Question

In general, the more negative the value of the reduction potential, the more likely it is to undergo oxidation (anode reaction). Consider the following reduction half-reactions:

Cu²⁺(aq)+2e⁻→Cu(s)E∘=−0.34V

Fe²⁺(aq)+2e⁻→Fe(s)E∘=−0.45V

Al³⁺(aq)+3e⁻→Al(s)E∘=−1.66V

Mg²⁺(aq)+2e⁻→Mg(s)E∘=−2.37V

Given the cell potentials above, calculate the cell potential (Ecell) of an electrochemical cell at 298 K while designating each as anode or cathode.

A cell with Mg/Mg²⁺ and Fe/Fe²⁺ electrodes

Answer 1

To determine the cell potential for a cell with Mg/Mg²⁺ and Fe/Fe²⁺ electrodes, subtract the anode's standard reduction potential from the cathode's. Magnesium (Mg/Mg²⁺) acts as the anode with a standard reduction potential of −2.37V, and iron (Fe/Fe²⁺) as the cathode with −0.45V. The calculated Ecell is −2.82V, indicating magnesium is the anode and iron is the cathode.

Step-by-step explanation:

To calculate the cell potential (Ecell) of an electrochemical cell using the given standard reduction potentials, we first need to identify which metal will act as the anode and which will act as the cathode. The more negative the reduction potential, the greater the tendency for that substance to be oxidized (lose electrons). Hence, it will act as the anode.

For the cell with Mg/Mg²⁺ and Fe/Fe²⁺ electrodes, magnesium with a standard reduction potential E° of −2.37V has the greater tendency to be oxidized compared to iron, which has a standard reduction potential of −0.45V. Therefore, Mg/Mg²⁺ will be the anode, and Fe/Fe²⁺ will be the cathode.

Since standard reduction potentials are given, we need to use the standard reduction potential for the cathode and subtract the standard reduction potential of the anode. The formula to calculate Ecell is:

Ecell = Ecathode − Eanode

In our case, the iron electrode serves as the cathode, and its standard reduction potential is −0.45V. The magnesium electrode, serving as the anode, has its reduction potential taken as positive since oxidation is occurring: +2.37V.

Therefore, we calculate the cell potential as follows:

Ecell = (−0.45V) − (+2.37V) = −2.82V

The negative sign indicates that electrons are flowing from magnesium to iron in the electrochemical cell, and the positive magnitude indicates that magnesium has a stronger driving force to undergo oxidation than iron has for reduction.