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Physical Chemistry GTM/13 1

A quote of the week

(or camel of the week):

A life spent making mistakes is not only more honorable, but more useful than a life spent doing nothing.

George Bernard Shaw

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Ion Transport Numbers

Ion transport number (also transference number) of an ion is a fraction of

total charge carried by the electrolyte ascribed to a given ion.

If in a solution there is only single substance dissociated

(neglecting water) then: otherwise:

Transference number is a ratio of charge carried by a given ion to

the charge carried by the electrolyte as a whole.

1tt

q

qt

q

qt

;

1i

it

Physical Chemistry GTM/13

ii

ii

q

qt

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Ion Transport Numbers (2)

Ion transport numbers can also be defined by:

i

it

i

it

;

vv

vt

vv

vt ;

Physical Chemistry GTM/13

ii

ii

i

it

ii

ii

v

vt

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Ion Transport Numbers (3)

For a solution containing several substances:

In particular, for an electrolyte solution containing only one

substance dissolved (neglecting water):

tt ;

Physical Chemistry GTM/13

ii

iit

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Conductivities of

Electrolytes (7)

Resistance (passive) is given by the following combination of

the 1st and 2nd Ohm’s law:

s

l

i

UR

1

s

i

l

U

1E

l

Uj

s

i

Physical Chemistry GTM/13

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Determination of Ion

Transport Numbers (1)

Moving border method (McInnes method).

Cathode

Anode

MB1

MB2

N+X–

M+X–

Leading

solution

Following solution

(indicating)

uM>uN

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Determination of Ion

Transport Numbers (2)

FzvcqM

001.0

q

qt tiq

ti

Fvct

001.0

Physical Chemistry GTM/13

Cathode

Anode

MB1

MB2

N+X–

M+X–

Moving border method (McInnes method).

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Determination of Ion

Transport Numbers(3) Hittorf’s method (electrolyser).

Cathode

Anode

anolyte

Catholyte

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Determination of Ion

Transport Numbers (4)

Hittorf method (calculations).

Solution: AgNO3 Cathode: Ag Anode: Ag

Cathodic reaction: Ag+(aq) + e– = Ag0(s)

Anodic reaction: Ag0(s) = Ag+(aq) + e–

We assume that we know the charge q, which may be

measured either as an i·t product or measured

independently by a coulometer.

This is just an example, the whole trick is to write the balance

for different systems of electrolyte and electrodes.

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Determination of Ion

Transport Numbers(5)

Hittorf’s method (material balance of catholyte in moles).

ion reaction migration total

Ag+ –q/zF +t+q/zF –t–q/zF

NO3– --- –t–q/zF –t–q/zF

Δ (decrease) –t–q/zF mole of AgNO3

Physical Chemistry GTM/13

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Determination of Ion

Transport Numbers (6)

ion reaction migration total

Ag+ +q/zF –t+q/zF +t–q/zF

NO3– --- +t–q/zF +t–q/zF

Δ (increase) +t–q/zF mole of AgNO3

Hittorf’s method (material balance of anolyte in moles).

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Faraday law

The law says that mass of an electrolysis product at a given

electrode is directly proportional to the charge passed across the

electrode and molar mass of the product.

dttizF

Mdttikqkm )()(

Number of moles of product is

equal to: dttizF

n )(1

In well defined half-cells the law is obeyed exactly. For many years

before the SI system, Coulomb was the basic electrical unit and it

was defined using Faraday law for a silver/silver nitrate cathode.

