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Chapter 7 Electrochemistry
Main contents
• Section 1: Electrolyte and electrolytic solution
• Section 2: Electrochemical Thermodynamics:
• Section 3: Irreversible electrochemical system
• Section 4: Applied electrochemistry
Section 1: Electrolytic solution
Part 1 Electrolyte and its solution
Main contents:
1) Electrolyte: origin of the concept: van’t Hoff, Arrhenius
2) Existence of ions in the solution: hydration and solvation
3) Hydration theory:
4) Interionic interaction: ionic pair
5) Motion under electric field
6) Conducting mechanism
7) Faraday’s law and its application
§7.1 Electrolyte and its solution
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.
Electrochemistry
A science that studies the relation between electric and
chemical phenomena and the disciplines that govern the
conversion between electric and chemical energies.
7.1.1 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.
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
expressed 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.
The equation for freezing point depression and boiling
point elevation contains the letter i. i stands for the van’t
Hoff Factor.
∆T = imKf
Since freezing point depression and boiling point elevation
depend only on the number of particles ( it does not matter
what the particles are), we need only determine the total m of
the particles.
If a solution is 0.2 m NaCl, the i would be about 2. The
true van’t Hoff factor is not exactly 2, but is close enough to
call it 2.
http://en.wikipedia.org/wiki/Van_'t_Hoff_factor
3) Dissociation theory for weak electrolytes
In 1887, Svant August 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.
Therefore, the number of particles present in solution is
actually larger than that predicted by van’t Hoff, which
resulted van’t Hoff factor.
New definitions:
Dissociation, ionization
Weak / strong electrolyte? True and potential?
Theory of Electrolytic Dissociation
Acid-base theory
Greenhouse effect
Cf. Levine p.295
7.1.2 Solvation (hydration) of ion
+

Solvation shells
The interaction between ions and water molecules
disturb the structure of liquid water.
Primary hydration shell
ion
secondary hydration shell
Disordered layer
Bulk solution
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.
Hydration of ion
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
7.1.3 Hydration Theory / Solvation Theory
H / kJ mol-1
Na+(g) + Cl(g)
1948, Robinson and Storks
hydration energy:
788
784
784 kJ mol-1
Na+(aq) + Cl(aq)
4
NaCl(s)
7.1.4 Interaction between cation and anion
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.
F 
+

At low
concentration
q1 q 2
4 r  0 r 2
+

At medium
concentration
+

At high
concentration
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
Activity coefficient is essential for quite dilute solutions
7.1.5 Motion under electric field
(1) Ionic mobility
dE

dl
dE
 U
dl
Ionic velocity
Ionic mobility (U) : the ionic velocity per unit electric field, is a constant.
(2) Transference number
I = I＋ + I －
Q = Q＋ + Q －
tj 
Qj
Q
t = t+ + t- = 1
The fraction of the current transported by an ion is its transference
number or transport number
(3) Relationship between ionic mobility and transfer number
B
A
C
For time t:
Q+ = A U+t C+ Z+ F
Q  = A Ut C Z F
C－, Z－, U－; C＋, Z＋, U＋;
U
t 
U U
U
t 
U U
9) Measurement of transference numbers
(1) 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
The final result
+ + +
+ + + + + +
+ + + + +
  
     
    
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
(2) The moving-boundary method
MA, MA’ have an ion in common.
The boundary, rather different in
color, refractivity, etc. is sharp.
In the steady state, the two ions move with
the same velocity.
When Q coulomb passes, the boundary
moves x, the cross-sectional area of the
tube is A, then:
xAcZ+F = t+Q
7.1.6 Conducting mechanism of electrolyte
(1) Category of conductor:
Charge carriers: electron; ion; hole; Cooper electron pair; polaron.
Conductor
Charge carrier
samples
1st
electron
2nd
ion
3rd
Semiconductor
4th
Electron and
hole
polaron
5th
electron pair
Superconductors
Mixed conductor
Ion and electron
Metals, carbonous materials, some metal
oxides
Electrolytic solution, solid-state electrolyte
(Al2O3, ZrO2)
Conducting polymers
PbO2, NiOOH
(2) Conducting mechanism
When current passes through dilute HCl solution

+
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
•Electric transfer of ion in solution
under electric field
How can current cross the
electrode / solution interface ?
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.
7.1.7 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) Electroanalysis, Electrolytic analysis
Q ↔m ↔ n ↔ c
Example:
Given A=1.05 × 10-5 m2, c(HCl)=10.0 mol·m-3, I =
0.01 A for 200 s, x was measured to be 0.17 m,
calculate t (H+)
EXAMPLE
The mobility of a chloride ion in water at 25 oC is 7.91  104 cm2·s-1·V-1. 1) Calculate the molar conductivity of the ion
at infinite dilution; 2) How long will it take for the ion to
travel between two electrodes separated by 4.0 cm if the
electric field is 20 V·cm-1.
Answer
 m,  U  F  96500C  mol1  7.91108 cm2  s-1  V-1
 7.63 103 Ω-1  mol-1  m2
 U
t
dE
 7.91108 m 2  s-1  V -1 2000C  m 1  1.58  104 m  s 1
dl
l
0.040m

 253s  4.2 min
4
1
v 1.58 10 m  s
Exercise-1:
A 0.100 molality solution of NaCl has a freezing-point
depression of -0.348 oC, whereas the expected decrease in the
freezing point is -0.186 oC. The van’t Hoff factor in this case is
1.87. if there were no ion pairing, we would expect the van’t Hoff
factor for NaCl to be 2.00. similarly, acetic acid in a 0.100 molal
solution has a van’t Hoff factor of 1.05. Calculate the
concentration of NaCl ion pairs and also the percent ionization of
acetic acid form the above information.
Exercise-2:
A current of 2.34 A is delivered to an electrolytic cell for 85
min. how many grams of (a) Au from AuCl3, (b) Ag form
AgNO3, and (c) Cu from CuCl2 will be plated out?
Exercise-3
Levine: p.317 10. exercise 48
Exercise -4
Yin: p. 217 exercise 1.