# Electrochemical cell

### Physical background

Electrical conductivity of electrolytes

Some salts split in water into mobile ions forming the charge carriers able to form electrical current. For characterization of electrolytes to conduct current we use the quantities electrical conductance G and electrical conductivity σ. Electrical conductance expressed by means of the Ohm’s law as a coefficient of proportion between voltage U current I

 I = GU (1)

The unit of electrical conductivity is siemens [G] = S = Ω–1. The resistance of the conductor R and its conductance G is given

 G = 1/R (2)

Electrical conductivity for the conductor with the constant cross-section S and the length l is

 σ = G*(l/S) (3)

The unit of conductivity is siemens per meter [σ] = Sm–1.
The conductivity of some electrolytes may be expressed

 (4)

where e is the elementary charge, c+ and c- are the concentration of positive and negative ions and b+ a b- are their mobility, [b]= m2 V-1 s-1.

Electrochemical cells

Figure 1: Electrochemical Cell Experiment (simulation)

Typical galvanic cell is formed by two metals – e.g. zinc and copper, immersed in water solutions of their respective salts (zinc into e.g. zinc nitrate and copper into copper nitrate). Both solutions with free ions so called electrolytes are separated by a material, not penetrable by the water, but transparent for ions (e.g. salt bridge or a membrane). In both parts of the cell (so called hlafcells) (Figure 2) the following reactions take place

Oxidation = taking off electrons (here from zinc electrode)

 Zn (s) → Zn2+ + 2 e (5)

and reduction = accepting of electrons (here accept the Cu2+ ions in solution)

 Cu2+ + 2e → Cu (s) (6)

Figure 2: Electrochemical Cell Experiment

If we connect both halfcells by a wire, in the external circuit flows the current formed by electrons, which are in both reactions exchanged, as long as the chemicals exhaust. The energy supplied to the external circuit is equal to the product of transmitted charge and the electromotive force of the cell. Electromotive force of the cell is equal to the sum of electromotive forces of both halfcells

 E článku = E pravého polčlánku + E ľavého polčlánku (7)

Electromotive force of the cell depends on both metals used and the concentration of both reacting electrolytes using the Nernst

 (8)

where R is the ideal gas constant 8,314 J.K-1 mol-1, F is the Faraday constant 96 485 C mol-1, E is the standard cell potential (given by the sum of the standard potentials of both metal used), z is the valence (in our case z = 2), i.e. the number of electrons exchanged during the reaction, c is the concentration and T is the absolute temperature (T = t °C + 273,15).

The concentration of the resulting solution c3 formed by mixing of two solutions with different concentrations c1 a c2 and volumes V1 a V2 is

 c1V1 + c2V2 = c3 (V1 + V2) (9)

Table 1: Standard potentials of metals E º [1]

 Li E º= -3,01 K E º= -2,92 Ca E º= -2,84 Na E º= -2,71 Mg E º= -2,38 Al E º= -1,66 Mn E º= -1,18 Zn E º= -0,71 Fe E º= -0,41 Ni E º= -0,23 Sn E º= -0,14 Pb E º= -0,13 H2 Cu E º= 0,34 Ag E º= 0,8 Pt E º= 1,2 Au E º= 1,42

The most active metals with positive standard potential Eº (with the ability to take off other substances electrons – to reduce) are situated in the upper part of the table. The least active metals with the negative standard potential (with the ability to accept electrons) are situated down.
Literature

[1] Daučík, P. et al.: Chemické laboratórne tabuľky, Proxima press, 2001, ISBN 80-85454-38-6)