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13

Examples of galvanic cells

analysis

Zn(s)|ZnCl2(aq)|AgCl(s)|Ag(s)

Cathode (right): AgCl(s) + e– = Ag0(s) + Cl–(aq)

Anode (left): Zn0(s) = Zn+2(aq) + 2e–

Overall (cell): 2AgCl(s) + Zn0(s) = 2Ag0(s) + Zn+2(aq) + 2Cl–(aq)

From the structure of the cell, the reactions may be deduced:

QF

RTEE cellcell ln

2

0

32

22 4 ZnClClZn

cccQ Assuming activity coefficients are equal to 1:

0

|

0

||

02

ZnZnClAgClAgcell EEE

Physical Chemistry GTM/13

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Examples of galvanic cells

analysis (2)

Cathode (reduction): MnO2(s) + 4H+(aq) + 2e– = Mn+2(aq) + 2H2O(l)

Anode (oxidation): 3I–(aq) = I3–(aq) + 2e–

Cell diagram: Pt| I3–(aq),I–(aq)||Mn+2(aq),H+(aq)|MnO2(s)|C

From the overall reaction, the half-reactions and cell structure may be

deduced:

QF

RTEE cellcell ln

2

0

43

32

HI

IMn

cc

ccQAssuming activity coefficients are equal to 1:

0

|

0

,|

0

32

2 IIHMnMnOcell EEE

3I–(aq) + MnO2(s) + 4H+(aq) = I3–(aq) + Mn+2(aq) + 2H2O(l)

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Equilibrium Constant and

Cell Potential

QRTGG rr ln0

Once more moving back to the study of chemical equilibria:

we can find that at equilibrium hence

KQGr and 0 KRTGr ln0

At the same time: 00 zFEGr

Therefore: RT

zFE

eKKRTzFE

0

and ln0

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Primary Batteries

Leclanché cell:

E0=1,5-1,6V

carbon rod with a copper cap (cathode)

zinc housing (anode)

seal

MnO2 paste

electrolyte paste

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Primary Batteries (2)

A: Zn(s) = Zn2+(aq) + 2e–

C: 2MnO2(s) + 2H2O(l) + 2e– = 2MnOOH(s) + 2OH–(aq)

E: Zn2+(aq) + 2NH4Cl(aq) + 2OH–(aq) = Zn(NH3)2Cl2(aq) + 2H2O(l)

O: 2MnO2(s) + Zn(s) + 2NH4Cl(aq) = 2MnOOH(s) + Zn(NH3)2Cl2(aq)

Zn(s)|NH4Cl(aq)|MnO2(s)|C

This is Leclanché cell chemistry for normal discharge rate.

Batteries with ZnCl2 electrolyte are also known.

Alkaline batteries: Zn(s)|NaOH(aq)|MnO2(s)|C

2MnO2(s) + Zn(s) + 2H2O(l) = 2MnOOH(s) +Zn(OH)2(s)

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Secondary batteries

Pb

mV

R

PbO2

H SO ; 36%2 4

Gaston Planté, 1859

Lead battery

E0 = 2.14 V

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Secondary batteries (2)

O2H +PbSO2e+2H+SOH +PbO 24

-+

422

gdischargin

charging

O2H +2PbSOSO2H+Pb +PbO 24422

gdischargin

charging

e22H +PbSOSOH +Pb 442

gdischargin

charging

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Secondary batteries (3)

222 Cd(OH)+2Ni(OH)O2H+Cd +2NiOOHgdischargin

charging

2n2 MOLiMO +nLigdischargin

charging

Thomas Alva Edison

Other secondary batteries:

Nickel-cadmium battery, E0=1,26 V

lithium battery (non-aqueous), E0<4 V

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Fuel cells

chemical energy→heat→mechanical energy→electric energy

fuel combustion steam rotation current

furnace boiler turbine generator

Traditional (conventional) way of production of electric energy:

Overall efficiency is low, esp. the heat → work (mechanical

energy) transition is strictly limited by the II law of

thermodynamics.

The new approach, environmentally friendly to some extent, though

also afflicted by some weaknesses is using fuel cells (FCs).

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Fuel cells (2)

William Robert Grove 1811 - 1896

First fuel cell The London Institution,

1839 Physical Chemistry GTM/13

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Fuel cells (3)

Almost any reaction may be

carried out in a galvanic cell !!!

