SO4
60
50
KOH
40
30
LiCl
20
MgSO4
10
0
HAc
5
10
15
c/mol·dm-3
2) Temperature-dependence of conductivity
 / S m-1
50 oC
30 oC
1.Why do we usually used 38 %
10 oC
H2SO4 in acid-lead battery;
-10 oC
2.Why do we usually conduct
ice
-30 oC
electrolysis and electroplating
using warm electrolyte?
wt % H2SO4
7.2.4 Molar conductivity
Why do we introduce molar conductivity?
1) Definition
m 

c
m 

1
V
 V
The physical meaning of m:
degree of dilution
m / S·mol-1·m2
2) Concentration-dependence of molar conductivity
HCl
KOH
NaOH
KCl
NaCl
HAc
c / mol·dm-3
Why does m decrease with
increasing concentration?
m / S·mol-1·m2
3) Kohlrausch’s empirical formula
0.04
HCl
0.03
H2SO4
0.02
KCl
Kohlrausch
Why did Kohlrausch plot
m against c1/2?
Within what concentration
range did the linear relation
appear.
Na2SO4
0.01
HAc
0.00 0.05 0.10
0.15
0.20
c / mol  dm3
Kohlrausch empirical formula
m  m  A c
m
limiting molar conductivity
Kohlrausch’s Square Root Law
Within what concentration
range is the Kohlrausch law
valid?
1·m2
m / S·mol-
0.04
0.03
0.02
0.01
0.00 0.05 0.10
0.15 0.20
c / mol  dm3
Problem: Can we obtain the limiting molar conductivity of weak
electrolytes just by extrapolating the m ~ c1/2 to infinite dilution?
Molar conductivity at infinite dilution for some
electrolytes in water at 298 K.
Salts


m /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
4) Kohlrausch’s law of independent migration
Salts
m/S mol-1 cm2
Δm
KCl
NaCl
KNO3
NaNO3
149.85
126.45
144.96
121.56
23.4
23.4
The difference in m of the two electrolytes containing the same
cation or anion is the same. The same differences in m led
Kohlrausch to postulate that molar conductivity at infinite
dilution can be broken down into two contributions by the ions.
 

m


m, / 

m,


m,
ionic conductivities at infinite dilution
 

m

m ,


m ,
m  vm,  vm,
m at infinite dilution is made up of independent
contributions from the cationic and anionic species.
Explanation to the same difference
m (KCl)  m (NaCl)  m,K  m,Cl  m,Na  m,Cl
+
-
+
-
 m,K+  m,Na +




m (KNO3 )  m (NaNO3 )  m,K
 m,NO
 m,Na
 m,NO



 m,K



m,Na 

3


3
How can we determine the limiting molar conductivity of
weak electrolyte
m (HAc)  m (H )  m (Ac )
 m (H )  m (Cl )  m (Na  )  m (Ac )  m (Na  )  m (Cl )
 m (HCl)  m (NaAc)  m (NaCl)
m (HAc)  (426.16  91.00 126.45)S  m-1  mol-1
 390.71S  m-1  mol-1
Key:
How to measure the ionic conductivity at infinite dilution?
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)
Ac  Z  F (U   U  )
G
V
l Ac Z  F (U   U  ) l
 G 
A
V
A
c Z F (U   U  )
  
 c Z  F (U   U  )
V
l


c
Z
F
(
U

U

 

 )
m 
c


c
Z
F
(
U

U

 

 )
m 
c
For uni-univalent electrolyte:

m


m  m,  m,


  F (U  U )


m, 


m, 

m





m, 
U F





U F
U F
 t


(U   U  ) F

m,

 t 

m
m,  tm
To measure m,+ or m,-, either t+ and t- or U+ and U- must be
determined

7.2.6 Influential factors for
m
1) Nature of ions
ions
r / nm
H+

Li+
102
m
102
m
ions
r / nm
3.4982
OH¯

1.98
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+
1.04
1.189
Fe(CN)63

3.030
Al3+
0.57
1.89
Fe(CN)64

4.420
Fe3+
0.67
2.04
La3+
1.04
2.09
Charge; Radius; charge character; transfer mechanism
Transport mechanism of hydrogen and hydroxyl ions
Grotthus mechanism
(1805)
The ion can move along an extended hydrogen-bond network.
Science, 2002, 297:587-590
2) Temperature
Transference number of K+ in KCl solution at different
concentration and temperature
c /mol·dm-3
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
T /℃
3) Co-existing ions
Table transference number on co-existing ions
Electrolyte
KCl
KBr
KI
KNO3
t+
0.4902
0.4833
0.4884
0.5084
Electrolyte
LiCl
NaCl
KCl
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?
Summary
Macroscopic
Microscopic

G
Dynamic

U
U
t
t
m


m


m, 
, 

m, 
Exercise-1
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.