每日一句 · PDF fileSolutions. Graphical Representation of the Role of pH and Potential."...

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Epictetus：《The meditations》中央编译出版社，北京，2015

Chapter 7 Electrochemistry

§7.9 Electrode potential and electromotive forces

7.9.4 pH-dependence of : Pourbaix diagram

For electrode reaction with H+ or OH- participating in, the

electrode potential will depend on pH.

O2 + 4H+ + 4e- 2H2O

= ⊖ + 0.05916 lgaH+

= 1.229 - 0.05916 pH

= ⊖ + 0.05916 lgaH+

= 0.000 - 0.05916 pH

2H+ + 2e- H2

pH-potential diagram/Pourbaix diagram


Marcel Pourbaix, (1904–1998), a

Russian-born, Belgian chemist,

“Atlas of electrochemical equilibria

in aqueous solutions”, National

Association of Corrosion Engineers,

1974.



By 1938, he had devised the potential-

pH diagrams for which he became

famous. In 1939, he presented to the

Faculty his doctoral dissertation,

accompanied by a thesis entitled

"Thermodynamics of Dilute Aqueous

Solutions. Graphical Representation of

the Role of pH and Potential."

Pourbaix (left) and Evans (right)

图形化方法（Graphic method, visualization）



Construction of Pourbaix diagram

Cu2+Cu(OH)2

Cu

pH

/ V

2 4 6 8 10 12 140

CuO22

Cu2O



(1) When we plate Cu,

why do we use acidic

copper sulfate solution?

(2) When we anodize

copper in neural solution,

what phenomenon can we

observed?

§7.10 Application of EMF and electrode potential

Levine

pp. 431--443

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

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

1 ,1

2 ,2

lnmRT

E EnF m

we have to use mean activity coefficient () which is

measurable in stead of the activity coefficient of individual

ion (+ or -) which is unmeasurable.

7.10.1 Computation of emf


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

Cu2O

0.0

0.5

1.0

1.5



Corrosion with hydrogen

evolution

Corrosion with oxygen

absorption

+Au 1e Au =1.7 V

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

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

-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?



元素电势图（Latimer diagram）

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

3

2

3 2 3 2 Fe

Fe

(Fe / Fe ) (Fe / Fe ) lnaRT

nF a

2I

2 2

I

(I / I ) (I / I ) lnaRT

nF a

3 2

2(Fe / Fe ) (I / I )

Fe3+ + I¯ Fe2+ + ½ I2

At equilibrium


Standard emf and standard equilibrium constant

lnr mG nFE RT K lnRT

E KnF

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



7.10.5 Potentiometric titrations

GEH+(mx)SCE

automatic potential titrator


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

For combined concentration cell

1,1

2,2ln

2

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

7.10.6 Determination of mean ion activity coefficients


7.10.7 Determination of transference number

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

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

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 2

Q H

SCE

ln2

0.6995 0.05916pH

E

aRT

F a a

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

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:

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

Reference-1Reference-2



4) Operational definition of pH

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 concentration

Ion-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.


7.10.9. Determination of ion concentration


antigen antibody

electrochemical sensor

of potential type

7.10.10 Electrochemical sensor

electrochemical sensor of current type

Electrochemical nose

Electroanalytical chip


7.10.10 Electrochemical sensor


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