Chapter 7 Electrochemistry
§7.5 Theories for strong electrolyte
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Self reading:
Ira N. Levine, Physical Chemistry, 5th Ed., McGraw-Hill, 2002.
pp. 300-304
Section 10.8 the Debye-Hückel theory of electrolyte solutions
Empirical formula for electrolyte solution
Stationary property
Dynamic property
ln 

m  m  A c

 A I
For ideal solution:
For nonideal solution:
 i   i (T )  R T ln m i
 i   i (T )  RT ln m i  RT ln  i
(  G ) T , P  RT ln  i  W r '
ln  i  
Wr '
RT
Theoretical evaluation of Wr’
Before 1894: treated solution as ideal gas
1918-1920: Ghosh – crystal structure
1923: Debye-Hückel: ionic atmosphere
1. The Debye-Hückel theory
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Ionic atmosphere
Radius:1~100 nm
Basic assumptions
1) Point charge
Peter J. W. Debye
1936 Noble Prize
Germany, Netherlands
1884/03/24~ 1966/11/02
Studies on dipole moments
and the diffraction of X rays
2) Only coulombic attraction
3) Dielectric constant keep unchanged
4) Boltzmann distribution, Poisson equation
Shielded Coulombic potential
 
Z je
4  0  r r
Z je
 
4 0  r r
e
b / r
1
+
  0  r kT  2
b

2
4
N
Ie

A
0 

ln  i  
Debye length
ln  i 
RT
1
1
 e N A2  02
3
ln  i 
 Zi e
2
Wr '
2
1
Zi
I
4  (  0  r kT ) 2
ln  i   AZ
2
i
I
2
8 0  r kTb
Group exercise:
Deduce
ln     A Z  Z 
I
Lewis’s empirical equation
from
ln  i   AZ
2
i
I
ln     A I
for aqueous solution at 298 K
lg     0 . 509 Z  Z 
I
ln     1 . 172 Z  Z 
I
Debye-Hückel limiting
law holds quite well for
dilute solutions (I< 0.01
m), but must be modified
to account for the drastic
deviations that occur at
high concentrations.
lg   
 A ZZ
1  
I

 A ZZ
I
Valid for c < 0.1 mol·kg-1
lg   
 A ZZ
1  
I
 bI
I
Valid for c < 1 mol·kg-1
1
I
I
2. Debye-Hückel-Onsage theory
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1) Relaxation effect
2) Electrophoretic effect
In 1927, Lars Onsager
pointed out that as the ion
moves across the solution, its
ionic atmosphere is repeatedly
being destroyed and formed again.
The time for formation of a new ionic
atmosphere (relaxation time) is ca.
10-7 s in an 0.01 mol·kg-1 solution.
Under normal conditions, the velocity
of an ion is sufficiently slow so that
the electrostatic force exerted by the
atmosphere on the ion tends to retard
its motion and hence to decrease the
conductance.

6

41.25( Z   Z 

 2.08  10 Z  Z  q 
 

3

 T
(  T ) 2 (1  q )



)



    (    ) I
Valid for 310-5 ~ 10-3 mol·kg-1
Fuoss: valid for < 0.1 mol·kg-1
Lars Onsager
1968 Noble Prize
USA, Norway
1903/11/27~1976/10/05
Studies on the thermodynamics
of irreversible processes
Falkenhagen: valid for < 5 mol·kg-1,
for LiCl: valid until 9 mol·kg-1
I
Progress of the theories for electrolyte
1800: Nicholson and Carlisle: electrolysis of water
1805: Grotthuss: orientation of molecules
1857: Clausius: embryo of dissociation
1886: vant’ Hoff: colligative property
1887: Arrhenius: dissociation and ionization
1918: Ghosh: crystalline structure
1923: Debye-Hückel: Debye-Hückel theory
1926: Bjerrum: conjugation theory
1927: Onsager: Debye-Hückel-Onsager theory
1948: Robinson and Stokes: solvation theory
Question:
Compare the solubility of AgCl(s) in NaCl solution,
pure water, and concentrated KNO3 solution using that
in pure water as standard.
AgCl(s) = Ag+(aq) + Cl¯(aq)
Solubility equilibrium and the effect of co-ion.
ionic strength on solubility: salt effect