Chemistry HW Help

Question

You are shown a voltaic cell in which the cathode is Cu and the anode is an unknown metal, X. You measure E°(cell) to be 3.23

V. The cell reaction is X(s) + Cu2+(aq) -> X2+(aq) + Cu(s). The standard reduction potential for the half-cell Cu2+ (aq)/Cu(s) is +0.34 V. Salts of both metals are in their standard states of 1.00 M concentration. Calculate the standard reduction potential of the metal X.

Answer 1

The standard cell potential E°(cell) is related to the standard reduction potentials of the half-cells by the equation:

E°(cell) = E°(reduction) + E°(oxidation)

where E°(reduction) is the standard reduction potential of the reduction half-reaction, and E°(oxidation) is the standard oxidation potential of the oxidation half-reaction.

In this case, the reduction half-reaction is Cu2+(aq) + 2e- -> Cu(s), with a standard reduction potential of +0.34 V. The oxidation half-reaction is X(s) -> X2+(aq) + 2e-, and its standard oxidation potential is the quantity we are trying to find, denoted as E°(X).

Substituting these values into the equation above, we get:

E°(cell) = E°(Cu2+/Cu) + E°(X)

3.23 V = +0.34 V + E°(X)

E°(X) = 3.23 V - 0.34 V = 2.89 V

Therefore, the standard reduction potential of the metal X is 2.89 V.