What is the standard cell potential for a voltaic cell using the Pb²⁺/Pb and Mg²⁺/Mg half-reactions? Which metal is the cathode?

Question

Quizplus · Accepted Answer

To determine the standard cell potential, we need to subtract the reduction potential of the anode from the reduction potential of the cathode.

For the cathode, we have: 
Mg2+ + 2e- -> Mg    E° = -2.37 V

For the anode, we have: 
Pb2+ + 2e- -> Pb    E° = -0.13 V

Adding the two half-cell reactions gives: 
Mg2+ + Pb -> Mg + Pb2+

The standard cell potential, E°cell, is the sum of the reduction potentials:

E°cell = E°cathode - E°anode

E°cell = (-2.37 V) - (-0.13 V) 
E°cell = -2.24 V

Since the standard cell potential is negative, the reaction is not spontaneous as written. To make the reaction spontaneous, we could reverse the direction of the anode or cathode half-reaction.

Since the standard cell potential is closer to Mg2+/Mg (-2.37 V) than to Pb2+/Pb (-0.13 V), we know that the Mg half-reaction is the cathode and the Pb half-reaction is the anode. Thus, choice D is the correct answer, with Pb as the anode and Mg as the cathode.

What Is the Standard Cell Potential for a Voltaic Cell