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http://docs.google.com/viewer?a=v&q=cache:S0tZ1k91fr0J:www.chemnew.sdu.edu.cn/cce/news/artdown.php%3Ftype%3Dxxkejian%26id%3D1055248383+Electrolytic+solution+,coductivity+ppt&hl=en&gl=uk&pid=bl&srcid=ADGEEShp5BE7ta0cGFnesWN515HmVzSp9-rxCzk8phu5ieDG47OwD9ZaFIyMoxhV_kzvq9Mi6la9bYJISGtwXIqjdMAye-iSBC3SpcJ3ndh3i-M6AjQWBYSO1QlqsrJQ233scC5CWP5u&sig=AHIEtbTu6UaI4zEZGUdPk-K41SDmsGlnWg
Conductivity of solutionThe work of an Asian professor was used after some modifications in addition to my work
Motion of ions in the solution:
Only the transfer can cause net electricity
1) Diffusion: due to difference in concentration
2) Convection: due to the difference in density or temperature
3) Transfer: due to electric field
Conductance and its measurement
For metals: Ohm’s Law I
ER
R: resistance ,unit (Ohm, )
resistivity ,
unit Ohm m, m
A
lR
For electrolytic solution:
conductivity () or spedific conductance:
Definition: = 1/
Dimension: -1 m-1 OR S m-1
electric conductance (G) : G = 1/R
G=l
Dimension: -1, mho, Siemens, S
The conductance cell is usually calibrated with standard KCl (potassium chloride ) solution.
xxRR 11RKcell
C/ mol dm-3 0 0.001 0.01 0.1 1.0
/ S m-1 0 0.0147 0.1411 1.289 11.2
Method of determining specific conductance :
1- Determine R1 from Wheatstone Bridge Circuit using KCl solution.
2- Determine Kcell for KCl from the equation
, specific conductance is known from table.
3- Put the unknown solution in the conductivity cell & determine R
4- Apply the equation to calculate specific conductance of unknown solution:
xxRR
RK cell
4
321 R
RRR
1. Acids and bases have higher conductance
2. C < 5 mol dm-3, increases with C
3. For CH3COOH conductance does not depend on C
Molar conductivity
Cm
V
V
m
11) Definition
V: degree of dilution
The conductivity of a solution is approximately proportional to the concentration
m is the conductivity contributed by 1 mole of electrolyte between electrodes of 1 m apart
Dependence of molar conductivity on concentration
m decreases with concentration.
Kohlrausch replotted m against C1/2
Due to the interaction between ions: interionic attraction
Linear
relationship between m and C1/2 can be observed for 1:1 electrolytes:
C < 0.002~ 0.003 mol dm-3
Kohlrausch empirical formula
cAmm
To extrapolate the linear part of m ~ C1/2 at low concentration to C = 0, m
can be obtained.m
the limiting value of m at infinite dilution: limiting molar conductivity. It is the conductivity of 1 mol of solution at infinite dilution.
Kohlrausch’s law of independent
ionic mobilities
mmm
At infinite dilution, m should be
the sum of the separate contributions of the ions
limiting molar conductivity of weak electrolyte
)()()( AcHHAc mmm
)()()(
)()()(
ClNaAc
NaClH
mmm
mmm
)()()( NaClNaAcHCl mmm
ions r / nm m/102 ions r / nm m
/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
Limiting molar conductivity of ions
2) Viscosity of the solvents
solvent
acetone Methyl alcohol
Ethyl alcohol
/ mPas
0.316 0.547 1.200
m/103
(K+)
0.0082 0.0054 0.0022
m/103
(Li+)
0.0075 0.0040 0.0015
Table. Effect of Viscosity of solvent on limiting molar conductivity of ions
Ionic mobility and transference number 1) Ionic mobility
dl
dVv uE
dl
dVusmv )/(
Under unit potential gradient: dV/dl = 1 V m-1: v = u , ionic mobility
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
3) Relation between ionic mobility and transference number
C-, Z-, u-; C+, Z+, u+;
For time t: Q+ = A Eu+ t C+ Z+ F
Q = A Eut C Z F
Relation between transference number and molar conductivity
I+ = AEu+Z+C+F I = AEuZ C F
I = I++ I = AC+Z+F E(u++ u)
V
uuFEZACG
)(
Measurement of transference numbers
1) Hittorf method (1853)
Electrolysis of HCl solution
Anodic region cathodic regionBulk solution
4 Cl- -4e- 2 Cl2 4 H+ +4e- 2 H2
When 4 Faraday pass through the electrolytic cell
3 mol H+ 1 mol Cl-
3 mol H+ 1 mol Cl-
Example
Pt electrode, FeCl3 solution:
In cathodic 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+
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:
xACZ+F = t+Q
Factors affecting transference number
a) temperature
T / oC KCl(0.0001 M)
0.005 M 0.01M 0.02M
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
Table : Transference number of K+ in KCl solution at different concentration and temperature
b) Co-existed ionselectrolyte 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
uu
ut
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
Problems
1. Make comparison between Hittorf’s method and moving boundary method.
2. Why the limiting molar conductivity of weak electrolyte can not be obtained by extrapolating of m ~ C1/2.
3. What experimental results back up the Kohlrausch’s Law of independent ionic mobilities
4. Summarize the effect of ionic nature on limiting molar conductivity of ions