Concentration Cells with and without Transport | Physical Chemistry PDF Download

CONCENTRATION CELL
The cells in which electrical current is produced due to transport of a substance from higher to lower concentration. Concentration gradient may arise either in electrode material or in electrolyte.  Thus there are two types of concentration  cell .
(i) Electrode concentration cell
(ii) Electrolyte concentration cell

Electrode Gas concentration cell 

Pt, H₂(P₁) | H⁺(C) | H₂(P₂), Pt
Here, hydrogen gas is bubbled at two different partial pressures at electrode dipped in the solution of same electrolyte.
Cell process :    1 / 2H₂ (p₁)→H⁺ (c)+e ^-       (Anode process)

or   

For sontaneity of such cell reaction, p₁> p₂

Electrolyte concentration cells: 

Zn(s) | ZnSO₄ (C₁) || ZnSO₄ (C₂) | Zn(s)

In such cells, concentration gradient arise in electrolyte solutions. Cell process may be given as,

Zn ( s ) → Zn ²⁺ ( C₁ ) + 2e ^- (Anodic process)

 (Over all process)
∴  From Nernst equation, we have

For spontanity of such cell reaction, C₂> C₁

CONCNETRATION CELLS WITHOUT LIQUID JUNCTION POTENTIAL

Concentration cells are made up of two half-cells which are similar chemcially but differ in the activity of some comon component. The common component may be the electrode or the electrolytic solution.
The emf of the cell is due to the differnece of activity of the common component. We descrribe below three categories of concentration cells without liquid junction.

Cells with Amalgam Electrodes

 Pb(Hg)(a_Pb = a₁) | Pb²⁺ (a_Pb²⁺) | Pb(Hg) (a_Pb = a₂)

Substracting Eq. (ii) from eq. (i), we get

Pb(Hg)(a₁) = Pb(Hg)(a₂)

and E_cell = 

Cells with gas electrodes operating at differnet Pressures

We have 

Substracting Eq. (ii) from eq. (i), we get

H₂(p₁) = H₂(p₂)

and E_cell = 

Cells with differnet Electrolytic Activities 

This type of cells can be formed by making a composite cell out of two cells differing only in the activity of the electrolytic solution. For example, the cell

Pt | H₂(p) | H⁺Cl^–(a_±)₁ | AgCl | Ag
may be combined with a cell

Pt | H₂(p) | H⁺Cl^–(a_±)₂ | AgCl | Ag
to give the following composite cell.
Pt | H₂(p) | H⁺Cl^–(a_±)₁ | AgCl(s) | Ag – Ag | AgCl | H⁺Cl^–(a_±)₂ | H₂(p) | Pt

E_cell = E_L + E_R

Writing the Nernst equation for each potential, we obtain

or

 The net cell reaction is obtained by adding the individual cell reactions. Thus, we have

Adding eqs. (i) and (ii), we get

H⁺(a₂) + Cl^–(a₂) = H⁺(a₁) + Cl^–(a₁)

Note that the emf o the cell may be derived directly from the cell reaction.
If one faraday of electricity is withdrawn from the cell, the net result that is produced is the transfer of 1 mol of each of hydrogen and chloride ions from the right-side cell to the left-side cell. A cell of this type is called a concentration cell wtihout transference. The operation of cell is not accompanied by the direct transfer of electrolyte from one solution to the other.

CONCENTRATION CELL WITH LIQUID JUNCTION POTENTIAL

Development of Liquid Junction Potential In a cell if two electrolytic solutions of different concentration are in contact with each other, a potential difference develops across the boundary of the two solutions This potential difference is called the liquid junction potential or the diffusion potential. It arises because of the difference in the rates of diffusion of positive and negative ions from more concentrated solution to less concentration solution.
The rate of diffusion of an ion is determined by its transference number. To illustrate how the liquid junction potential arises.

