Question

The cell reaction \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+14 \mathrm{H}^{+}(a q)+6 \mathrm{Fe}^{2+}(a q) \longrightarrow 6 \mathrm{Fe}^{3+}(a q)+2 \mathrm{Cr}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l)\) is best represented by : (a) \(\operatorname{Pt}(s)\left|\mathrm{Fe}^{+2}(a q), \mathrm{Fe}^{3+}(a q) \| \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q), \mathrm{Cr}^{3+}(a q)\right| \operatorname{Pt}(s)\) (b) \(\mathrm{Pt}(s)\left|\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q), \mathrm{Cr}^{+3}(a q) \| \mathrm{Fe}^{3+}(a q), \mathrm{Fe}^{+2}(a q)\right| \mathrm{Pt}(s)\) (c) \(\mathrm{Fe}^{2+}(a q)\left|\mathrm{Fe}^{3+}(a q) \| \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)\right| \mathrm{Cr}^{3+}(a q)\) (d) \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)\left|\mathrm{Cr}^{3+}(a q) \| \mathrm{Fe}^{3+}(a q)\right| \mathrm{Fe}^{2+}(a q)\)

Short answer

Option (a) \(\mathrm{Pt}(s) | \mathrm{Fe}^{2+}(aq), \mathrm{Fe}^{3+}(aq) || \mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}(aq), \mathrm{Cr}^{3+}(aq) | \mathrm{Pt}(s)\) is the correct representation of the cell reaction.

Step-by-step solution

Understanding Cell Notation

The cell notation represents an electrochemical cell where reactants and products are separated by two vertical lines which denote a salt bridge. The anode (oxidation) is shown on the left, and the cathode (reduction) on the right. A single vertical line indicates a change of phase or boundary between different states of matter.

Identify the Anode and Cathode Reactions

The given reaction is a redox reaction. To write the cell notation, identify the oxidation and reduction half-reactions. Oxidation (anode): \[ \mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{3+} + e^- \] Reduction (cathode): \[ \mathrm{Cr}_{2}\mathrm{O}_{7}^{2-} + 14 \mathrm{H}^+ + 6 e^- \rightarrow 2\mathrm{Cr}^{3+} + 7\mathrm{H}_{2}\mathrm{O} \]

Write the Cell Notation

Combine the anode and cathode half-reactions into the cell notation. The anode part comes first, then the cathode part, separated by a double vertical line representing a salt bridge. Also, use platinum electrodes (Pt) where inert conductors are necessary which is common for solutions without solid conducting species. \[ \mathrm{Pt}(s) | \mathrm{Fe}^{2+}(aq), \mathrm{Fe}^{3+}(aq) || \mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}(aq), \mathrm{Cr}^{3+}(aq) | \mathrm{Pt}(s) \]

Key concepts

Redox Reactions

One of the fundamental concepts in chemistry is the redox reaction, which stands for reduction-oxidation. These reactions are all about the transfer of electrons between substances. A substance that loses electrons is said to be oxidized, while a substance that gains electrons is reduced. To make sense of redox reactions, we track the changes in oxidation states of the elements involved.

For instance, in a redox reaction, iron (Fe) ions can be oxidized from a 2+ oxidation state to a 3+ oxidation state, signifying a loss of an electron. Conversely, the dichromate ion \(\mathrm{Cr}_2\mathrm{O}_7^{2-}\) is reduced to chromium (Cr) ions with a 3+ oxidation state, where it gains electrons. These electron transfers are integral to the functioning of an electrochemical cell, as they are responsible for the generation of an electric current.

It's important to realize that in such reactions, the number of electrons lost is always equal to the number of electrons gained to maintain charge balance. Analyzing redox reactions involves identifying the oxidation states before and after the reaction, which can delineate the aforementioned transformations of Fe and Cr ions in the given exercise.

Anode and Cathode Determination

Identifying the anode and cathode in an electrochemical cell is essential, as these are the sites where oxidation and reduction occur, respectively. The anode is the electrode where oxidation occurs, corresponding to the loss of electrons. The cathode, on the other hand, is where reduction takes place, with the gain of electrons.

Remember, electrons flow from anode to cathode. However, another critical point is that positively charged ions move towards the cathode, and negatively charged ions move towards the anode in the solution. This means that in our exercise, the iron ions (Fe²⁺) that change to Fe³⁺ are oxidized and this occurs at the anode. Conversely, the dichromate ions (Cr₂O₇²⁻) that become Cr³⁺ ions are reduced, and this takes place at the cathode.

Due to these transformations, it is possible to allocate which side of the cell notation each species belongs on, with the anode on the left and the cathode on the right, divided by a double vertical line which indicates a salt bridge that allows ions to flow without mixing the different solutions.

Cell Notation in Electrochemistry

Cell notation is a streamlined way to represent the setup of an electrochemical cell—the apparatus for generating electric current through redox reactions. The convention for writing cell notation is to place the anode on the left and the cathode on the right, separated by double vertical lines which symbolize the salt bridge. The salt bridge is crucial for maintaining electrical neutrality by allowing ions to flow.

In cell notation, phases and states of matter are indicated with single vertical lines. When solid conductors or electrodes, like platinum, are used mainly because reactants and products are in the aqueous phase without solid metal ions to act as electrodes, they are included at either end of the notation, as seen in the correct answer of the exercise.

To write an accurate cell notation, we place the elements of the anode half-reaction on the left, followed by their states (like (aq) for aqueous). Then come the double vertical lines representing the salt bridge, followed by the elements of the cathode half-reaction and their states on the right. It is a simple yet effective shorthand that allows scientists and students to quickly understand the specifics of an electrochemical cell just by reading a single line of symbols and abbreviations.