Galvanic Cell - Cell Voltage

Cell Voltage

The standard electrical potential of a cell can be determined by use of a standard potential table for the two half cells involved. The first step is to identify the two metals reacting in the cell. Then one looks up the standard electrode potential, E0, in volts, for each of the two half reactions. The standard potential for the cell is equal to the more positive E0 value minus the more negative E0 value.

For example, in the figure above the solutions are CuSO₄ and ZnSO₄. Each solution has a corresponding metal strip in it, and a salt bridge or porous disk connecting the two solutions and allowing SO₄2− ions to flow freely between the copper and zinc solutions. In order to calculate the standard potential one looks up copper and zinc's half reactions and finds:

Cu2+ + 2 e− Cu: E0 = +0.34 V

Zn2+ + 2 e− Zn: E0 = −0.76 V

Thus the overall reaction is:

Cu2+ + Zn Cu + Zn2+

The standard potential for the reaction is then +0.34 V − (−0.76 V) = 1.10 V. The polarity of the cell is determined as follows. Zinc metal is more strongly reducing than copper metal, equivalently, the standard (reduction) potential for zinc is more negative than that of copper. Thus, zinc metal will lose electrons to copper ions and develop a positive electrical charge. The equilibrium constant, K, for the cell is given by

where F is the Faraday constant, R is the gas constant and T is the temperature in kelvins. For the Daniell cell K is approximately equal to 1.5×1037. Thus, at equilibrium, a few electrons are transferred, enough to cause the electrodes to be charged.

Actual half-cell potentials must be calculated by using the Nernst equation as the solutes are unlikely to be in their standard states,

where Q is the reaction quotient. This simplifies to

where {Mn+} is the activity of the metal ion in solution. The metal electrode is in its standard state so by definition has unit activity. In practice concentration is used in place of activity. The potential of the whole cell is obtained by combining the potentials for the two half-cells, so it depends on the concentrations of both dissolved metal ions.

The value of 2.303R/F is 0.19845×10−3 V/K, so at 25 °C (298.15 K) the half-cell potential will change by if the concentration of a metal ion is increased or decreased by a factor of 10.

These calculations are based on the assumption that all chemical reactions are in equilibrium. When a current flows in the circuit, equilibrium conditions are not achieved and the cell potential will usually be reduced by various mechanisms, such as the development of overpotentials. Also, since chemical reactions occur when the cell is producing power, the electrolyte concentrations change and the cell voltage is reduced. A consequence of the temperature dependency of standard potentials is that the voltage produced by a galvanic cell is also temperature dependent.