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**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, H_{2}(P_{1}) | H^{+}(C) | H_{2}(P_{2}), Pt

Here, hydrogen gas is bubbled at two different partial pressures at electrode dipped in the solution of same electrolyte.**Cell process : ** 1 / 2H_{2} (p_{1})→H^{+} (c)+e ^{-} (Anode process)

or

For sontaneity of such cell reaction, p_{1}> p_{2}

**Electrolyte concentration cells: **

Zn(s) | ZnSO_{4} (C_{1}) || ZnSO_{4} (C_{2}) | Zn(s)

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

Zn ( s ) → Zn ^{2+ }( C_{1} ) + 2e^{ -} (Anodic process)

(Over all process)

∴ From Nernst equation, we have

For spontanity of such cell reaction, C_{2}> C_{1}

**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 }= a_{1}) | Pb^{2+} (a_{Pb}^{2+}) | Pb(Hg) (a_{Pb }= a_{2})

Electrode Reduction reaction Reduction Potential |

Right Left |

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

Pb(Hg)(a_{1}) = Pb(Hg)(a_{2})

and E_{cell }=

**Cells with gas electrodes operating at differnet Pressures**

We have

Electrode Reduction reaction Reduction potential |

Right Left |

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

H_{2}(p_{1}) = H_{2}(p_{2})

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 | H_{2}(p) | H^{+}Cl^{–}(a_{±})_{1} | AgCl | Ag

may be combined with a cell

Pt | H_{2}(p) | H^{+}Cl^{–}(a_{±})_{2} | AgCl | Ag

to give the following composite cell.

Pt | H_{2}(p) | H^{+}Cl^{–}(a_{±})_{1} | AgCl(s) | Ag – Ag | AgCl | H^{+}Cl^{–}(a_{±})_{2} | H_{2}(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

Cell Cell reaction |

Right Left |

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

H^{+}(a_{2}) + Cl^{–}(a_{2}) = H^{+}(a_{1}) + Cl^{–}(a_{1})

**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 H_{2}(1 bar) → H^{+}(a_{1}) + e^{- }

(ii) Electrode reaction at cathode H^{+}(a_{2}) + e^{-} → 1/2H_{2}(1 bar)

(iii) Transfer of t_{+} mole of H+ from left to right t_{+} H^{+}(a_{1}) → t_{+} H^{+} (a_{2})

(iv) Transfer of t_{-} mole of Cl^{-} from right to left t_{-} Cl^{-}(a_{2}) → t_{-} Cl^{-} (a_{1})

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 a_{2 }to that of activity

a_{1}.

**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 H_{2}(1 bar) → H^{+}(a_{1}) + e^{-}

Electrode reaction at cathode H^{+}(a_{2}) + e^{-} → 1/2H_{2}(1 bar)

The net cell reaction is H^{+}(a_{2}) → H^{+}(a_{1})

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^{–}(a_{1}) → AgCl(s) + e^{- }

(ii) Electrode reaction at cathode AgCl(s) + e^{- }→ Ag(s) + Cl^{-}(a_{2})

(iii) Migration of H^{+} ions t_{+} H^{+}(a_{1}) → t_{+} H^{+} (a_{2})

(iv) Migration of Cl^{-} ions t_{-}Cl^{-}(a_{2}) → t^{-}Cl^{- }(a_{1})

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 a_{1} to that of activity

a_{2}.

The free energy change of the net cell reaction is

Hence E_{cell(wlj)} =

**Cell without liquid junction potential**

Cl^{–}(a_{1}) → Cl^{-}(a_{2})

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

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