Chapter 7 Electrochemistry

§7.10 Application of EMF and electrode potential

I. N. Levine

pp. 431--443

14.7 Standard electrode potentials

14.8 Concentration cell

14.9 Liquid-junction potential

14.10 Applications of EMF measurements

14.12 ion-selective membrane electrodes

7.10.1 Computation of emf

For cell with single solution:

Cd(s)|CdSO4(a±) |Hg2SO4(s)|Hg(l)

2 24SO Cd

2

ln ln

( ) ln

E

RT RTa a

nF nF

RTa

nF

y y

y y

Because a is a measurable quantity, E of the cell with

single electrolyte can be calculated exactly.

E

For cell with two electrolytic solutions:

Zn(s)|ZnSO4(m1) ||CuSO4(m1) |Cu(s)

2

2

Cu

Zn

lnaRT

E EnF a

y

1 ,1

2 ,2

lnmRT

E EnF m

y

we have to use mean activity coefficient () which is

measurable in stead of the activity coefficient of individual

ion (+ or -) which is unmeasurable.

7.10.2. Judge the strength of the oxidizing and reducing agents

⊖ (Fe3+/Fe2+) = 0.771 V

⊖ (I2/I) = 0.5362 V

Oxidative form: Fe3+, I2

Reductive form: Fe2+, I-

The oxidative form with higher (standard) electrode

potential is stronger oxidizing species, while the reductive

form with lower (standard) electrode potential is stronger

reducing agent. Why? E > 0 criterion

(Ox)1 + (Red)2 = (Red)1+ (Ox)2

7.10.3 Determination of the reaction direction

When concentration differs far from the standard concentration, should be used in stead of ⊖.

Stronger oxidizing species oxidizes stronger reducing species to produce weaker reducing and weaker oxidizing species.

⊖ (Fe3+/Fe2+) = 0.771 V; ⊖ (I2/I) = 0.5362 V

Fe3+ + I = Fe2+ + 1/2I2

Application of Pourbaix diagram

Cu2+ Cu(OH)2

Cu

pH

/ V

2 4 6 8 10 12 140

CuO22

Cu2O0.0

0.5

1.0

1.5

+Au 1e Au =1.7 Vy

2 2O +2H O+4e 4OH =0.401y

Example

In order to make Au in mine dissolve in alkaline solution

with the aid of oxygen, people usually add some

coordinating agent into the solution. Which coordination

agent is favorable? Please answer this question based on

simple calculation.

Divergent /Disproportionation reaction

Cl2 + 2NaCl = NaCl + NaClO + H2O

Divergent reaction occur when R > L

HIO IO3 + I2

R 2

L 3

(HIO/I ) 1.45V

(IO /HIO) 1.13V

y

y

-1+7 +5 +1 01.7 1.13 1.45 0.534- -25 6 3H I O I O H I O I I

which species can undergo divergent reaction?

Exercise

Can what species undergo divergent reaction?

7.10.4. Advance of reaction (equilibrium constants)

1 mol dm-3 iodine solution + Fe2+ (2 mol dm-3)

32

2

22

3

I3 2 Fe2

I Fe

IFe

Fe I

(Fe / Fe ) (I / I ) ln ln

ln ln a

a aRT RT

nF a nF a

a aRT RTE K

nF a a nF

y y

y y

32

2

22

3

I3 2 Fe2

I Fe

IFe

Fe I

(Fe / Fe ) (I / I ) ln ln

ln ln a

a aRT RT

nF a nF a

a aRT RTE K

nF a a nF

y y

y y

3

2

3 2 3 2 Fe

Fe

(Fe / Fe ) (Fe / Fe ) lnaRT

nF a

y

2I2 2

I

(I / I ) (I / I ) lnaRT

nF a

y

3 22(Fe / Fe ) (I / I )

Fe3+ + I¯ Fe2+ + ½ I2

At equilibrium

Standard emf and standard equilibrium constant

lnr mG nFE RT K y y y

lnRT

E KnF

y ylnRT

E KnF

y y

For any reaction that can be designed to take place in an electrochemical cell, its equilibrium constant can be measured electrochemically.

Four equilibria in solution

1) Dissolution equilibrium

2) Reaction equilibrium

3) Dissociation equilibrium

4) Coordination equilibrium

Example

Determine the solubility products of AgCl(s).

