Chapter 19, Problem 1PE

Sketch and label a galvanic cell that makes use of the following spontaneous redox reaction.

$\text{Mg}\left(s\right)+{\text{Fe}}^{\text{2+}}\left(aq\right)\to {\text{Mg}}^{\text{2+}}\left(aq\right)+\text{Fe}\left(s\right)$

Write the half-reactions for the anode and cathode. Give the standard cell notation. (Hint: Determine which half-reaction represents oxidation and which represents reduction.)

Interpretation Introduction

Interpretation:

For the given spontaneous redox reaction, a galvanic cell is to be labeled and sketched, the half- reactions for anode and cathode are to be written, and a standard cell notation is to be given.

Concept Introduction:

The electrode at which reduction occurs is known as cathode and the electrode at which oxidation occurs is known as anode.

The experimental apparatus that creates electric current from the spontaneous redox reaction is known as galvanic cell.

In the standard cell notation, the single vertical line represents the phase boundary and the double vertical line represents the salt bridge, the anode half-cell is described to the left of the double line and the cathode half-cell is described to the right of the double line.

Answer to Problem 1PE

Solution:

Cathode: ${\text{Fe}}^{2+}\left(aq\right)+2{\text{e}}^{-}\to \text{Fe}\left(s\right)$

Anode: $\text{Mg}\left(s\right)\to {\text{Mg}}^{2+}\left(aq\right)+2{\text{e}}^{-}$

Cell notation: $\text{Mg}\left(s\right)|{\text{ Mg}}^{2+}\left(aq\right)\Vert {\text{Fe}}^{2+}\left(aq\right)|\text{ Fe}\left(s\right)$

Explanation of Solution

The given spontaneous redox reaction is as:

$\text{Mg}\left(s\right)+{\text{Fe}}^{2+}\left(aq\right)\to {\text{Mg}}^{2+}\left(aq\right)+\text{Fe}\left(s\right)$

At anode, oxidation takes place, whereas, at cathode, reduction takes place. In this galvanic cell, magnesium acts as the anode and iron acts as the cathode. In order to balance the redox reaction, iron gains two electrons while magnesium loses two electrons. Salt bridge enables the flow of ions which neutralize the charge imbalance. Within the salt bridge, the negative charge flows towards the anode to neutralize the accumulation of positive charge. Similarly, the positive charge flows towards the cathode to neutralize the accumulation of negative charge.

The half-cell reactions that take place at cathode and anode are as:

Half-cell reaction at cathode: ${\text{Fe}}^{2+}\left(aq\right)+2{\text{e}}^{-}\to \text{Fe}\left(s\right)$

Half-cell reaction at anode: $\text{Mg}\left(s\right)\to {\text{Mg}}^{2+}\left(aq\right)+2{\text{e}}^{-}$

The sketch of a galvanic cell is as:

In the standard cell notation, the magnesium anode half-cell is placed on the left and the cathode half-cell is placed on the right separated by the salt bridge. The standard cell notation for the given spontaneous redox reaction is represented as:

$\text{Mg}\left(s\right)|{\text{ Mg}}^{2+}\left(aq\right)\Vert {\text{Fe}}^{2+}\left(aq\right)|\text{ Fe}\left(s\right)$

Conclusion

The half-cell reaction for anode and cathode and the standard notation cell notation have been written as:

Cathode: ${\text{Fe}}^{2+}\left(aq\right)+2{\text{e}}^{-}\to \text{Fe}\left(s\right)$

Anode: $\text{Mg}\left(s\right)\to {\text{Mg}}^{2+}\left(aq\right)+2{\text{e}}^{-}$

Cell notation: $\text{Mg}\left(s\right)|{\text{ Mg}}^{2+}\left(aq\right)\Vert {\text{Fe}}^{2+}\left(aq\right)|\text{ Fe}\left(s\right)$