internal energy

Mechanics

Oct 27, 2013 (5 years and 2 months ago)

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Electrochemistry

Prof. Dr. Sabine
Prys

http://www.iccb.org/student/mod/science/mod_chem1/mod1/p1.html

@designed by
ps

3.3 Normal & Standard Conditions

normal conditions:

normal pressure

p = 1
atm

= 101,325
kPa

= 1013,25 mbar

normal temperature

T

= 0
°
C = 273.15 K

standard conditions:

standard pressure p = 1
atm

= 101,325
kPa

= 1013,25 mbar

standard temperature

T

= 25
°
C = 298.15 K

Such definitions can vary according to different sources: IUPAC, NIST, …

3.4 Enthalpy

Enthalpy

is a measure of the total energy of a thermodynamic system
including

the internal energy (energy required to create a system),

the amount of energy required to make room for it by displacing its
environment and establishing its volume and pressure.

Enthalpy is a thermodynamic potential, a state function and
an extensive
quantity
(i.e. depending on amount material).

H

enthalpy

U

internal energy

P

pressure

V

volume

http://goldbook.iupac.org

3.8 GIBBS’ Free Energy G

Useful energy, or energy available to do work G

G

= free energy

H

= GIBBS’ energy (enthalpy)

U

= internal energy

T

= Kelvin temperature

S

= entropy

p

= pressure

V

= volume

T
D
S

is the energy not available for doing work

3.9 Spontaneity of
Redox

Reactions

D
H

D
S

Spontaneity

Exothermic

D
H < 0

Increase

D
S > 0

+

D
G < 0

Exothermic

D
H < 0

Decrease

D
S < 0

+ if

|T
D
S| < |
D
H|

Endothermic

D
H > 0

Increase

D
S > 0

+ if

T
D
S >
D
H

Endothermic
D
H > 0

Decrease

D
S < 0

-

D
G > 0

3.10
Thermodynamical

Equilibrium

Reversible processes ultimately reach a point where the rates in both
directions are identical, so that the system gives the appearance of
having a static composition at which the Gibbs energy G is a
minimum

D
G = 0

At equilibrium the sum of the chemical potentials of the reactants
equals that of the products, so that:

D
G =
D
G
298

+ RT

.
lnK

= 0

D
G
298

=
-

RT

.
lnK

The

equilibrium constant K

is given by the

mass
-
law effect.

http://goldbook.iupac.org

3.12 Maximum Work

W
max

= maximum work

G

= Gibbs free energy

R

= gas constant

T

= Kelvin temperature

K

= equilibrium constant

z

= ion charge

n

= moles

F

E

= galvanic cell potential

U

= voltage

I

= currant

t

= time

4.0 Chemical Solutions

Suspension

(particle diameters

10
-
4

-

10
-
5

cm )

solid particles in homogeneous fluid

Colloid

(particle diameters

10
-
5

-

10
-
7

cm )

microscopically dispersed particles in another substance

Solution

(particle diameters

10
-
7

-

10
-
8

cm )

Homogeneous phase with at least 2 components:

solvent and solute

»
gas in liquid

e.g. O
2

in H
2
O

»
gas in solid

e.g. H
2

»
liquid in liquid

e.g. petroleum

»
solid in liquid

e.g.
NaCl

in H
2
O

»

electrolytes in water

4.6 Ion activity

High ion concentrations in aqueous solutions

ion

ion interactions:

pH
measured

< pH
calculated

(1m, 0.1 m solution of acids)

ion activity:

a = activity, f = activity coefficient, c = concentration

f (
HCl
, 25
°
C): 0.001m/0.965 0.01m/0.905 0.1m/0.794 1m/0.809

4.7 Colloidal Solutions

Larger particles in solvent, e.g. macromolecules / polymers

Properties depend on solute size and not on solute concentration !

