Question

How do you calculate the standard cell potential of a cell constructed from `Mg^(2+)`/`Mg` and`Ni^(2+)`/`Ni`. Which half-cell is the anode and which half-cell is the cathode?

Answer 1

`E_"Cell"^theta=+2.115 color(white)(l) "V"`

• Cathode `"Mg"^(2+) "/" "Mg"`
• Anode `"Ni"^(2+) "/" "Ni"`

Explanation:

Look up the reduction potential for each cell in question on a table of standard electrode potential like this one from Chemistry LibreTexts. [1]

• `"Mg"^(2+) (aq) + 2color(white)(l) "e"^(-) to "Mg"(s) color(white)(-)E^theta = -2.372 color(white)(l) "V"`
• `"Ni"^(2+) (aq) + 2color(white)(l) "e"^(-) to "Ni"(s) color(white)(-)E^theta = -0.257 color(white)(l) "V"`

The standard reduction potential `E^theta` resembles the electrode's strength as an oxidizing agent and equivalently its tendency to get reduced. The reduction potential of a Platinum-Hydrogen Electrode under standard conditions (`298 color(white)(l) "K"`, `1.00 color(white)(l) "kPa"`) is defined as `0 color(white)(l) "V"` for reference. [2]

A cell with a high reduction potential indicates a strong oxidizing agent- vice versa for a cell with low reduction potentials.

Two half cells connected with an external circuit and a salt bridge make a galvanic cell; the half-cell with the higher `E^theta` and thus higher likelihood to be reduced will experience reduction and act as the cathode, whereas the half-cell with a lower `E^theta` will experience oxidation and act the anode.

`E^theta ("Ni"^(2+) "/" "Ni") > E^theta("Mg"^(2+) "/" "Mg")`

Therefore in this galvanic cell, the `"Ni"^(2+) "/" "Ni"` half-cell will experience reduction and act as the cathode and the `"Mg"^(2+) "/" "Mg"` the anode.

The standard cell potential of a galvanic cell equals the standard reduction potential of the cathode minus that of the anode. That is:

`E_"cell"^theta = E^theta ("Cathode") - E^theta ("Anode")`
`color(white)(E_"cell"^theta) = -0.257 - (-2.372)`
`color(white)(E_"cell"^theta) = +2.115`

Indicating that connecting the two cells will generate a potential difference of `+2.115 color(white)(l) "V"` across the two cells.

References
[1] "1.2: Standard Electrode Potentials", Chemistry LibreTexts,
https://chem.libretexts.org/LibreTexts/University_of_California_Davis/UCD_Chem_002C/UCD_Chem_2C%3A_Larsen/Chapters/Unit_1%3A_Electrochemistry/1.2%3A_Standard_Electrode_Potentials

[2] "17.3: Standard Reduction Potentials", Chemistry LibreTexts, https://chem.libretexts.org/Textbook_Maps/General_Chemistry/Book%3A_Chemistry_(OpenSTAX)/17%3A_Electrochemistry/17.3%3A_Standard_Reduction_Potentials