Solution of Electrolyte
※ Definition:
Electrochemistry - A science concerned with the properties of
solutions of electrolytes and with processes occurring
when electrodes are immersed in these solutions.
※ Electrolyte:
Nonelectrolyte - solution can not dissociate, e.g. sucrose.
Electrolyte - solution can be dissociated into ions, e.g. NaCl,
CH3COOH.
★ Strong electrolyte - greater extent of dissociation,
e.g. NaCl.
★ Weak electrolyte - weak extent of dissociation,
e.g. CH3COOH.
※ Molar conductivity:
From Ohm’s law, the resistance R is defined to be:
R V
I
The reciprocal of the resistance is the electrical conductance,
G, which is defined by G 
1
R
.
The electrical conductance of material of length l and
1
cross-sectional area A is given by:
G 
A
l
For a solution of an electrolyte,κis called the electrolytic
conductivity.
Its unit is  cm .
1
-1
However, the electrolytic conductivity is not a suitable
quantity for comparing the conductivities of different solutions,
since the electrolytic conductivity depends on the concentration
of solution.
It is defined the molar conductivity as.
 cm mol
1
2
1
C
Strong electrolyte - the molar conductivity
of strong electrolyte falls very slightly as the
concentration is raised.
Weak electrolyte - the molar conductivity of
weak electrolyte decreases largely when
concentration is raised.
※ Weak electrolytes: The Arrhenius theory
☆ Kohlrausch observations: The heat of neutralization of a
2
strong acid by a strong base in dilute solution was
practically the same (~54.7 kJ/mole@25℃)
☆ Arrhenius theory: electrolyte produces certain degree of
dissociation.

The degree of dissociation is defined by

0
☆ Van’t Hoff observations: The osmotic pressures of
solutions of electrolytes were always considerably
higher than predicted by the osmotic pressure equation
for nonelectrolyte.
  i C R Tfor electrolyte solutions
where i is the Van’t Hoff factor.
The degree of dissociation could be determined by:

i1
 1
whereυis the number of ions produced.
☆ Ostwald’s dilution law:
 For weak electrolyte AB, the equilibrium constant is
given by K 
n
2

2
 1   
 V is larger; C is smaller  αis larger
C

C
V 1
※Strong electrolytes:
3
Concentration
Observed freezing point (℃) Freezing point lowering/mole
0.0001m NaCl
-0.000372
3.72
0.001m NaCl
-0.00366
3.66
0.01m NaCl
-0.0361
3.61
0.1m NaCl
-0.347
3.47
☆ Arrhenius theory fails in strong electrolyte because the
conductivity of strong electrolyte does not vary largely
compared with that of weak electrolyte.
☆ Debye-Huckel theory:
 Ions in electrolyte solutions are completely random.
 More negative ions tend to be attracted into the
neighborhood of positive ions.
 The decrease in the molar conductivity of a strong
electrolyte was attribute to the interaction between
opposite ions.
 The concentration is higher, the interaction is larger.
 Two effects are pronounced in the strong electrolytes:
 Asymmetry effect (非對稱效應):
Ions motion under potential applied is retarded by the
interaction of opposite solute ions in the behinds.
 Electrophoretic effect (電泳效應):
Ions motion under potential applied is retarded by the
interaction of opposite solvent ions in the behinds.
4
 Conductivity slight decrease due to the asymetry effect
and electrophoretic effect.
 Debye-Huckel-Omsager equation:
     P  Q  C
0
0
where P and Q are constant.
The D-H-O equation fails to predict the conductivity
of strong electrolyte when ions association is enhanced:
 Solvent with low dielectric constant - low dipole
moment
 Higher valence of ions, e.g. Zn2+SO42- - ion
association.
 Electrolyte with different valence of ions, e.g.
Na2SO4 - ion association of Na+SO42-.
☆ The theory of ions association:
 An associated ion is formed when the separation
between the opposite charge of ions is≦0.358 nm.
※ Independent migration of ions:
◇ Kohlrausch’s observations (1875):
Each ion make its own contribution to the molar
conductivity, irrespective of the nature of the other ion
with which it is associated.
Electrolyte

0
Electrolyte
5

0
difference
1
2
KCl
149.9
NaCl
126.5
23.4
KI
150.3
NaI
126.9
23.4
130.1
23.4
153.5
K SO
2
Na SO
1
4
2
2
4
◇ Kohlrausch’s law of independent migration of ions:
  
0
0
0


where  and  are the ion conductivities of cation and
0
0


anion, respectively.
◇ The ion conductivity is given by
 the volume of the cube : unit
 the potential drop: V
 the concentration of
univalent positive ion: C+
 the mobility of ion: u+
 the speed of ion: u+V
charge
k 

current
potential drop
unit time

FC u V


 Fu C

potential drop


V
The molar conductivity is given by:  
0


 Fu
C

where F is the Faraday’s constant, u+ is the ionic
mobility (m2V-1s-1) and C+ is the ion concentration.
6

※ Transport numbers(遷移數):
☆ Ion mobility is hard to determine; the conductivity is
determined using the transport number.
☆ Transport number is the fraction of the current by each ion
present in solution.
☆t 

u
u  u
n 
0


0
 for positive ion ; t


u
u  u
n 
0


0
 for negative ion
※ Faraday’s law of electrolysis:
 The mass of an element produced at an electrode is
proportional to the quantity of electricity Q passed through
the liquid.
 The mass of an element liberated at an electrode is
proportional to the equivalent weight of the element.
 Faraday’s law is independent of P, T, electrode materials,
and electrolyte solution.
※ Determination of transport number:
☆ Hittorf method (1853):
7

The solution contains M+A-.