Coagulation: growth of larger particles by smaller particles
consumption

Hydrophobe

colloids: large surface, large adsorption properties

Hydrophile

colloids

4.9 Electrolytes

Electrolyte: solution which conducts electrical current

Hydrated H
3
O
+

Hydrated OH
-

4.9.1 Electrical Conductivity in
Solutions

Electrolytes

solutions which support ion transport

salts in aqueous solutions, e.g.
KCl
,
ZnSO
4
, CuCl
2
, etc.

molten salts

Conductivity L

(resistance R)

0.0548 µS/cm
at

25
°
C.

cathode

cat ions

anode

anions

_

+

-

+

+

+

+

+

+

-

-

-

-

-

H
2
O

4.9.2 Specific Conductivity

absolute electrolyte conductivity

R = solution resistance

specific electrolyte conductivity

A = electrode surface, l = electrode distance

4.9.3 Example: Proton Migration

Grotthuss Diffusion

structural defect migration

mesomeric structures between H
9
O
4
+

and H
5
O
2
+
,

5.0 Electrochemical Cells

Cl
2

H
2

+

-

Cl
2

H
2

+

-

electrolytic cell

galvanic cell

2
HCl

(
aq
)

H
2

(g)
+ Cl
2

(g)

H
2

(g)
+ Cl
2

(g)

2
HCl

(
aq
)

electrical energy

chemical energy

chemical energy

electrical energy

5.1 Electrolysis

electrolysis: decomposing materials by electric current

H
2
SO
4

+ 2H
2
O

2H
3
O
+

+ SO
4
2
-

water electrolysis

cathodic

reduction

4H
3
O
+

+ 4e
-

2 H
2

+ 2 H
2
O

anodic oxidation

4 OH
-

2 H
2
O + O
2

+ 4 e
-

total

2 H
2
O
(l)

2 H
2

(g)
+ O
2

(g)

H
2
0 + H
2
SO
4

1:10

electrods

battery

ca. 15 V

5.1.1 Electrochemical Equivalent

Q

=

electric charge in C

n

=

yield in mol

F

=

=

96485,309 As / mol

E
c

=

electrochemical equivalent

M

=

ion weight

z

=

ion charge

N
L

=

Lohschmidt‘s number

e

=

elementary charge

m
a

,
m
b

=

mass yield in g

for material a / b

M
a
,M
b

=

molecular weight

for material a / b

z
a
,
z
b

=

chemical
valency

for material a / b

m

=
E
c

. Q =
E
c

.I. t

m

=

mass yield in g

E
c

=

electrochemical

equivalent

Q

=

electric charges

in Coulomb

I

=

current strength

t

=

electrolysis time

5.2 Galvanic Elements

Daniell

Element:

2 galvanic half cells + bridge

Zn / ZnSO
4

// CuSO
4

/ Cu

electrode reactions

Zn
(cathode)

Zn
2+

+ 2e
-

Cu
2+
+ 2e
-

Cu
(anode)

Zn metal in ionic solution

Cu ions in Cu metal

electrical current results from
different oxidation affinities

voltmeter ca 1,1 V

Zn

Cu

1 m

ZnSO
4

1 m

CuSO
4

diaphragma

(pottery)

bridge containing

KCl solution

5.4 Standard Hydrogen Electrode

standard hydrogen electrode (SHE)

=

reference potential =

E
0

= 0 V

H
2


2H
+

+ 2e
-

p = 1,01325 bar

T = 25
°
c

a(H
+
) = 1 mol / l

c(H
+
) = 1,235 mol / l (
HCl
)

Pt electrode

H
2
gas

Pt electrode

H
2

gas

68

5.5 Metal Standard Potentials

standard hydrogen electrode

=

reference potential

E
0

= 0 V

metal electrode / metal salt solution

at standard conditions

=

standard metal potential

M

M
z
+

+
ze
-

p = 1,01325 bar

T = 25
°
c

c(
M
z
+

) = 1 mol / l

pH < 6 precipitation prevention

5.5.1 Metal Standard Potential Tables

pH
-
dependant

Galvanic Corrosion Potential Chart

K, Na, Mg, Al, Zn, Fe,
Pb
, Cu, Ag, Au

passivation

of Al, Mg,
Mn
, Cr

alternative corrosion potential charts for industrial materials

5.5.2
Calvanic

Corrosion Potential
Chart

cathode

least noble

corroded metals

strong oxidation affinity

negative oxidation potential

anode

most noble

protected metals

weak oxidation affinity

positive oxidation potential

5.6.3 Exercise: Gibbs Free Energy

What

happens

if

Δ
G = 0

5.7 NERNST‘s Equation 1

electrode potential dependency on temperature and concentration

E

= measured cell potential

E
0

= standard reaction potential

R

= gas constant ( 8,3145 J . mol
-
1
. K
-
1
)

T

= Kelvin temperature

z

= charges

F

[ ]

= concentration of oxidant /
reductant

in mol / l

5.7.1 NERNST’s Equation 2

1.
type electrode

( = metal electrode in metal salt solution)

[red] = const

E

= measured cell potential

E
0

= standard reaction potential

R

= gas constant ( 8,3145 J . mol
-
1
. K
-
1
)

T

= Kelvin temperature

z

= charges

F

[ox]

=
concentrationen

of oxidant in mol / l

5.7.2 Exercise: Maximum Electrical Voltage

1.
Calculate the maximum electrical voltage for the
Daniell

element
when standard conditions !

