What is the value of Ecell?

Question

A voltaic cell based on different concentrations of ions, such as seen in the diagram below with copper, is set up with the following materials: solid zinc electrodes, 0.200 M Zn(NO₃)₂, and 5.00 ×× 10^–4 M Zn(NO₃)₂.

Answer 1

A voltaic cell based on different concentrations of ions, such as seen in the diagram below with copper, is set up with the following materials: solid zinc electrodes, 0.200 M Zn(NO₃)₂, and 5.00 ×× 10^–4 M Zn(NO₃)₂.

"the diagram below" is not shown, and therefore the significance of "with copper" is not clear. We will treat this problem as a simple voltaic concentration cell with the same metal electrodes and salt type in both sides. The Nernst equation for this cell is

E = E^o_cell - (0.0592 / n) * log Q

Since both the anode and cathode reactions involve Zn and Zn+2, but in opposite directions, the standard cell voltage E^o_cell is zero. Also, we are dealing with zinc ions, so that n = 2.

The reaction quotient Q is the ratio of concentrations for oxidation/reduction. For cases such as this (same metal electrodes, same salt, different concentrations), Q = [M]_lo / [M]_hi . Therefore the net cell voltage is given by

E = - (0.0592 / 2) * log {[M]_lo / [M]_hi} = - 0.0296 * log (0.0005/0.2)

E = 0.077 V

(assuming that calculation of the cell voltage was the point)