Question

The standard cell potential for the nickel–cadmium battery is 1.35 V, and the cell reaction can be written as
2NiO(OH)(s) + 2H2O(l) + Cd(s) ? 2Ni(OH)2(s) + Cd(OH)2(s)

Which one of the following statements do you expect to be true based on the Nernst equation? Note Q =
reaction quotient, and K = equilibrium constant for the cell reaction:

a. As the battery is used, the cell voltage approaches zero because Q approaches K, in value.
b. When the battery no longer works, the cell voltage is zero because Q = K.
c. As the battery is used, the cell voltage does not change because Q equals 1.
d. When the battery is fully charged, Q > K.

Answer 1

     
            R T     [C]c [D]dE = E° - ----- ln ---------
                 n F     [A]a [B]b

This is known as the Nernst equation. The equation allows us to calculate the cell potential of any galvanic cell for any concentrations.

When a system is at equilibrium,E = 0, and Q_eq = K. Therefore, we have,

            R T     [C]c [D]dE° = ----- ln ---------,    (for equilibrium concentrations)
            n F     [A]a [B]b

Thus, the equilibrium constant and E° are related. So the option (a) As the battery is used, the cell voltage approaches zero because Q approaches K, in value is correct.