A galvanic (voltaic) cell consists of an electrode composed of magnesium in a 1.0 M magnesium ion solution and another electrode composed of copper in a 1.0 M copper(I) ion solution, connected by a salt bridge. Calculate the standard potential for this cell at 25 dC.
To calculate the standard potential for the galvanic cell, we can use the standard reduction potentials for the half-reactions involved. The overall cell potential is calculated by subtracting the reduction potential of the anode reaction from the reduction potential of the cathode reaction.
The half-reactions for this cell are:
1. Mg(s) → Mg2+(aq) + 2e-
2. Cu+(aq) + e- → Cu(s)
The standard reduction potential for the first half-reaction is -2.37 V (reference: NIST Standard Reference Database).
The standard reduction potential for the second half-reaction is +0.52 V (reference: NIST Standard Reference Database).
Since the cell potential is calculated by subtracting the reduction potential of the anode reaction (Mg(s) → Mg2+(aq) + 2e-) from the reduction potential of the cathode reaction (Cu+(aq) + e- → Cu(s)), we have:
Ecell = Ecathode - Eanode
= +0.52 V - (-2.37 V)
= +0.52 V + 2.37 V
= +2.89 V
Therefore, the standard potential for this cell at 25 °C is +2.89 V.
To calculate the standard potential for the galvanic cell, we need to use the standard reduction potentials for the half-reactions occurring at each electrode. The standard reduction potential is a measure of the tendency of a species to gain electrons and undergo reduction.
First, let's write the balanced half-reactions and their standard reduction potentials:
1. At the magnesium electrode (anode):
Mg(s) → Mg2+(aq) + 2e- (standard reduction potential: E°Mg2+ = -2.37 V)
2. At the copper electrode (cathode):
Cu+(aq) + e- → Cu(s) (standard reduction potential: E°Cu+ = +0.52 V)
Next, we need to determine the overall cell potential by subtracting the reduction potential of the anode reaction from the reduction potential of the cathode reaction:
Ecell = E°Cu+ - E°Mg2+
Ecell = (+0.52 V) - (-2.37 V)
Ecell = +2.89 V
The standard potential of the galvanic cell is therefore +2.89 V.
Note: The standard reduction potentials used in this calculation are typically standardized with respect to the hydrogen electrode, which has a standard reduction potential of 0 V. However, since the hydrogen electrode is not directly involved in this cell, we do not need to consider it in our calculations.