LECTURE NOTE ON CONCENTRATION CELL

-Dr S P Singh

A cell in which the transference of a substance from a system of high concentration to one at low concentration results in the production of electrical energy is called concentration cell. It consists of two half cells having two identical electrodes and identical electrolytes but with different concentration. EMF of this cell depends upon the difference of concentration. Concentration cell

Electrode concentration cell Electrolyte concentration cell (Amalgam cell) (Electrodes of different concentration) (Electrolytes of different concentration)

Concentration cell without transference Concentration cell with transference (No direct transference of electrolyte but it (There is direct transference with occurs due to the result of chemical electrolyte. The same electrode is reaction.) Each electrode is reversible with reversible with respect to one of the

respect to one of the ions of the electrolyte. ions of electrolyte

1. Concentration cell without transference Let us consider a cell having electrodes reversible with respect to H+ and Cl- as H2(1 atm) │ HCl (a1), AgCl(s) │ Ag where a1 = Apparent concentration i.e. Activity of HCl Hydrogen at left hand electrode dissolves to form H+ ion whereas silver gets deposited at right hand electrode from AgCl as follows; 1 퐻 (1 푎푡푚) → 퐻+ + 푒 2 2

퐴푔퐶푙 (푠) + 푒 → 퐴푔 + 퐶푙−

1 The net cell reaction, 퐻 (1 푎푡푚) + 퐴푔퐶푙(푠) → 퐻퐶푙(푎 ) + 퐴푔(푠) ------(i) 2 2 1 EMF of the cell may be expressed as 푅푇 퐸1 = 퐸° − 푙표푔 푎 ------(ii) 퐹 푒 1 where, Eo = Electrode potential R = Gas constant T = Absolute temperature F = Faraday Another cell with a2 activity of HCl may be represented by; H2 (1 atm) │ HCl (a2), AgCl (s) │ Ag

The net cell reaction in this case is 1 퐻 (1 푎푡푚) + 퐴푔퐶푙(푆푠) → 퐻퐶푙(푎 ) + 퐴푔(푠) ------(iii) 2 2 2

The EMF of the cell is 푅푇 E2 = 퐸° − 푙표푔 푎 ------(iv) 퐹 푒 2 When the two cells containing HCl of activities a1 and a2 are connected with EMF E1 & E2 opposing each other, the resulting cell may be expressed as H2(1atm)│HCl(a1), AgCl(s)│Ag│AgCl(s), HCl(a2)│H2(1 atm) ------(v)

The net cell reaction from equation (i) and (iii), HCl(a1) = HCl(a2) The EMF of the cell formed E = E1 – E2 푅푇 푅푇 = (퐸° − 푙표푔 푎 ) − (퐸° − 푙표푔 푎 ) 퐹 푒 1 퐹 푒 2 푅푇 = (푙표푔 푎 + 푙표푔 푎 ) 퐹 푒 1 푒 2 푅푇 푎2 = 푙표푔푒 ------(vi) 퐹 푎1 As a2 > a1, there is transference of electrolyte from concentrated to dilute solution. Since activity (a) = m2γ2 where m = molality γ = activity coefficient So the equation (6) may be written as 2 2 푅푇 푚2γ2 E = 푙표푔푒 2 2 퐹 푚1γ1 푅푇 푚2γ2 = 2 푙표푔푒 ------(vii) 퐹 푚1γ1 The activities could be expressed in terms of concentrations as 푎 = 푐2푓2 Where c = actual concentration f = Fugacity The equation (vi) may further be written as 2 2 푅푇 푐2 푓2 퐸 = 푙표푔푒 2 2 퐹 푐1 푓1 2 2 푅푇 푐2 푓2 = 2 푙표푔푒 2 2 ------(viii) 퐹 푐1 푓1 For dilute solution, f2 = f1 = 1 (unity), the equation (viii) may be written as 푅푇 푐2 퐸 = 2 푙표푔푒 ------(ix) 퐹 푐1 Since the EMF of the cell without transference depends upon concentration of the solution in both sides so the equation (vi) may be re-written as ν 푅푇 푎2 E= ± 푙표푔푒 ------(x) ν±푍± 퐹 푎1 where ν+ and ν˗ are the number of (+)ve and (-)ve ions and ν is the total number of ions where z+ and z- are valencies (+)ve and (-)ve ions w.r.t. electrodes with which these are reversible.

