The chemical reaction, \(2 \mathrm{AgCl}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{HCl}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})\) taking place in a galvanic cell is represented by the notation: (a) \(\mathrm{Pt}(\mathrm{s})\left|\mathrm{H}_{2}(\mathrm{~g}), 1 \mathrm{bar}\right| 1 \mathrm{M} \mathrm{KCl}(\mathrm{aq})|\mathrm{AgCl}(\mathrm{s})| \mathrm{Ag}(\mathrm{s})\) (b) \(\mathrm{Pt}(\mathrm{s})\left|\mathrm{H}_{2}(\mathrm{~g}), 1 \operatorname{bar}\right| \mathrm{l} \mathrm{M} \mathrm{KCl}\) (aq) \(\mid \mathrm{l} \mathrm{M} \mathrm{Ag}^{+}\) (aq) \(\mid \mathrm{Ag}(\mathrm{s})\) (c) \(\mathrm{Pt}(\mathrm{s})\left|\mathrm{H}_{2}(\mathrm{~g}), 1 \mathrm{bar}\right| 1 \mathrm{M} \mathrm{KCl}\) (aq) \(|\mathrm{AgCl}(\mathrm{s})| \mathrm{Ag}(\mathrm{s})\) (d) \(\operatorname{Pt}(\mathrm{s})\left|\mathrm{H}_{2}(\mathrm{~g}), 1 \mathrm{bar}\right| 1 \mathrm{M} \mathrm{KCl}(\mathrm{aq})|\mathrm{Ag}(\mathrm{s})| \mathrm{AgCl}\)

Step by step solution

01

Understand the Galvanic Cell Notation

A galvanic cell's notation consists of electrodes and solutions separated by vertical lines, with the anode (oxidation half) on the left and the cathode (reduction half) on the right side. The reaction components are written from left to right in sequence as they appear in the cell.

02

Identify Anode and Cathode

For the reaction given, hydrogen gas, \(\mathrm{H}_{2}\), is oxidized to hydrogen ions, \(\mathrm{HCl}\), releasing electrons. This constitutes the anode. Silver chloride, \(\mathrm{AgCl}\), is reduced to silver metal, \(\mathrm{Ag}\), and accepts electrons, constituting the cathode.

03

Write the Cell Notation

The anode is written first followed by the electrolyte, which is followed by the cathode. The correct notation will include \(\mathrm{Pt}\) electrode for \(\mathrm{H}_{2}\) gas at 1 bar, the electrolyte which is 1M KCl solution, the insoluble \(\mathrm{AgCl}\), and the silver electrode \(\mathrm{Ag}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electrochemical Cell Representation

Understanding electrochemical cell representation is fundamental in the study of galvanic cells. The notation serves as a concise description of the cell's components and the reactions taking place. Each cell comprises two electrodes (the anode and the cathode) and the electrolyte solution they are immersed in. The notation is arranged with the anode components on the left, moving through to the cathode components on the right, with single vertical lines (|) separating different states of matter and double lines (||) indicating a salt bridge or membrane.

The notation thus follows this pattern: Anode | Anode's electrolyte || Cathode's electrolyte | Cathode. When representing a galvanic cell, it's essential to ensure that the reactants and products are correctly placed in relation to the anode and cathode. By looking at the chemical reaction, we can decipher the flow of electrons from the anode to the cathode and translate this into correct cell notation.

Anode and Cathode Identification

Identification of the anode and cathode within a galvanic cell is crucial to understanding the direction of electron flow and the overall chemical reaction. Anodes are where oxidation occurs—loss of electrons—while cathodes are where reduction—gain of electrons—takes place. To identify them, remember this handy mnemonic: 'An Ox and a Red Cat'—anode oxidation, cathode reduction.

In our given reaction, the hydrogen gas, \textbf{H\(_2\)}, loses electrons and thus is undergoing oxidation. This places the hydrogen electrode as the anode. Conversely, silver chloride, \textbf{AgCl}, sees silver ions gaining electrons and forming metallic silver; this indicates that the reaction at the silver/silver chloride interface is reduction, defining it as the cathode. The components associated with the anode and cathode in the notation provide crucial details for understanding the reactions taking place within the cell.

Oxidation and Reduction Reactions

Oxidation and reduction reactions are fundamental to electrochemistry and Galvanic cells. They refer to the transfer of electrons between chemical species. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. Each half-cell reaction in a galvanic cell has an oxidation and a reduction component, crucial for the cell's ability to generate an electric current.

In the exercise provided, hydrogen gas is oxidized to form hydrogen ions, which can be represented as: \textbf{H\(_2 \rightarrow 2H^+ + 2e^-\)}. This half-reaction takes place at the anode. The reduction half-reaction occurs at the cathode, where silver ions in \textbf{AgCl} gain electrons to form silver metal: \textbf{Ag\(^+ + e^- \rightarrow Ag\)}. The full cell reaction is the sum of these half-reactions, demonstrating the complementary nature of oxidation and reduction in a functioning electrochemical cell.