TRANSPORT OF IONS IN SOLUTION

Jaslin Ikhsan, Ph.D.Chemistry Ed. Department

State University of Yogyakarta

Conductivity of electrolyte

solutions

Strong and weak electrolyte

Ion Mobility

Ion mobility and conductivity,

Transport number

Diffusion

Conductivity of Electrolyte Solution

Ions in solution can be set in motion by applying a

potential difference between two electrodes.

The conductance (G) of a solution is defined as the

inverse of the resistance (R):

For parallel plate electrodes with area A, it

follows:

GR

in units of 1 1,

GA

L

Where,

Κ: the conductivity,

L : the distance separating the plates

Units:

G → S (siemens)

R → Ωκ → S m-1

Conductivity of Electrolyte Solution

The conductivity of a solution depends on the number of ions

present. Consequently, the molar conductivity Λm is used

C is molar concentration of electrolyte and

unit of Λm is S m2 mol-1

mC

In real solutions, Λm depends on the concentration

of the electrolyte. This could be due to:

Ion-ion interactions γ 1

The concentration dependence of conductance

indicates that there are 2 classes of electrolyte Strong electrolyte: molar conductivity depends

slightly on the molar concentration

Weak electrolyte: molar concentration falls

sharply as the concentration increases

Conductivity of Electrolyte Solution

In real solutions, Λm depends on the concentration of the

electrolyte. This could be due to:

1. Ion-ion interactions γ 1

2. Incomplete dissociation

of electrolyte

strong electrolyte,

weak dependence of Λm on C

weak electrolyte,

strong dependence of Λm on C

Strong Electrolyte

Fully ionized in solution

Kohlrausch’s law

Λ0m is the limiting molar conductivity

K is a constant which typically depends on the

stoichiometry of the electrolyte

C1/2 arises from ion-ion interactions as estimated by the

Debye-Hückel theory.

m m KC 0 1 2/

Strong Electrolyte

Law of the independent migration of ions: limiting molar

conductivity can be expressed as a sum of ions contribution

ions migrate independently in

the zero concentration limi0

m

Weak Electrolyte

Not fully ionized in solution

HA aq H O l H O aq A aq

c c c

( ) ( ) ( ) ( )

( )

2 3

1

Kc

a

2

1,

2

2

2

2

0

4

2

2

4

2

c K K

c K K

K K K c

c

K

c

K K c

c

a a

a a

a a a

a a a

K

c

K

c

c

K

K

c

c

K

a a

a

a

a

2 21

4

21

41

1 2

1 2

/

/

11

c

Ka

is degree of ionisation

Weak Electrolyte

The molar Conductivity (at

higher concentrations) can

be expressed as:

At infinite dilution, the

weak acid is fully

dissociated (α = 100%)

It can be proven by the

Ostwald dilution law which

allows estimating limiting

molar conductance:

m m 0

m m

m m

m m

m m a

m m a m

m

m

x

xc

K

c

Kx

0

0

0

0

0 0 0

1 1

1 1 1

1 11

1 1

1 10 0 2

m m

m

a m

c

K

( )

Weak Electrolyte

The limiting molar conductance:

1 10 0 2

m m

m

a m

c

K

( )

Graph to determine the limiting

value of the molar conductivity of

a solution by extrapolation to zero

concentration

The Mobility of Ions

Ion movement in solution is random. However, a migrating

flow can be onset upon applying an electric field ,

EL

is the potential difference between 2 electrodes

separated by a distance L

F accelerates cations to the negatively charged electrode and

anions in the opposite direction. Through this motion, ions

experience a frictional force in the opposite direction.

Taking the expression derived by Stoke relating friction and

the viscosity of the solvent (), it follows:

F zeEze

L

F rs for ions with raidus r and velocity vfric 6 , ( )

The Mobility of Ions

When the accelerating and retarding forces balance each

other, s is defined by:

u is mobility of ions, and r is hydrodynamic

radius, that might be different from the ionic

radius, small ions are more solvated than the

bulk ones.

szeE

rE where

ze

r

6 6

,

Mobility in water at 298 K. Viscosity of liquids at 298 K

The Mobility of Ions and Conductivity

Finally, it can be shown that:

Fully dissociated electrolyte:

z F where F N eA,

J ionss tA vcN

A tsvcN

J ch e zervcN zrvcF z EvcF

I J A z EvcFA z vcFAL

IR

GL

AA

A

( ).

( arg )

.

z vcF

z F

z v z v Fm0 ( )

In solution:

The Mobility of Ions and Conductivity

Example:

1. if =5x10-8 m2/Vs and z=1, Λ=10mS m2 mol-1.

2. From the mobility of Cl- in aqueous solution, calculate the molar

ionic conductivity.

= 7.91 x 10-8 m2 s-1V-1 x 96485 Cmol-1 = 7.63x10-3 sm2 mol-1

z F

The Mobility of Ions and Conductivity

• Taking a conductimetre cell with electrodes separated by 1 cm and

an applied voltage of 1 V, calculate the drift speed in water at 298 K.

rCs = 170 pm

H2O = 0.891x10-3 kg m-1 s-1

ze

r

x C

x x x kgm s x x m

x m V s

EL

V

mVm

s E x m V s x Vm x ms

6

1602 10

6 31416 0891 10 170 10

5 10

1

0 01100

5 10 100 5 10

19

3 1 1 12

8 2 1 1

1

8 2 1 1 1 6 1

.

. .

.

It will take a Cs+ ion 2000 s to go from one electrode to another.

For H+ ion, H+=36.23 x10-8 m2 s-1 V-1, it will take 276 s.

Transport Numbers

Diffusion

Diffusion

Diffusion

Diffusion

Diffusion

Diffusion

Solution of Diffusion Equation

Diffusion Probablities

Random Walk

Problems

Summary

Migration: Transport of ions induced by an electric field.

The concentration dependence of the molar conductivity

strongly differs for strong and weak electrolytes.

Diffusion: Mass transport generated by a gradient of

concentration.

m m KC 0 1 2/

02

m z v D z v DF

RT ( )

DRT

zF D

k T

r

B6

Thank You