Anode(–): Zn0=Zn2+ + 2e–

Cathode(+): Cu2+ + 2e– =Cu0

Overall: Zn0 + Cu2+ = Cu0 + Zn2+

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Fuel cells (3a)

Almost any reaction may be

carried out in a galvanic cell !!!

Anode(–): Zn0=Zn2+ + 2e–

Cathode(+): Cu2+ + 2e– =Cu0

Overall: Zn0 + Cu2+ = Cu0 + Zn2+

Anode(–): 2H2(g) = 4H+ + 4e–

Cathode(+): O2(g) + 4e– +4H+ = 2H2O

Overall: 2H2(g) +O2(g) = 2H2O

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Fuel cells (3b)

Almost any reaction may be

carried out in a galvanic cell !!!

Anode(–): Zn0=Zn2+ + 2e–

Cathode(+): Cu2+ + 2e– =Cu0

Overall: Zn0 + Cu2+ = Cu0 + Zn2+

Anode(–): 2H2(g) = 4H+ + 4e–

Cathode(+): O2(g) + 4e– +4H+ = 2H2O

Overall: 2H2(g) +O2(g) = 2H2O

Anode(–): CH3OH + H2O = CO2 + 6H+ + 6e–

Cathode(+): 1½O2 + 6H+ + 6e– = 3H2O

Overall: CH3OH + 1½O2 = CO2 + 2H2O

Physical Chemistry GTM/13

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Fuel cells (4)

The simplest model of

a hydrogen/oxygen FC

E0 = 1.23 V Pt

mV

R

Pt

mostek elektrolityczny

p=1 Atm

H2

p=1 Atm

O2

H SO2 4H SO2 4

Liquid junction

Pt(black)|H2(g,P0)|H+(aq,1M)||H+(aq,1M)|O2(g,P0)|Pt

Physical Chemistry GTM/13

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Fuel cells (5)

A real hydrogen/oxygen PEMFC

paliwo

spaliny

obwód elektryczny

katalizatoranodowy

katalizatorkatodowy

membrana(elektrolit polimerowy)

fuel anodic

catalyst cathodic

catalyst

exhaust

gases

membrane,

(polymeric electrolyte)

external circuit

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28 Physical Chemistry GTM/13

Cell type Acronym. electrolyte Temperature

of work [oC] Anodic reaction Cathodic reaction

Anodic

catalyst

Cathodic

catalyst

Alkaline AFC KOH 50-90 H2+2OH-2H2O

+2e-

0.5 O2+ H2O+2e-

2OH

Pt/Au , Pt

,Ag

Pt/Au , Pt

,Ag

Proton exchange

membrane PEMFC

Constant

conducting

polymer

50-125 H22e-+2H+ O2+4e-+4H+2H2O Pt, Pt/Ru Pt

Phosphoric acid PAFC H3PO4 190-210 H22e-+2H+ O2+4e-+4H+2H2O Pt Pt/Cr/Co ,

Pt/Ni

Molten carbonate MCFC Li2CO3/K2CO3 630-650 H2+CO3

2-2e-+

H2O+CO2

0.5 O2+2e-+ CO2

CO32-

Ni , Ni/Cr Li/NiO

Solid oxides SOFC ZrO2 900-1000 H2+O2- H2O 0.5 O2+2e- O2- Ni/ZrO2 LaSrMnO3

Direct methanol DMFC H2SO4 or

polymer 50-120

CH3OH + H2O →

CO2 + 6H+ + 6e-

1.5O2 + 6H+ + 6e-

→ 3H2O Pt, Pt/Ru Pt

Fuel cells (6)

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Fuel cells (7)

Main types of FCs:

• alkaline FCs

• proton exchange membrane FCs

• phosphoric acid FCs

• molten carbonate FCs

• solid oxides FCs

• direct methanol FCs

Physical Chemistry GTM/13