An electrochemical cell is set up so that the reaction...

An electrochemical cell is set up so that the reaction described by the equation $$ \begin{array}{r} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+14 \mathrm{H}^{+}(a q)+6 \mathrm{Fe}^{2+}(a q) \leftrightharpoons \\ 2 \mathrm{Cr}^{3 \cdot}(a q)+6 \mathrm{Fe}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$ occurs. At $25^{\circ} \mathrm{C}$, the standard cell voltage is $0.461 \mathrm{~V}$. Calculate the value of $\Delta G_{\mathrm{rxn}}^{\circ}$

An electrochemical cell is set up so that the reaction described by the equation
$$
\begin{array}{r}
\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+14 \mathrm{H}^{+}(a q)+6 \mathrm{Fe}^{2+}(a q) \leftrightharpoons \\
2 \mathrm{Cr}^{3 \cdot}(a q)+6 \mathrm{Fe}^{3+}(a q)+7 \mathrm{H}_{2} \mathrm{O}(l)
\end{array}
$$
occurs. At $25^{\circ} \mathrm{C}$, the standard cell voltage is $0.461 \mathrm{~V}$. Calculate the value of $\Delta G_{\mathrm{rxn}}^{\circ}$

Key Concepts

Faraday Constant

The Faraday constant (F) is the charge per mole of electrons, approximately 96485 coulombs per mole. It enables the conversion of electrical measurements (voltage and charge) into energy terms in joules, making it a critical component in the equation that connects cell potential to Gibbs free energy.

Number of Electrons Transferred

This concept focuses on the stoichiometry of an electrochemical reaction, specifically the total number of electrons exchanged between the oxidized and reduced species. It is essential for scaling the relationship between the cell potential and the overall free energy change, ensuring that calculations accurately reflect the reaction’s electron transfer process.

Standard Cell Voltage

This refers to the electromotive force (EMF) of a cell measured under standard conditions (1 M concentrations, 1 atm pressure, 25°C). It serves as an indicator of the driving force for electron flow within an electrochemical cell and plays a crucial role in connecting electrical work to chemical energy changes.

Gibbs Free Energy Change

The Gibbs free energy change (?G°) determines the spontaneity of a reaction under constant temperature and pressure. In electrochemistry, it is related to the standard cell voltage by the equation ?G° = -nFE°, linking the electrical energy available from the cell to the maximum non-expansion work obtainable from the reaction.

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