CELL IN WHICH ELECTRODES ARE REVERSIBLE WITH RESPECT TO CATION

A Typical Example
Consider the cell

Working of the cell

(i)  Electrode reaction at anode 1/2 H₂(1 bar) →  H⁺(a₁) + e^- 
(ii)  Electrode reaction at cathode H⁺(a₂) + e^- →  1/2H₂(1 bar)
(iii)  Transfer of t₊ mole of H+ from left to right t₊ H⁺(a₁)  →  t₊ H⁺ (a₂)
(iv)  Transfer of t_- mole of Cl^- from right to left t_- Cl^-(a₂)  →  t_- Cl^- (a₁)

The net change in the cell is obtained by adding the above four changes.

Thus, we have

Cancelling the comon term, we get

which on rearranging gives

Thus, the net cell reaction is to transfer t- mole of HCl from the solution of activity a₂ to that of activity
a₁.

Free-energy of cell Reaction

The total free energy change of the net cell reaction is

=  

= 

Cell without liquid Junction Potential
Electrode reaction at anode 1/2 H₂(1 bar) →  H⁺(a₁) + e^-
Electrode reaction at cathode H⁺(a₂) + e^- →  1/2H₂(1 bar)
The net cell reaction is H⁺(a₂)  →  H⁺(a₁)
and the cell potential is

 where a_H+ has been replaced by the mean ionic activity a_±.

Expression of liquid junction potential 

E_lj 

Since t₊ + t_– = 1, equation above may be written as

E_lj   = 

Comparing Eqs we get
E_cell(wlj) = 2t–E_cell(wolj) 

If the cell without liquid junction is to function s pontaneously, we must have
(a_±2)HCl > (a_±1)HCl

Comment on liquid junction potential

In a cell with (a_±2)HCl > (a_±1)HCl, we will have
E_lj positive            if t_– > t₊ 

E_lj negative           if t_– < t₊ 
and E_lj zero          if t_– = t₊

From equation above, we get

E_cell(wlj) > E_cell(wolj)              if t_– > t₊ 
E_cell(wlj) < E_cell(wolj)            if t_– < t₊
and E_cell(wlj) = E_cell(wolj)      if t_– = t₊

CELL IN WHICH ELECTRODES ARE REVERSIBLE WITH RESPECT TO ANIONS

A typical Example Consider the cell

 Working of the cell

(i)  Electrode reaction at anode Ag(s) + Cl^–(a₁) →  AgCl(s) + e^- 
(ii)  Electrode reaction at cathode AgCl(s) + e^- →  Ag(s) + Cl^-(a₂)
(iii)  Migration of H⁺ ions t₊ H⁺(a₁)  →  t₊ H⁺ (a₂)
(iv)  Migration of Cl^- ions t_-Cl^-(a₂)  →  t^-Cl^- (a₁)

The net effect is obtained by adding the above

Thus, the net cell reaction is to transfer t₊ mole of HCl from the solution of activity a₁ to that of activity
a₂.
The free energy change of the net cell reaction is

Hence E_cell(wlj) =  

Cell without liquid junction potential

Cl^–(a₁)  →  Cl^-(a₂)

The cell potential would be  

where aCl^- has been replaced by the mean ionic activity a_±.

Expression of liquid Junction potential Now since

E_ij = E_cell(wlj) – E_cell(wolj)  we get

E_lj =    

or E_lj =  

or E_lj =   

E_cell(wlj) = 2t₊ E_cell(wolj) 

If the cell without liquid junction is to function spontaneously, we must have

(a_±1)HCl > (a_±2)HCl

Comment on liquid junction potential

In general, the sign and magnitude of the liquid function potential depends on the transference numbers of involved cations and anions. In a cell with
(a_±1)HCl > (a_±2)HCl,
we have E_lj 
positive                   if t₊ > t_– E_lj
negative                  if t₊ < t_– 
and E_lj zero             if t₊ = t_–

From above equation we get
E_cell(wlj) > E_cell(wolj)                 if t₊ > t_–
E_cell(wlj) < E_cell(wolj)                 if t₊ < t_–
and E_cell(wlj) = E_cell(wolj)          if t₊ = t_– 

Generalization of Results

E_cell(wlj) =  

E_cell(wlj) =   

E_cell(wlj) =    

Elj