Write the shorthand notation for a galvanic cell that uses the following cell reaction. Include inert electrodes if necessary. 2 Fe1s2 + Cr2O72-1aq2 + 14 H+1aq2¡2 Fe3+1aq2 + 2 Cr3+1aq2 + 7 H2O1l2

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Identify the oxidation and reduction half-reactions from the given overall cell reaction.

Write the oxidation half-reaction: \( 2 \text{Fe}^{2+} \rightarrow 2 \text{Fe}^{3+} + 2e^- \).

Write the reduction half-reaction: \( \text{Cr}_2\text{O}_7^{2-} + 14 \text{H}^+ + 6e^- \rightarrow 2 \text{Cr}^{3+} + 7 \text{H}_2\text{O} \).

Balance the number of electrons transferred in both half-reactions by multiplying the oxidation half-reaction by 3 and the reduction half-reaction by 1.

Combine the balanced half-reactions and write the cell notation: \( \text{Pt(s)} | \text{Fe}^{2+}(aq), \text{Fe}^{3+}(aq) || \text{Cr}_2\text{O}_7^{2-}(aq), \text{H}^+(aq), \text{Cr}^{3+}(aq) | \text{Pt(s)} \).

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Galvanic Cell Notation

Galvanic cell notation is a shorthand way to represent the components and reactions occurring in an electrochemical cell. It typically follows the format: anode | anode solution || cathode solution | cathode. The anode is where oxidation occurs, and the cathode is where reduction takes place, with the double vertical line indicating the salt bridge separating the two half-cells.

Oxidation and Reduction

Oxidation and reduction are fundamental processes in electrochemistry. Oxidation involves the loss of electrons, while reduction involves the gain of electrons. In the given reaction, iron (Fe) is oxidized to Fe3+, and chromium (Cr) is reduced from Cr2O7^2- to Cr3+, illustrating the transfer of electrons between the reactants.

Inert Electrodes

Inert electrodes, such as platinum or graphite, are used in electrochemical cells when the reactants or products are not solid. They provide a surface for the electron transfer without participating in the chemical reaction. In the context of the given cell reaction, an inert electrode may be necessary if either the oxidation or reduction half-reaction involves ions in solution rather than solid reactants.