Electrochemical Cell Potentials

The cell potential (voltage) for an electrochemical cell can be predicted from half-reactions and its operating conditions (chemical nature of materials, temperature, gas partial pressures, and concentrations).

Determining Standard State Cell Potentials

A cell's standard state potential is the potential of the cell under standard state conditions, which is approximated with concentrations of 1 mole per liter (1 M) and pressures of 1 atmosphere at 25oC.

To calculate the standard cell potential for a reaction

Eocell = Eoreduction + Eooxidation

Example:  Find the standard cell potential for an electrochemical cell with the following cell reaction.

Zn(s) + Cu2+(aq) --> Zn2+(aq) + Cu(s)

oxidation:   Zn(s) --> Zn2+(aq) + 2 e- Eoox. =  - Eored. = - (- 0.762 V) = + 0.762 V 
reduction:  Cu2+(aq) + 2 e---> Cu(s)  Eored. = + 0.339 V

overall:  Zn(s) + Cu2+(aq) --> Zn2+(aq) + Cu(s) Eocell = + 1.101 V


Determining Non-Standard State Cell Potentials

To determine the cell potential when the conditions are other than standard state (concentrations not 1 molar and/or pressures not 1 atmosphere):

Ecell = Eocell - (RT/nF) ln Q

            Ecell = cell potential at non-standard state conditions
            Eocell = standard state cell potential
            R = constant (8.31 J/mole K)
            T = absolute temperature (Kelvin scale)
            F = Faraday's constant (96,485 C/mole e-)
            n = number of moles of electrons transferred in the balanced equation for the reaction occurring
                  in the cell
            Q = reaction quotient for the reaction.  aA + bB --> cC + dD,

Reaction Quotient

If the temperature of the cell remains at 25oC, the equation simplifies to:

Ecell = Eocell - (0.0257/n) ln Q

or in terms of log10

Ecell = Eocell - (0.0592/n) log Q

Example:  Predict the cell potential for the following reaction when the pressure of the oxygen gas is 2.50 atm, the hydrogen ion concentration is 0.10 M, and the bromide ion concentration is 0.25 M.

O2(g) + 4 H+(aq) + 4 Br-(aq) -->  2 H2O(l) + 2 Br2(l)

Ecell = + 0.152 V - (0.0257/4) ln(1.02 x 106)
Ecell = 0.063 V


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