The Voltage of a Cell

The Voltage of a Cell

Each oxidizing agent/reducing agent pair has a standard potential E°, a quantity measured in volts that reflects its tendency to capture or give up electrons. Two values to know for the Daniell cell:

E°(Cu2+/Cu) = +0.34 V
E°(Zn2+/Zn) = -0.76 V

Calculating the Open-Circuit Voltage

The voltage (electromotive force) of a cell is calculated as the difference between the potential of the pair at the cathode and that of the pair at the anode:

E(cell) = E°(cathode) - E°(anode)

For the Daniell cell, the cathode is the Cu2+/Cu pair, the anode the Zn2+/Zn pair:

E(cell) = 0.34 - (-0.76) = 1.10 V

This is indeed a positive value, consistent with the fact that the reaction Zn + Cu2+ -> Zn2+ + Cu is spontaneous in this direction: the greater the gap between the two potentials, the higher the voltage the cell delivers.

A Cell That Wears Out

As the cell operates, the Zn2+ concentration increases in one compartment, while the Cu2+ concentration decreases in the other. The delivered voltage gradually decreases, until it becomes zero when the system reaches an equilibrium state (or when one of the reactants is used up): the cell is then "dead," it can no longer supply useful current.

Common Mistake

Don't think that a cell's voltage is fixed and unchanging: it depends on the concentrations of the species in solution, and decreases with use. The value of 1.10 V calculated here corresponds to standard conditions (reference concentrations of 1 mol/L), not necessarily to the voltage measured at any given moment.