1F current passing.

M+: t  96500C electricity.

M-: t  96500C electricity.

Anode: loss of t+ mole of M+.

Cathode: loss of t- mole of A-.
+
-
loss of anode compartment

loss of cathode compartment

t
t
☆ Moving boundary method (Lodge, 1886/Dampier, 1893):
 the transport numbers of the ions in the
electrolyte MA is to be measured.
 Two indicators, M’A and MA’ which have a
common ion with MA are selected.
 M’+ moves slowly than M+; A’- moves slowly
than A-.
 The original boundary at a and b.
 As the current flows, the new boundary at a’
and b’.

aa 
aa   bb
t ;

bb
aa   bb
☆ One-boundary movement: aa  
where Q: the charge flow
8
t
t Q
FCA

F: the Faraday’s constant
C: the concentration of electrolyte
A: the cross section of tube.
※ Determination of ion conductivity:
 Determination of transport number:   t  ;   t 
0

 For any strong electrolyte:     
0



0

 For any weak electrolyte:

Applying Kohlrausch’s law.
  MA    MCl     NaA    NaCl 
0
0
0
0
where MCl, NaA, and NaCl are strong electrolyte.
e.g.  CH COOH     HCl    CH COONa     NaCl 
0
0
0
3
0
3
※ Effect of ion conductivity:
(A) Hydration: water approaches the small ion more closely.
Rb+>K+>Na+>Li+
(B) Solvent effect: especial for H+ in hydroxylic solvent e.g.
water, methanol, and ethanol etc.
H H O H O

2

3
H O  H O  H O+ H O Grotthuss mechanisms (1805)

3

2
2
3
※ Application of ionic conductivity:
(A) Diffusion coefficient:
9
D
K BT
Q
u
RT
2
F z
where Q is the charge of the ion   Fz  and z is the
N 

A
charge number of the ion.
(B) Viscosity: Walden’s rule
  constant
※ Activity coefficient:
(A) Review of ideal solution:
★ Properties of ideal solution:
Property 1: The equilibrium partial vapor pressure of each
component of an ideal solution is equal to the product of
the equilibrium vapor pressure of the pure substance time
its mole fraction, i.e. P  P x .
*
i
i
i
Property 2: The entropy change of mixing of an ideal solution
is the same as the mixing of ideal gases.
(B) Activity coefficient for real solution:
Most solutions are not ideal, because there is an interaction
between molecules.
Especially, there is electrostatic interaction
between ions in electrolyte solution.
The extent to which the
activity of a non-ideal solution deviates from that of an ideal
solution is specified by the activity coefficient,γ, which is
10
 a
defined by:
i
i
xi
.
(C) Ionic strength (I):
The activity coefficient is affected by the electrostatic
interactions.
For an electrolyte solution, the electrostatic
interaction could be described by the ionic strength, which is
introduced by G. N. Lewis:
I
1
C z
2
1
 C z  ...... C z
2
2
1
2
2
i
2
i

where Ci is the molar concentration of the ion i.
zi is the charge number of the ion i.
(D) The Debye-Hückel limiting law:
The activity coefficient of real solution is given by:
log    z B I
2
i
i
1
1
if water is used as solvent @25℃, B is 0.51 mol  .
2
2
For an electrolyte solution, at least two types of ions must be
present; therefore, a mean activity coefficient is used to describe
the activity coefficient of real solution.
coefficient is defined by:  
 

The mean activity
      ; e.g.    






2


1
3
for
ZnCl2.
For aqueous solution＠25℃, the mean activity coefficient
can be determined by: log   0 . 51 z z


11

I

mole


This equation is called the Debye-Hückel limiting law
(DHLL).
(E) Mean activity coefficient in high concentration:
The Debye-Hückel limiting law is only valid at extremely
low concentrations.
At high concentration, the electrostatic
interaction becomes very large.
The activity coefficient may be
determined by using the extend Debye-Hückel law:
log  

B z z
I
1  aB I
 CI
where B and B’ are constants; a is the mean ionic diameter.
※ Effect of ionic strength on equilibrium:
☆ Dissociation constant:
HA  H  A

For the dissociation of weak acid:
 H  A   

 HA 

K
a




HA
Assumed dissociation constant isα.
If solution is dilute,
  1 and     , then K 
2

HA


a
C
2
1-

2

the activity coefficient is given by og    z z B I   B I

 C 
 og 
  og K  2B I
1  
2
a

☆Solubility product:
12
I 


For AgCl, the solubility product is given by:
K   Ag
s

Cl  



  Ag

Cl 

2

 At low I, 
decreases

as I increases.
 At high I, 

increases
as I increases.
  ↓, solubility↑,

called salting in.
  ↑, solubility↓,

called salting out.
☆ Donnan equilibrium:
◆ Situation 1: Na+ and Cl- both are diffusible through
membrane.
at equilibrium,
[Na+] 1=[Na+] 2
[Cl-] 1=[Cl-] 2
◆ Situation 2: one side with
Na+ and non-diffusible P-; another
side with Na+ and Cl-.
13
 Na+ and Cl- are both
diffusible.
 P- are nondiffusible.
 Charge balance.
 x
2
c2
c1  2c 2
 Donnan equilibrium.
14