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Conductivity of solutionThe work of an Asian professor was used after some modifications in addition to my work

Conducting mechanism of electrolytic solution

MzF

Qm

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

Type 206

conductance electrode

conductivity cell

Wheatstone

Bridge

Circuit

High-frequency alternative current,

frequency = 1000 Hertz

R1 / R2 = R3 / R4

4

321 R

RRR

1

1

RG

GKA

lG cell

RK cell

Cell constant of a conductivity cell

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

Influential factors for conductivity

1) Concentration.

2) Type of electrolyte

3) Temperature

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

(2) Temperature- dependence of conductance

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

Influential factors for m

1)Nature of ions

(a) Charge

(d) Mechanism of transfer

(b) Radius

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

( c) Mechanism of hydrogen and hydroxyl ions transfer

Grotthus mechanism (1805)

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

The Stokes’s law

r

eFZm )300(6

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

Q = Q+ + Q = AtF E( u+C+ Z+ + u C Z)

C+ Z+ = C Z

Q = AtF C+ Z+ E( u+ + u)

uu

ut

uu

ut

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

)(

)(

)()(

)(

uuFZC

E

uuFEZC

lV

uuFEZCA

l

V

uuFEZAC

A

lG

C

uuFZCm

)(

For uni-univalent electrolyte:

)(

uuzFm

mmm Fum

Fum

Cm

t

Fuu

Fu

m

m

)(

mm t

mm t

To measure m+ or m- , either t+ and t- or u+ and u- must be determined

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-

Cresidual = Cinitial – Creact + C transfer

For anodic region:

Hittorf’s

transference cell

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