Daniell

Element: Cu/Cu
++
//Zn
++
/Zn

Cu/Cu
++
/

+0,34 V

Zn
++
/Zn/

+0,76 V

S

=

+ 1,1 V

2.
Calculate the maximum electrical voltage for a galvanic cell with
Ni/Ni
++
//Zn
++
/Zn when standard conditions !

Ni/Ni
++
//

-
0,23 V

Zn
++
/Zn/

+0,76 V

S

=

+ 0,53 V

5.7.3 Exercise: Nernst Equation

What is the electrode potential for a silver electrode at 0
°
C when the Ag+
concentration is 1 mol ?

5.8 Ag /
AgCl

Electrode

2. type electrode

= metal electrode in saturated
metal salt solution

= electrode with constant potential
(no concentration changes)

T = 25
°
C:

1 m KCl E
0

= + 0,220 V

sat. KCl E
0

= + 0,1958 V

Ag

AgCl
sat

K
+

Ag
+

Cl
-

5.8.1
Concentration

Cells

Cu
(s) | Cu
2+

(0.05 M) || Cu
2+

(2.0 M) |
Cu
(s)

half
cell

reactions

:

oxidation
:

Cu
(s)

→ Cu
2+

(0.05 M) + 2 e

reduction
:

Cu
2+

(2.0 M) + 2 e

Cu
(s)

overall

reaction
:

Cu
2+

(2.0 M)

→ Cu
2+

(0.05 M)

cell's

emf

:

E = E
°
-

(0.05916
\
2) log [0,05/2] = 0.0474 V

E
°

= 0 , (
electrodes

and

ions

are

the

same in
both

half
-
cells
)

5.15 Dry Cells

Leclanché's

cell

anode is a zinc container surrounded by a thin layer of MnO2

Cathode a carbon bar inserted on the cell's electrolyte

moist electrolyte paste NH
4
Cl + ZnCl
2

mixed with starch

Anode:

Zn(s) → Zn
2+
(
aq
)

+ 2 e

Cathode:

2 NH
4+
(
aq
)

+ 2 MnO
2
(s) + 2 e

→ Mn
2
O
3
(s) + 2 NH
3(
aq
)

+ H2O(l)

Overall reaction:

Zn(s) + 2 NH
4+
(
aq
)

+ 2 MnO
2
(s) → Zn
2+
(
aq
)

+ Mn
2
O
3
(s) + 2 NH
3(
aq
)

+ H
2
O(l)

E = ~ 1.5 V

moist electrolyte paste

5.16
Zn

Battery

Graphics:
http://en.wikipedia.org/wiki/File:Zincbattery.png

5.17 Mercury
Battery

amalgamated anode of mercury and zinc surrounded by a
stronger alkaline electrolyte and a paste of
ZnO

and
HgO

Mercury battery half reactions are shown below:

Anode:

Zn(Hg) + 2 OH

(
aq
)

ZnO
(s) + H
2
O(l) + 2 e

Cathode:

HgO
(s) + H
2
O(l) + 2 e

→ Hg(l) + 2 OH

(
aq
)

Overall reaction: Zn(Hg) +
HgO
(s) →
ZnO
(s) + Hg(l)

no changes in the electrolyte's composition when working

1.35 V of direct current

Not rechargeable

Graphics:
http://en.wikipedia.org/wiki/File:Mercurybattery.png

-
Acid

battery

six identical cells assembled in series (6 x 2V ) = 12 V

Electrolyte sulfuric acid

Anode:

Pb
(s) + SO
4
2

(
aq
)

→ PbSO
4
(s) + 2 e

Cathode:

PbO
2
(s) + 4 H
+
(
aq
)

+ SO
4
2

(
aq
)

+ 2 e

→ PbSO
4
(s) + 2 H
2
O(l)

Overall reaction:
Pb
(s) + PbO
2
(s) + 4 H
+
(
aq
)

