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Chapter 7 Electrochemistry
A science that studies the relation between electric and
chemical phenomena and the disciplines that govern the
conversion between electric and chemical energies.
Chapter 7 Electrochemistry
Main contents
• Section 1: Electrolyte and electrolytic solution
• Section 2: Electrochemical Thermodynamics:
• Section 3: Irreversible electrochemical system
• Section 4: Applied electrochemistry
§7.1 Electrolyte and electrolytic solution
Main contents:
1) Electrolyte: origin of the concept
2) Existence of ions in solution
3) Ion-dipole interaction--Hydration theory
4) Interionic interaction
5) Motion under electric field
6) Conducting mechanism
7) Faraday’s law and its application
1. Origin of the concept – electrolyte
1) Definition of electrolyte
An electrolyte is a substance that, when dissolved in
solvent, produces a solution that will conduct electricity.
Progress of the definition:
(1) molten salt; (2) solid-state electrolyte
(3) room-temperature ionic liquids (RTIL).
2) Dissociation of substance
In 1886, van’t Hoff published his
quantitative research on the colligative
properties of solution.
For sucrose, the osmotic pressure ()
can be expressed as:
=cRT
But for some other kind of solvates such
as NaCl, the osmotic pressure had to be
modified as:
=icRT
i , van’t Hoff factor, is larger than 1.
In the paper written in Achieves Neerlandaises (1885) and Transactions of the Swedish.
Academy (1886), van't Hoff showed analogy between gases and dilute solutions.
3) Dissociation theory for weak electrolytes
In 1887, Svant A. Arrhenius postulated that,
when dissolved in adequate solvent, some
substances can split into smaller particles,
the process was termed as dissociation.

+
AB
molecule


 +

A+
cation
positive ion
+
B–
anion
negative ion
The charged chemical species are named as ions and the
process is termed as ionization.
New definitions:
Ion, cation, anion;
Dissociation, ionization
Weak / strong electrolyte?
True / potential electrolyte?
Theory of Electrolytic Dissociation
Acid-base theory
Cf. Levine p.295
2. Ions in solution
In what state do ions exist in solution?
Solvated (hydrated) ion
Primary hydration shell
ion
secondary hydration shell
Disordered layer
Bulk solution
Solvation shells
Hydration of ion
The water molecules in the hydration sphere and bulk water have
different properties which can be distinguished by spectroscopic
techniques such as nuclear magnetic resonance (NMR), infrared
spectroscopy (IR), and XRD etc.
Coordination number:
Li+: 4, K+: 6
Primary solvation shell:
4-9, 6 is the most common number
Secondary slovation shell:
6-8, for Al3+ and Cr3+: 10-20
3. Hydration Theory / Solvation Theory
Why does NaCl only melt at higher temperature, but dissolve
in water at room temperature?
H / kJ mol-1
Na+(g) + Cl(g)
hydration energy:
784 kJ mol-1
788
784
Na+(aq) + Cl(aq)
NaCl(s)
4
1948, Robinson and Storks
F 
q1 q 2
4 r  0 r
2
Long-range forces
The interionic distance for NaCl crystal is 200 pm, while for 0.1
moldm-3 solution is 2000 pm.
To draw Na+ and Cl apart from 200 nm to 2000 nm, the work
is:
W (/kJ) = 625 / r
for melting: r =1, W = 625 kJ, m.p. = 801 oC。
for dissolution in water: r = 78.5, W = 8 kJ.
Therefore, NaCl is difficult to melt by easy to dissolve in
water at room temperature.
4. Interaction between cation and anion
F 
+

At low
concentration
q1 q 2
4 r  0 r 2
+

At medium
concentration
In equilibrium -- Bjerrum
+

At high
concentration
Cf. Levine, p. 304
Owing to the strong interaction, ionic pair forms in concentrated
solution.
ionic pair vs free ion
In an ionic pair, the cation and anion are close to each other,
and few or no solvent molecules are between them. Therefore,
HCl does not ionize and NaCl does not dissociate completely in
solvents.
Some facts about strong electrolytes
solution
present species
0.52 mol·dm-3 KCl
95% K+ + 5% KCl
0.25 mol·dm-3 Na2SO4
76 % Na+ + 24% NaSO4¯
0.1 mol·dm-3 CuSO4
44% CuSO4
For concentration-dependence of ion pair, see Levine p. 305, Figure 10.10
Degree of association
Activity coefficient is essential for quite dilute solutions
5. Conducting mechanism of electrolyte

