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

G

m

m

U U

t t

Macroscopic Microscopic

, ,, m m

Dynamic

Summary

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

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