+ 2 SO
4
2

(
aq
)
→ 2 PbSO
4
(s) + 2 H
2
O(l)

Rechargeable (external voltage

electrolysis of the products)

http://en.wikipedia.org/wiki/Lithium
-
ion_battery

5.19 Lithium
rechargeable

battery

(1)

Positive
electrodes

Electrode

material

Average

potential
difference

Specific

capacity

Specific

energy

LiCoO2

3.7 V

140
mA∙h
/g

0.518
kW∙h
/kg

LiMn2O4

4.0 V

100
mA∙h
/g

0.400
kW∙h
/kg

LiNiO2

3.5 V

180
mA∙h
/g

0.630
kW∙h
/kg

LiFePO4

3.3 V

150
mA∙h
/g

0.495
kW∙h
/kg
Li2FePO4F

3.6 V

115
mA∙h
/g

0.414
kW∙h
/kg

LiCo1/3Ni1/3Mn1/3O2

3.6 V

160
mA∙h
/g

0.576
kW∙h
/kg

Li(
LiaNixMnyCoz
)O2

4.2 V

220
mA∙h
/g

0.920
kW∙h
/kg

Negative
electrodes

Graphite (LiC6)

0.1
-
0.2 V

372
mA∙h
/g

0.0372
-
0.0744
kW∙h
/kg

Hard

Carbon

(LiC6)

Titanate

(Li4Ti5O12)

1
-
2 V

160
mA∙h
/g

0.16
-
0.32
kW∙h
/kg

Si (Li4.4Si)[27]

0.5
-
1 V

4212
mA∙h
/g

2.106
-
4.212
kW∙h
/kg

Ge

(Li4.4Ge)[28]

0.7
-
1.2 V

1624
mA∙h
/g

1.137
-
1.949
kW∙h
/kg

Lithium
rechargeable

battery

(2)

The following equations are in units of moles, making it possible to use the coefficient x.

Overdischarge

supersaturates lithium cobalt oxide, leading to the production of lithium oxide

Overcharge up to 5.2 Volts leads to the synthesis of cobalt(IV) oxide

In a lithium
-
ion battery the lithium ions are transported to and from the cathode or anode,

with the transition metal, cobalt (Co), in LixCoO2 being oxidized from Co3+ to Co4+

during charging, and reduced from Co4+ to Co3+ during discharge.

http://en.wikipedia.org/wiki/Lithium
-
ion_battery

Exercises 1

1.
What is the internal energy of 1 mole
Ar

at 0
°
C ?

2.
What is the volume of 1 mole hydrogen gas at 25
°
C ?

3.
What is the entropy change in 1 mole hydrogen gas at standard
conditions when increasing the volume to
D
V = 1 m
3

?

4.
The equilibrium constant for acetic acid in water at 25
°
C is 4,76.
What is Gibbs Free Energy at that temperature ?

5.
Calculate the maximum electrical voltage for the DANIELL element
when normal pressure and 10
°
C !

6.
Calculate the maximum electrical voltage for a galvanic cell with
Ni/Ni
++
//Zn
++
/Zn when normal pressure and 10
°
C !

7.
Explain the difference between a galvanic and an electrolytic cell !

8.
What is the standard hydrogen potential ?

Exercises 2

9.
What is the standard metal potential ?

10.
How can you decide whether an ion will precipitated at a given electrode ?

11.
What is the electrode potential for a silver electrode at 10
°
C when the Ag+
concentration is 1 mol ?

12.
How can you calculate the amount of elementary metal to be formed on an
electrode ?

13.
How can you calculate the maximum energy which can be obtained from a
battery

14.
Explain the chemical potential !

16.

17.
Explain the mercury battery !

http://en.wikipedia.org/wiki/Electrochemistry#Principles

http://goldbook.iupac.org/

References

A.
Burrows
, A. Parsons , G. Price, J.
Holman

, G. Pilling;
Chemistry:
Introducing inorganic, organic and physical chemistry ; Oxford
University Press 2009

J.
Hoinkins
; E. Lindner; Chemie für Ingenieure; Verlag:
Wiley
-
VCH
Verlag GmbH & Co. KGaA, 2007

P.W.
Attkins
; L.
Jobnes
; Chemie

einfach alles; Verlag:
Wiley
-
VCH
Verlag GmbH & Co. KGaA, 2006

Römpp‘s

Chemie Lexikon

DTV
-
Atlas zur Chemie