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2. Concentration cell with transference

Let us consider a cell of this type having the liquid function potential between the function of two solutions. 퐻2(1 푎푡푚)| HCl (a1) ⁞ HCl (a2)|H2(1 푎푡푚) E1 E E2 Two solution of HCl are in contact with each other and the dotted line represents the liquid junction potential. There is a direct transfer of HCl from more concentrated solution (a2) to the less concentrated one (a1). If 1 Faraday of electricity is passed through the cell, 1gm atom of hydrogen dissolves at negative electrode. Whenever two solutions of electrolytes of two concentration are placed together and the electrodes reversible with respect to one of the ions of the electrolyte is kept in each solution then a concentration cell with transport will be obtained. If a2> a1, the left hand electrode will become negative. 1 퐻 − 푒 → 퐻+(푎 ) ------(i) Oxidation reaction 2 2 1 At positive electrode (i.e., the right hand electrode) 1 퐻+(푎 ) + 푒 → 퐻 ------(ii) Reduction reaction 2 2 2 The overall reaction is + + 퐻 (푎2) → 퐻 (푎1) ------(iii)

Thus electron flows from left to right. As the electric current is constituted by H+ and Cl-, it means that H+ ions are moving from left to right while Cl- ions are moving from right to left.

+ - Let us assume that tc and ta are the transport numbers of hydrogen (H ) ion and Chloride (Cl ) ion respectively. + Thus tc equivalent of current is carried by H ions whereas ta equivalent of the current is carried by Cl- ions. For the passage of 1 Faraday of electricity through the cell, tc Faraday is carried by tc gm ion of hydrogen cation from the solution of activity a1 to a2. + + 푡푐퐻 (푎1) = 푡푎퐻 (푎2) ------(iv) 푡푐 + 푡푎 = 1 푡푎 = 1 − 푡푎 ------(v)

where 푡푐 푖푠 푡푟푎푛푠푝표푟푡 푛표. 표푓 푐푎푡푖표푛 & 푡푎푖푠 푡푟푎푛푠푝표푟푡 푛표. 표푓 푎푛푖표푛 Equation (iv) & (v) can be rewritten as + + (1 − 푡푎)퐻 (푎1) = (1 − 푡푎)퐻 (푎2) ------(vi)

- Similarly, 푡푎 Faraday of electricity will be carried by 푡푎 gm of Cl ion from right to left i.e., from the solution of activity a2 to a1 − − 푡푎퐶푙 (푎2) = 푡푎퐶푙 (푎1) ------(vii)

On adding equation (iii), (vi) and (vii) + + − + + − 퐻 (푎2) + (1 − 푡푎)퐻 (푎1) + 푡푎퐶푙 (푎2) = = 퐻 (푎1) + (1 − 푡푎)퐻 (푎2) + 푡푎퐶푙 (푎1) + − + − ⇒ 푡푎퐻 (푎2) + 푡푎퐶푙 (푎2) = 푡푎퐻 (푎1) + 푡푎퐶푙 (푎1) ------(viii)

Thus ta equivalent of HCl is transferred from the solution of activity a2 to a1 by passing 1 Faraday of electricity. EMF of the complete cell, E = E1- E2 푅푇 푅푇 = (퐸° − 푙표푔 푎 푡 ) − (퐸° − 푙표푔 푎 푡 ) 퐹 푒 1 푎 퐹 푒 2 푎 푅푇 푅푇 = − 푙표푔 푎 푡 + 푙표푔 푎 푡 ) 퐹 푒 1 푎 퐹 푒 2 푎 푅푇 푎1푡푎 = − 푙표푔푒 퐹 푎2푡푎 푅푇 푎1 = − 푡푎 푙표푔푒 퐹 푎2 푅푇 푎2 = 푡푎 푙표푔푒 ------(ix) 퐹 푎1 2 2 푅푇 푚2γ2 = 푡푎 푙표푔푒 2 2 퐹 푚1γ1 푅푇 푚2γ2 = 2푡푎 푙표푔푒 ------(x) 퐹 푚1γ1

The EMF in terms of valencies from equation (ix) may be written as ν 푅푇 푎2 퐸 = 푡푎 푙표푔푒 ν ± 푧 ± 퐹 푎1 Where 풱 is the total no. of ions and z is the valency of ions.

In H2/HCl cell, 풱 = 2, 풱± = 1, 푍±= 1, thus the EMF may be 푅푇 푎2 퐸 = 2푡푎 푙표푔푒 ------(xi) 퐹 푎1

Two equivalent half-cells of the same composition differing only in concentrations constitute a concentration cell, a limited form of galvanic cell. It is easier to calculate the potential developed by such a cell using the Nernst equation. When the concentration of reactant in both half-cells are equal, a concentration cell produces a small voltage as it attempts to reach chemical equilibrium, which occurs. In the thermodynamic free energy of the electrochemical system a concentration cell generates electricity from the reduction as the difference in the chemical concentrations in the two half-cells is reduced. The energy is generated from thermal energy that the cell absorbs as heat, as the electricity flows. This generation of electricity from ambient thermal energy, without a temperature gradient, is possible because the convergence of the chemical concentrations in the two half-cells increases entropy, and this increase more than compensates for the entropy decrease when heat is converted into electrical energy.

Applications of concentration cell 1. A pH meter is a specific type of concentration cell that is used to determine the acidity / basicity of a specific solution. 2. The concentration cells are used in reactions where ion selective electrodes are required, to bring on the electrolysis or any other electrochemical reaction.

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