Transport in electrolyte
solutions
Sähkökemian peruseet
KE-31.4100
Tanja Kallio
tanja.kallio@aalto.fi
C213
CH 3.1 – 3.2
Ion distribution in the bulk and near the
surface
Spatial distribution of ions obeys Boltzmann
distribution
ci (r )  cib e  zi ( r )
J. Israelachivili,
Intermolecular and surface
forces
Transport and reactions
electrode
electrolyte
i) mass transfer
Cu2+ + e  Cu+
ii) adsorption
r
i
  J Cu 2
F
x 0
 J Cu 
r  kred cCus 2  kox cCus 
e-
r = reaction rate
Ji = flux of i
iii) (electo)chemical reaction
iv) desorption
v) mass transfer
x 0
Transport and mobility
charged particle in an electric field (Fc)
Fc  Ff
v
Ff
q
Einstein
Fc
qE  zeE   f v
kT
zeE 
v
D
f 

mobility
v  uE  u 
Ff = friction force
q = charge of the particle
E = electric field
v = velocity
D = diffusion coefficient
u = mobility
zFD
RT
v
zeD
zFD
E
E
kT
RT
kT
D
Mobility, molar conductivity and
diffusion coefficient
Ohm’s law
adapted Faraday’s law
i  F  zk J k  F  zk vk ck
i  E
k
    k ck
k
k
from previous slide
F2
i
RT
F 2 z k2 Dk
k z Dk ck  E  k  RT & k  zk uk F
2
k

Stokes’ law can be applied to determine friction coefficeint for ions
f  6a  D 
kT
6a
 = viscosity
a = ion radius
am
idi
DM
SO
HC
OO
H
n-p
rop
ano
li
NM
F
et a
nol
i
ves
i
DM
F
me
tan
oli
TH
F
DM
OE
AC
N
ase
t on
i
for
m

Walden rule
D
0.7
0.6
kT
6a
 D  constant
0.8
K+(●)
Cs+ (■)
0.5
0.4
0.3
0.2
0.1
Measuring conductivity
F2

RT
 zk2 Dk ck
& D
k
    k ck
k
johtokykymittari
Rs 
1 l
 A
• Exchange current
• Pt-electrodes
• calibration
kT
6a
Electronic vs. ionic conductivity
Electronic conductivity: current is
transported by electrons
i) conductors
ii) semi conductors
iii) insulators
Ionic conductivity: current is transported
by ions
i) strong electrolytes
ii) weak electrolytes
iii) non electrolytes
Material
Cond / S cm-1
Ag
1.59×105
Cu
1.68×105
Au
2.44×105
Pt
1.06×104
C (amorphous)
5-8×101
C (graphite)*
2.5-5.0×103 / 3.0×101
Ge
4.6×10−2
Si
10-1 - 10-5
Water
10-9
Glass
10-16 - 10-12
PTFE (Teflon®)
10-16 -10-12
http://wiki.answers.com/Q/Wh
ich_metals_are_the_most_co
nductive#ixzz25OZd6XAR
Structure, mobility
i
Proton transport via
Grothus or hopping
mechanism
ii
iii
Strong electrolytes - Kohlrausch’s law (1/2)
Dependency of diffusion coefficient on concentration
  ln  i 

Di  Di,  1 

ln
c
i

Debye-Hückel limiting law for 1:1 electrolytes
I
log    z  z  A I  A c
1
zi2 ci

2 i
c
Using above diffusion coefficient can be written as
 ln  i
 ln  i
1
c
 B c
 ln c
c
2
 2.303

Di  Di , 1 
A c
2


B = 2.303 A
Strong electrolytes - Kohlrausch’s law
(2/2)
      
F 2 z k2 Dk
k 
RT
 2,303

Di  Di , 1 
A c
2


    K c
Kohlrausch’s law
Weak electrolytes – Ostwald dilution law
(1/2)
(1 -  )c
  c   c
A B    A   B

Kd 

 A cA    B cB  
c AB




  
      c      1

1 
 is small  ± ~ 1. So for 1:1 electrolytes
 2c
Kd 
1 

Weak electrolytes – Ostwald dilution law
(2/2)
c+ and c- are low  + ~ +, and - ~ -,
  c  c ,  ,   c 



Combining this with rearranged equation for equilibrium constant for 1:1
electrolytes
1
c
 1

Kd

1
1
c


   K d 2
Ostwald dilution law
Comparison of a weak and a strong
electrolyte
KCl
http://chemguide.blogspot.fi/2010/04/vari
ation-of-conductivitywith.html
Electrolyte dissociation in an organic
solvent
Dissociation is incomplete → Ostwald dilution law
Because of interactions ± must be included
For 1:1 electrolytes

 A cA   BcB 


Kd

cAB
 2 2 c

1
K d  1  4 2 c / K d  1



2 2 c
It has been noted experimentally that

      K c

tetrabutyyliammoniumtetrakis
(4-klorofenyyli)borate in 1,2diklooriethane