Question

Write the cell notation for the following galvanic cells. For half-reactions in which all the reactants are in solution or are gases, assume the use of inert platinum electrodes. $$ \begin{array}{l} \text { (a) } \mathrm{NO}_{3}^{-}(a q)+4 \mathrm{H}^{+}(a q)+3 \mathrm{Fe}^{2+}(a q) \longrightarrow \\ 3 \mathrm{Fe}^{3+}(a q)+\mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O} \\ \text { (b) } \mathrm{Cl}_{2}(g)+2 \mathrm{Br}^{-}(a q) \longrightarrow \mathrm{Br}_{2}(a q)+2 \mathrm{Cl}^{-}(a q) \\ \text { (c) } \mathrm{Au}^{3+}(a q)+3 \mathrm{Ag}(s) \longrightarrow \mathrm{Au}(s)+3 \mathrm{Ag}^{+}(a q) \end{array} $$

Short answer

\((a) \mathrm{Pt|Fe}^{2+}(aq)|\mathrm{Fe}^{3+}(aq)||\mathrm{NO}_{3}^{-}(aq), \mathrm{H}^{+}(aq)|\mathrm{NO}(g)|\mathrm{Pt}; (b) \mathrm{Pt|Br}^{-}(aq)|\mathrm{Br}_{2}(aq)||\mathrm{Cl}_{2}(g)|\mathrm{Cl}^{-}(aq)|\mathrm{Pt}; (c) \mathrm{Ag}(s)|\mathrm{Ag}^{+}(aq)||\mathrm{Au}^{3+}(aq)|\mathrm{Au}(s)\)

Step-by-step solution

Writing cell notation for reaction (a)

Identify the oxidation and reduction half-reactions. In this case, \(\mathrm{Fe}^{2+}(aq) \rightarrow \mathrm{Fe}^{3+}(aq) + e^-\) is the oxidation half-reaction, and \(\mathrm{NO}_{3}^{-}(aq) + 4 \mathrm{H}^{+}(aq) + 3e^- \rightarrow \mathrm{NO}(g) + 2 \mathrm{H}_{2}O\) is the reduction half-reaction. Write the anode reaction on the left and the cathode reaction on the right, separated by a double vertical line which represents the salt bridge. Include platinum electrodes since the reactants and products are in solution. The cell notation becomes: \(\mathrm{Pt|Fe}^{2+}(aq)|\mathrm{Fe}^{3+}(aq)||\mathrm{NO}_{3}^{-}(aq), \mathrm{H}^{+}(aq)|\mathrm{NO}(g)|\mathrm{Pt}\)

Writing cell notation for reaction (b)

Identify the oxidation and reduction half-reactions for reaction (b). \(2 \mathrm{Br}^{-}(aq) \rightarrow \mathrm{Br}_{2}(aq) + 2e^-\) is the oxidation half-reaction, and \(\mathrm{Cl}_{2}(g) + 2e^- \rightarrow 2 \mathrm{Cl}^{-}(aq)\) is the reduction half-reaction. Write the anode on the left and cathode on the right with inert platinum electrodes: \(\mathrm{Pt|Br}^{-}(aq)|\mathrm{Br}_{2}(aq)||\mathrm{Cl}_{2}(g)|\mathrm{Cl}^{-}(aq)|\mathrm{Pt}\)

Writing cell notation for reaction (c)

In reaction (c), \(\mathrm{Ag}(s) \rightarrow \mathrm{Ag}^{+}(aq) + e^-\) is the oxidation half-reaction, and \(\mathrm{Au}^{3+}(aq) + 3e^- \rightarrow \mathrm{Au}(s)\) is the reduction half-reaction. As both half-reactions involve solid metals, no inert platinum electrode is needed for these half-reactions. The cell notation thus is: \(\mathrm{Ag}(s)|\mathrm{Ag}^{+}(aq)||\mathrm{Au}^{3+}(aq)|\mathrm{Au}(s)\).

Key concepts

Electrochemistry

Electrochemistry is a branch of chemistry that deals with the relationship between electrical energy and chemical reactions. It involves the study of the movements of electrons in redox reactions, which occur in devices called electrochemical cells. One of the most common types of electrochemical cells is the galvanic or voltaic cell, which converts chemical energy into electrical energy through spontaneous redox reactions.

In a galvanic cell, there are two electrodes: the anode, where oxidation occurs, and the cathode, where reduction happens. These electrodes are often made of different materials and are connected by an external circuit that allows for electron flow. Separating the two electrodes is a salt bridge or a permeable membrane, which helps to maintain charge balance by allowing ions to move between the two half-cells.

The importance of electrochemistry lies in its wide range of applications, including batteries, fuel cells, and electrolysis processes. It's through understanding how to harness these reactions that we have been able to develop technologies for energy storage and more efficient chemical production methods.

Redox Reactions

Redox reactions are chemical reactions that involve the transfer of electrons between two species. The term 'redox' is a contraction of 'reduction-oxidation.' In these reactions, one substance is oxidized (loses electrons) and another is reduced (gains electrons).

Oxidation Numbers

Understanding redox reactions requires familiarity with oxidation numbers, which help in identifying the electron transfer process. The oxidation number of an element in a molecule or ion reflects its gain or loss of electrons relative to its elemental state.

Identification of Redox Couples

A redox couple consists of one oxidized and one reduced form of a molecule or ion, linked by the gain or loss of electrons. For example, in the reaction given in the exercise, \(\mathrm{Fe}^{2+}(aq)\) is oxidized to \(\mathrm{Fe}^{3+}(aq)\), and \(\mathrm{NO}_{3}^{-}(aq)\) is reduced to \(\mathrm{NO}(g)\).

To balance redox reactions, one must ensure that the number of electrons lost in the oxidation half-reaction equals the number gained in the reduction half-reaction. This ensures the conservation of charge and mass in the reaction.

Half-Cell Reactions

Half-cell reactions are the individual oxidation or reduction reactions that occur in separate compartments of an electrochemical cell. Each half-cell contains an electrode and an electrolyte where either oxidation or reduction takes place.

The Anode and Cathode Processes

In the anode compartment, the oxidation half-reaction occurs, where electrons are released. Contrastingly, in the cathode compartment, the reduction half-reaction takes place, where electrons are accepted. Together, these processes contribute to the overall cell reaction when connected by an external circuit.

Writing Half-cell Notations

Representing the half-cells involves writing the reactants and products in a specific order. Anode reactions are noted on the left, followed by a double vertical line, indicating the salt bridge, with the cathode reactions on the right. The compounds participating in the reaction are separated by either a single vertical line (indicating a phase boundary) or a comma (for species in the same phase). For example, the cell notation for reaction (a) is as follows: \(\mathrm{Pt|Fe}^{2+}(aq)|\mathrm{Fe}^{3+}(aq)||\mathrm{NO}_{3}^{-}(aq), \mathrm{H}^{+}(aq)|\mathrm{NO}(g)|\mathrm{Pt}\).

The understanding of half-cell reactions and their proper notation is key to deciphering the electrochemical processes and contributing to the design and analysis of galvanic cells.