+
I
+
+
+
+
+
+
+
E
+
•Electric transfer of ion in
solution under electric field
How can current cross the
electrode / solution interface ?
Motion of ions in the solution:
1) diffusion: due to difference in
concentration
2) convection: due to the difference in
density
3) transfer: due to the effect of electric
field
e
e
e
Cl
Cl
H+
Cl
e
H+
Cl
H+
Cl
Cl
Cl
e
H+
H+
Cl
H+
e
H+
H+
Cl
H+
Cl
H+
At anode:
At cathode:
2Cl  2e  Cl2
2H+ + 2e  H2
Conducting mechanism:
1) Transfer of ion in solution under electric field;
2) electrochemical reaction at electrode/solution interface.
6. Law of electrolysis
For quantitative electrolysis:
Q
m 
M
zF
Faraday’s Law
where m is the mass of liberated matter; Q the
electric coulomb, z the electrochemical equivalence,
F a proportional factor named as Faraday constant,
M the molar weight of the matter.
Faraday’s constant
Micheal Faraday
Great Britain 1791-1867
Invent the electric motor
and generator, and the
principles of electrolysis.
F = (1.6021917  10-19  6.022169  1023 ) C·mol-1
= 96486.69 C·mol-1 usually round off as 96500
C·mol-1, is the charge carried by 1 mole of
electron.
Current efficiency ()
Qtheoretical

Qeffective

meffective
mtheoretical
Current efficiency is lower than 100% due to side-reactions.
For example, evolution of hydrogen occur during electrodeposition of copper.
Application of Faraday’s law
1) Definition of ampere:
IUPAC: constant current that would deposit 0.0011180 g of
silver per second from AgNO3 solution in one second: 1
ampere.
2) Coulometer: copper / silver / gas (H2, O2) coulometer
3) Electrolytic analysis – electroanalysis
Q ↔m ↔ n ↔ c
7. Transfer of ion under electric field
How do we describe the motion of ions under electric field?
1) Ionic mobility
Rate of electric transfer: Ionic velocity
dE

dl
dE
 U
dl
Ionic mobility (U) :
the ionic velocity per unit electric field, is a constant.
measure ionic mobility using moving boundary method
MA, MA’ have an ion in common.
The boundary, rather different in
color, refractivity, etc. is sharp.
x
v
t
v
x
U 
V tE
l
8. Transference number
Transference number (transfer/ transport number), is the
fraction of the current transported by an ion.
plane A
I = I＋ + I－
Q = Q＋ + Q－
I + Q+
t+  
I
Q
I－
I - Qt-  
I Q
I＋
tj 
I
Supporting electrolyte?
Ij
I

Qj
Q
t+ + t- = ?
(1) Principle for measuring transference number
C
A
B
For time t:
Q+ = A U+t c+ Z+ F
I＋
Q  = A Ut c Z F
U t
Owing to electric migration, on the left side of plane A,
there are more anions, while on the right side, more cations.
Is this real?
(1) Principle of Hittorf method (1853)
Example: Electrolysis of HCl solution
+
=1F
+ + + + + +
+ + + + + +
+ + + + + +
     
     
     
bulk solution
cathodic region
anodic region
When 4 Faraday pass through the electrolytic cell
+ + + + + +
+ + + + + +
+ + + + + +
     
     
     
4Cl- -4e-  2Cl2
3 mol H+
1 mol Cl- 
3 mol H+
1 mol Cl- 
4H+ +4e-  2H2
+ + + + + +
+ + + + + +
+ + + + + +
     
     
     
4Cl- -4e-  2Cl2
final
result
3 mol H+
1 mol Cl- 
3 mol H+
1 mol Cl- 
4H+ +4e-  2H2
+ + +
+ + + + + +
+ + + + +
  
     
    
anodic region
bulk solution
cathodic region
For anodic region:
cresidual  cinitial  creacted  ctransfered
EXAMPLE
Cock stopper
Pt electrode, FeCl3 solution:
In cathode compartment:
Initial: FeCl3 4.00 mol·dm-3
Final: FeCl3 3.150 mol·dm-3
FeCl2 1.000 mol·dm-3
Calculate the transference
number of Fe3+
Anode
chamber
Cathode
chamber
Hittorf’s transference cell
What factors will affect the
accuracy of the measurement?
(2) Principle for the moving-boundary method
When Q coulomb passes, the boundary
moves x, the cross-sectional area of the
tube is A, then:
xAcZ+F = Q+ = t+Q
Why is the moving-boundary method
more accurate that the Hittorf method?
Are there any other methods for measuring
transfer number?
(3) Influential factors
(1) Temperature and (2) Concentration
Transference number of K+ in KCl solution at different
concentration and temperature
c /mol·dm-3
0.000
0.005
0.01
0.02
15
0.4928
0.4926
0.4925
0.4924
25
0.4906
0.4903
0.4902
0.4901
35
0.4889
0.4887
0.4886
0.4885
T /℃
(3) Co-existing ions
Table transference number on co-existing ions
Electrolyte
KCl
KBr
KI
KNO3
t+
0.4902
0.4833
0.4884
0.5084
Electrolyte
LiCl
NaCl
KCl
HCl
t–
0.6711
0.6080
0.5098
0.1749
Problem: Why does the transference number of certain ion
differ a lot in different electrolytes?
Outside class reading
Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002.
pp. 294-310
Section 10.6 solutions of electrolytes
Section 10.9 ionic association
pp. 512-515
Section 16.6 electrical conductivity of electrolyte solutions.