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

An electrochemical cell is set up so that the reaction described by the equation $$ \begin{aligned} 2 \mathrm{NO}_{\mathrm{s}}(a q)+4 \mathrm{H}^{+}(a q)+& \mathrm{Cu}(s) \leftrightharpoons \\ & 2 \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cu}^{2 *}(a q) \end{aligned} $$ occurs. At $25^{\circ} \mathrm{C}$, the standard cell voltage is $0.65 \mathrm{~V}$. Calculate the value of $\Delta G_{\mathrm{rxan}}^{\circ} .$

An electrochemical cell is set up so that the reaction described by the equation
$$
\begin{aligned}
2 \mathrm{NO}_{\mathrm{s}}(a q)+4 \mathrm{H}^{+}(a q)+& \mathrm{Cu}(s) \leftrightharpoons \\
& 2 \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Cu}^{2 *}(a q)
\end{aligned}
$$
occurs. At $25^{\circ} \mathrm{C}$, the standard cell voltage is $0.65 \mathrm{~V}$. Calculate the value of $\Delta G_{\mathrm{rxan}}^{\circ} .$

Key Concepts

Electrochemical Cells

Electrochemical cells are devices that convert chemical energy into electrical energy (or vice versa) through redox reactions. They consist of two electrodes immersed in electrolyte solutions, and the potential difference between these electrodes drives current through an external circuit. Understanding how these cells are set up and operate is fundamental to studying energy conversion and reaction spontaneity in chemistry.

Standard Cell Potential

The standard cell potential (E°) is the voltage difference between the cathode and anode of an electrochemical cell under standard conditions (1 M concentration for solutions, 1 atm pressure for gases, and pure solids or liquids as reactants). It indicates the driving force of the redox reaction; a positive E° suggests a spontaneous reaction under standard conditions.

Relationship Between Gibbs Free Energy and Cell Potential

The relationship between the Gibbs free energy change (?G°) and the standard cell potential of an electrochemical cell is given by the equation ?G° = -nFE°. This equation directly links the electrical work obtainable from the cell to the thermodynamic favorability of the redox reaction, with n representing the number of electrons transferred and F the Faraday constant.

Faraday's Constant

Faraday's constant (F) represents the amount of electric charge carried by one mole of electrons. It is a crucial factor in converting between electrical units (volts and coulombs) and chemical energy (joules) when using the equation ?G° = -nFE°. This constant is essential in quantifying the energy changes in redox reactions.

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