Chapter 7 Electrochemistry

§7.2 Conductivity and its application

Out-class extensive reading:

Levine: pp. 506-515,

16.5 electric conductivity

16.6 Electrical conductivity of electrolyte solutions

Key problem:

How to evaluate the ability of an electrolytic solution to

conduct electricity?

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

~

G

AC

B

D

R2

R1

R3R4

I Wheatstone Bridge Circuit

conductance electrode with smooth or platinized platinum foil electrodes

conductance cell

Conductance cell and conductance electrode

R3 R2 = R4 R1

4

321 R

RRR

1

1

RG

2. Measurement of conductance:

~

G

AC

B

DF

R2

R1

R3R4

I

R2

l

AG

High-frequency alternative

current, ca. 1000 Hertz ?

Conductometer

a capacitor!

GKA

lG cell

xxss RR

Calibration: 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

sx

sx R

R

Cell constant

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.

3. Influential factors of conductivity

(1) Concentration

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

1.Why do we use 38 % H2SO4 in

acid-lead battery?

2.Why do we do electrolysis and

electroplating using warm

electrolyte?

ice

4. Molar conductivity

H2SO4

5 10 15

c/mol·dm-3

0

10

20

30

40

50

60

70

80

Definition

Why do we introduce the concept of molar conductivity?

c

m c

mc

(2) Concentration-dependence of molar conductivity

c / mol·dm-3

m /

S·m

ol-1·m

2

HCl

KOH

NaOHKCl

NaCl

HAc

(1) Why does molar conductivity decrease with increasing concentration?

(2) Does the curve shape inspire you?

Why did Kohlrausch plot m

against c1/2?

Within what concentration range does the linear relation appear?

Kohlrausch

5. 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 applicable?

For strong electrolyte

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

6. 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, ,

7. Measuring limiting molar conductivity of ions

C － , Z － , U － ; C ＋ , Z ＋ , U ＋ ;

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 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

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