Question

Use cell notation to depict an electrochemical cell based upon the following reaction that is productfavored at equilibrium. \(\mathrm{Fe}^{3+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})+\mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq})+\mathrm{AgCl}(\mathrm{s})\)

Short answer

The cell notation is \( \mathrm{Ag}(\mathrm{s}) | \mathrm{AgCl}(\mathrm{s}) | \mathrm{Cl}^-(\mathrm{aq}) || \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \).

Step-by-step solution

Identify the Half Reactions

First, identify the oxidation and reduction half-reactions from the given full reaction. The reduction half-reaction involves the gain of electrons: \[ \mathrm{Fe}^{3+}(\mathrm{aq}) + e^- \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq}) \]The oxidation half-reaction involves the loss of electrons and formation of a solid compound:\[ \mathrm{Ag}(\mathrm{s}) + \mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s}) + e^- \]

Write the Anode and Cathode Reactions

In an electrochemical cell, the anode is where oxidation occurs. From the identified half-reactions,\[ \text{Anode (Oxidation): } \mathrm{Ag}(\mathrm{s}) + \mathrm{Cl}^{-}(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s}) + e^- \]The cathode is where reduction occurs:\[ \text{Cathode (Reduction): } \mathrm{Fe}^{3+}(\mathrm{aq}) + e^- \rightarrow \mathrm{Fe}^{2+}(\mathrm{aq}) \]

Combine the Half Reactions

Combine the half-reactions, ensuring that the electrons cancel out:\[ \mathrm{Ag}(\mathrm{s}) + \mathrm{Cl}^{-}(\mathrm{aq}) + \mathrm{Fe}^{3+}(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s}) + \mathrm{Fe}^{2+}(\mathrm{aq}) \] Both half-reactions already have one electron involved, so they can be directly combined without needing to multiply through by any factors.

Write the Cell Notation

Cell notation lists the anode reaction on the left and the cathode reaction on the right. Use a single vertical line \(|\) to indicate a phase boundary and a double vertical line \(||\) to represent the salt bridge:\[ \text{Cell Notation: } \mathrm{Ag}(\mathrm{s}) | \mathrm{AgCl}(\mathrm{s}) | \mathrm{Cl}^-(\mathrm{aq}) || \mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq}) \].

Key concepts

Oxidation and Reduction

Oxidation and reduction are two fundamental concepts in electrochemistry that describe how electrons are transferred between substances in a reaction.
Oxidation refers to the process where a substance loses electrons, increasing its oxidation state. A classic mnemonic to remember this is 'OIL RIG,' which stands for "Oxidation Is Loss, Reduction Is Gain."
On the other hand, reduction involves the gain of electrons. As seen in our example, \[\text{Fe}^{3+}(\text{aq}) + e^- \rightarrow \text{Fe}^{2+}(\text{aq})\] this half-reaction illustrates reduction as iron ions gain an electron, moving from a +3 oxidation state to a +2 oxidation state.

• Oxidation: Loss of electrons
• Reduction: Gain of electrons

Half-Reactions

Half-reactions split the full electrochemical reaction into two parts: oxidation and reduction. They help us understand which species are losing or gaining electrons.
In an electrochemical cell, the chemical equation is broken into two half-reactions to clearly show the individual processes occurring at the anode and the cathode.
For example, in the entire reaction given:

• The oxidation half-reaction is: \[\text{Ag}(\text{s}) + \text{Cl}^-(\text{aq}) \rightarrow \text{AgCl}(\text{s}) + e^-\]
• The reduction half-reaction is: \[\text{Fe}^{3+}(\text{aq}) + e^- \rightarrow \text{Fe}^{2+}(\text{aq})\]

Half-reactions are essential because they help us balance the electrons exchanged, ensuring that the cell's overall electron transfer is equal.

Cell Notation

Cell notation is a shorthand way to represent the components and reactions of an electrochemical cell. It provides a concise way to show the electrodes, the reactants, and the products in their respective phases.
Standard notation places the anode on the left side and the cathode on the right side, using lines to separate different phases and a double line to represent the salt bridge.
In our example, cell notation is written as:\[ \text{Ag}(\text{s}) | \text{AgCl}(\text{s}) | \text{Cl}^-(\text{aq}) || \text{Fe}^{3+}(\text{aq}), \text{Fe}^{2+}(\text{aq}) \]
Here:

• "|" stands for phase boundaries.
• "||" denotes the salt bridge that completes the circuit between half-cells.

The notation provides a quick and clear reminder of what happens in each part of the cell.

Anode and Cathode Reactions

In electrochemical cells, understanding the anode and cathode reactions is crucial.
Each half-reaction occurs at a different electrode: oxidation at the anode and reduction at the cathode.

• **Anode Reaction (Oxidation)**: At the anode, Ag(s) undergoes oxidation as it loses an electron, forming AgCl(s). \[\text{Ag}(\text{s}) + \text{Cl}^-(\text{aq}) \rightarrow \text{AgCl}(\text{s}) + e^-\]
• **Cathode Reaction (Reduction)**: At the cathode, Fe ions gain an electron to reduce from Fe^{3+} to Fe^{2+}. \[\text{Fe}^{3+}(\text{aq}) + e^- \rightarrow \text{Fe}^{2+}(\text{aq})\]

By visualizing and separating these reactions, we can always determine the direction of electron flow: from anode to cathode. This process powers various electrochemical devices and is central to many spontaneous redox reactions.