AgCl(s) Ag+ + Cl¯

The designed cell is

Ag(s)|AgNO3(a1)||KCl(a2)|AgCl(s)|Ag(s)

lnRT

E KnF

y y

7.10.5 Potentiometric titrations

GEH+(mx)SCE

automatic potential titrator

0.00 10.00 20.00 30.00 40.00 50.00

0.300

0.100

0.500

0.700

3NaOH / cmV

E /

V

HAc-NaOH

HCl-NaOH

30.0020.00 40.003

NaOH / cmV

Δ

Δ

E

V 0.4

0.2

inflexion point

Differential plot

7.10.6 Determination of mean ion activity coefficients

Pt(s), H2 (g, p⊖)|HCl(m)|AgCl(s)-Ag(s)

1/2 H2 (g, p⊖) + AgCl(s) = Ag(s) + H+(m) + Cl(m)

H Cl

2 2ln ln ln

RT RT RTE E a a E m

nF nF nF y y

For combined concentration cell

1,1

2,2ln2

m

m

F

RTE

Using one electrolytic solution with known mean activity coefficient, the mean activity coefficient of another unknown solution can be determined.

Answer: = 0.9946

Example:

Pt(s), H2 (g, p) |HBr(m) | AgBr(s)-Ag(s)

Given E = 0.0714 V, m = 1.262 10-4 mol·kg-1, E = 0.5330 V,

calculate .

2lnRT

E E mF

y

7.10.7 Determination of transference number

Zn|ZnSO4(a,1) |ZnSO4(a,2) |ZnZn|ZnSO4(a,1) |ZnSO4(a,2) |Zn

Zn(s)|ZnSO4(a,1)|Hg2SO4(s)-Hg(l)-Hg2SO4(s)|ZnSO4(a,2)|Zn(s) Zn(s)|ZnSO4(a,1)|Hg2SO4(s)-Hg(l)-Hg2SO4(s)|ZnSO4(a,2)|Zn(s)

2,

1,

2,

1, ln)12(ln)(

a

a

F

RTt

a

a

F

RTttE j

The relationship between transference number and liquid junction potential can be made use of to determine the transference number of ions.

Electromotive forces of cell with and without liquid junction potential gives liquid junction potential.

7.10.8 Measurement of pH

1909, Sorensen defined: pH = log [H+]

present definition: H

H logp a Non-operational definition

1) Hydrogen electrode

Pt(s), H2 (g, p⊖)|H +(x) |SCE

+ +2

SCE H /H H

SCE

lg

0.05916pH

RTE a

nF

y

poison of platinized platinum

The way to determine pH

2) Quinhydrone electrode

supramolecule :

1:1 quinone: hydroquinone

1) Equal concentrations of both

species in the solution.

2) Being nonelectrolytes, activity

coefficients of dilute Q and

H2Q is unity.

Q + 2H + + 2e- H2Q

Pt(s)|Q, H2Q, H+(mx) |SCE

2

2

2

SCE Q/H Q

H Q

SCE Q/H Q 2Q H

SCE

ln2

0.6995 0.05916pH

E

aRT

F a a

y

2

2

2

SCE Q/H Q

H Q

SCE Q/H Q 2Q H

SCE

ln2

0.6995 0.05916pH

E

aRT

F a a

y

O

O H

H O

O

O

O

2e-2H+

OH

OH

+ +

3) Glass electrode

0.1 molkg-1 HCl内充液 离子选择性膜

membrane potential

2 4 6 8 10 12 14 160-2

GE

/ m

V

pH

GE = ⊖ GE - 0.05915 pH

Linear relation of GE and pH exists within pH range from 0 to 14.

GE H+(mx)(SCE)Test cell:

Inner

fixed

Outer

Variable

Ag(s) AgCl(s) HCl(as) GM H+(ax)(SCE)

Reference-1 Reference-2

4) Operational definition of pH

s x( )pH(x) pH(s)

2.303

E E F

RT

s x( )pH(x) pH(s)

2.303

E E F

RT

Buffer A B C D E

pH 3.557 4.008 6.865 7.413 9.180

pH meter with standard buffer solution

pH of standard buffer solutions at 25 oC

Es = ⊖SCE –(⊖GE - 0.05915 pHs )

Ex = ⊖SCE –(⊖GE - 0.05915 pHx )

Calibration

Measurement

What is the concentration of hydrogen ion in this solution?

Composite electrode:

with reference electrode, usually AgCl/Ag electrode embedded on the side of glass electrode.

7.10.9. Determination of ion concentrationIon-selective electrode

Cutaway view of an ion selective electrode

For F- electrode, thin film of LaF3 single crystal is used as ion selective membrane.

For S2- electrode, compressed thin film of AgCl-Ag2S mixture is used as ion-selective membrane.

antigen antibody

electrochemical sensor

of potential type

7.10.10 Electrochemical sensor

electrochemical sensor of current type

Electrochemical nose

Electroanalytical chip

PbO2

Ion-exchange membrane

amplifierannunciator

Pt electrode

Gas-permeable membrane