Chapter 7 Electrochemistry
§7.2 Conductivity and its application
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:
I
UR
R: resistance,
Unit: Ohm,
A
lR
resistivity
Unit: ·m
Ohm’s Law
For electrolyte solution:
conductivity () : Definition: = 1/ Unit: S·m-1
electric conductance (G) :
Definition: G = 1/R
Unit: -1, mho, Siemens, S
Reciprocal of resistance
l
AG
conductance cell conductance electrode with smooth or platinized platinum foil
~
G
AC
B
D
R2
R1
R3R4
I
It is also a capacitor!
High-frequency alternative current, ca. 1000 Hertz
R3 R2 = R4 R1
4
321 R
RRR
1
1
RG
7.2.2 Measurement of conductance:
~
G
AC
B
DF
R2
R1
R3R4
I
R2
Wheatstone Bridge Circuit
l
AG
Conductometer
GKA
lG cell
RK cell
Cell constant
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.
xxss RR
The conductance cell is usually calibrated using standard aqueous KCl (potassium chloride ) solution.
11.21.2890.14110.01470/ S m-1
1.000.1000.01000.0010c/ mol·dm-3
Relative standards are often used in scientific measurement.
sx
sx R
R
RK cell
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
1) concentration – dependence of conductivity
H2SO4
KOH
LiCl
MgSO4
HAc5 10 15
c/mol·dm-3
0
10
20
30
40
50
60
70
80
/S
·m-1
What can we learn form this figure?
wt % H2SO4
/ S m-1
50 oC
30 oC
10 oC
-10 oC
-30 oC
2) Temperature-dependence of conductivity
1.Why do we use 38 % H2SO4 in
acid-lead battery?
2.Why do we do electrolysis and
electroplating using warm
electrolyte?
ice
7.2.4 Molar conductivity
c
V
V
m 1
1) Definition
degree of dilution
Why do we introduce molar conductivity?
The physical meaning of m:
H2SO4
5 10 15c/mol·dm-3
0
10
20
30
40
50
60
70
80
Is there linear relationship between conductivity and concentration?
m c
mc
2) Concentration-dependence of molar conductivity
Is molar conductivity m independent of concentration?
c / mol·dm-3
m /
S·m
ol-1·m
2
HCl
KOH
NaOHKCl
NaCl
HAc
Why does molar conductivity decrease with increasing concentration?
Does the curve shape inspire you?
Why did Kohlrausch plot m a
gainst c1/2?
Within what concentration range does the linear relation appear.
Kohlrausch
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·m
ol-1·m
2
3/ mol dmc
HCl
H2SO4
KCl
Na2SO4
HAc
Kohlrausch empirical formula
m m A c
limiting molar conductivitym
Kohlrausch’s Square Root Law
Within what concentration range is the Kohlrausch law valid?
Problem: Can we obtain the limiting molar conductivity of weak
electrolytes just by extrapolating the m ~ c1/2 to infinite dilution?
0.01
0.02
0.03
0.04
0.00 0.05 0.10 0.15 0.20
m /
S·m
ol-1·m
2
3/ mol dmc
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
Molar conductivity at infinite dilution for some electrolytes in water at 298 K.
m
Salts KCl NaCl KNO3 NaNO3
/S mol-1 cm2 149.85 126.45 144.96 121.56
23.4 23.4
m m, m,
m, / ionic conductivities at infinite dilution
m
Δ m
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.
m
m
4) Kohlrausch’s law of independent migration
m m m, ,
m at infinite dilution is made up of independent contributions from the cationic and anionic species.
m at infinite dilution is made up of independent contributions from the cationic and anionic species.
Explanation to the same difference
+ - + -
+ +
m m m,K m,Cl m,Na m,Cl
m,K m,Na
(KCl) (NaCl)
3 3m 3 m 3 m,K m,NO m,Na m,NO
m,K m,Na
(KNO ) (NaNO )
m m, m,v v
How can we determine the limiting molar conductivity of weak electrolyte
m m m(HAc) (H ) (Ac )
m m m m m m(H ) (Cl ) (Na ) (Ac ) (Na ) (Cl )
m m m(HCl) (NaAc) (NaCl)
-1 -1m
-1 -1
(HAc) (426.16 91.00 126.45)S m mol
390.71S m mol
Key:
How to measure the ionic conductivity at infinite dilution?
Key:
How to measure the ionic conductivity at infinite dilution?
m m m, ,
1) Ionic mobility
d
d
E
l d
d
EU
l
Ionic mobility (U) : the ionic velocity per unit electric field, is a constant.
Ionic velocity
7.2.5 measurement of limiting molar conductivity of ions
C - , Z - , U - ; C + , Z + , U + ;
For time t:
Q+ = A U+t C+ Z+ F
Q = A Ut C Z F
B A C
I+ = AU+Z+c+F I = AUZ c F
I = I++ I = Ac+Z+F(U++ U)
V
UUFZAcG
)(
)()(
)(
UUFZc
lV
UUFZcA
l
V
UUFZAc
A
lG
c
UUFZcm
)(
For time t:
Q+ = A U+t C+ Z+ F Q = A Ut C Z F
For uni-univalent electrolyte:
)(
UUFm
,, mmm
FUm
, FUm
,
t
FUU
FU
m
m
)(,
,m mt ,m mt
mm t ,
mm t ,
To measure m,+ or m,-, either t+ and t- or U+ and U- must be determined.
c
UUFZcm
)(
UU
Ut
UU
Ut
Transference number
I = I + + I -
Q = Q + + Q -Q
Qt j
j
The fraction of the current transported by an ion is its transference number or transport number
t = t+ + t- = 1
2) transference number
How to measure ionic mobility and transference number?
,m mt ,m mt
mm t ,
mm t ,
3) Measure transference number
(1) Hittorf method (1853)
Example: Electrolysis of HCl solution
When 4 Faraday pass through the electrolytic cell
anodic region cathodic regionbulk solution
+ + + + + + + + + + + + + + + + + +
+ = 1 F
+ + + + + + + + + + + + + + + + + +
4Cl- -4e- 2Cl2 4H+ +4e- 2H23 mol H+ 1 mol Cl-
3 mol H+ 1 mol Cl-
anodic region cathodic regionbulk solution
+ + + + + + + + + + + + + +
For anodic region:
transferedreactedinitialresidual cccc
The final result
EXAMPLE
Pt electrode, FeCl3 solution:
In cathode compartment:
Initial: FeCl3 4.00 mol·dm-3
Final: FeCl3 3.150 mol·dm-3
FeCl2 1.000 mol·dm-3
Calculate the transference number of Fe3+
Hittorf’s transference cell
Anode chamber
Cathode chamber
Cock stopper
(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
Can you measure ionic mobility using this apparatus?
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+)
(1) Temperature and concentration
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
Transference number of K+ in KCl solution at different concentration and temperature
T /℃c /mol·dm-3
4) Influential factors
(3) 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
Table transference number on co-existing ions
Problem: Why does the transference number of certain ion differ a lot in different electrolytes?
ions r / nm 102 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+ 1.04 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
1) Nature of ions
Charge; Radius; charge character; transfer mechanism
7.2.7 Influential factors form
mm
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
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.
Exercise-1
Yin, p. 227, exercise 8
exercise 12
exercise 15