The electrode potential for the electrode Cl^-|Cl2(g)| Pt is given by E^∘ / V= 1.484867+

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The electrode potential for the electrode Cl^-|Cl2(g)| Pt is...

The electrode potential for the electrode $\mathrm{Cl}^{-}\left|\mathrm{Cl}_{2}(\mathrm{g})\right| \mathrm{Pt}$ is given by \[ \begin{aligned} E^{\circ} / \mathrm{V}=& 1.484867+\left(3.958492 \times 10^{-4}\right)(T / \mathrm{K}) \\ &-\left(2.750639 \times 10^{-6}\right)(T / \mathrm{K})^{2} \end{aligned} \] in the range $273-373$ K. Calculate $E^{\circ}, \Delta_{\mathrm{r}} G^{\circ}, \Delta_{\mathrm{r}} H^{\circ}, \Delta_{\mathrm{r}} S^{\circ},$ and $\Delta_{\mathrm{r}} C_{P}^{\circ}$ at $298.15 \mathrm{K}$

The electrode potential for the electrode $\mathrm{Cl}^{-}\left|\mathrm{Cl}_{2}(\mathrm{g})\right| \mathrm{Pt}$ is given by
\[
\begin{aligned}
E^{\circ} / \mathrm{V}=& 1.484867+\left(3.958492 \times 10^{-4}\right)(T / \mathrm{K}) \\
&-\left(2.750639 \times 10^{-6}\right)(T / \mathrm{K})^{2}
\end{aligned}
\]
in the range $273-373$ K. Calculate $E^{\circ}, \Delta_{\mathrm{r}} G^{\circ}, \Delta_{\mathrm{r}} H^{\circ}, \Delta_{\mathrm{r}} S^{\circ},$ and
$\Delta_{\mathrm{r}} C_{P}^{\circ}$ at $298.15 \mathrm{K}$

Key Concepts

Electrode Potential

The electrode potential is a measure of the tendency of a chemical species to be reduced or oxidized and is expressed in volts. In electrochemistry, it is determined by the standard electrode potential and any additional contributions from concentration, pressure, and temperature effects. Here, the temperature dependence of the electrode potential is expressed as an equation, illustrating how the potential varies with temperature due to inherent thermodynamic processes.

Gibbs Free Energy

Gibbs free energy (?G°) is a thermodynamic quantity that indicates the spontaneity of a reaction. In electrochemistry, there is a direct relationship between the electrode potential and the Gibbs free energy through the relation ?G° = -nFE°, where n is the number of electrons transferred and F is Faraday’s constant. This connection provides a pathway to calculate the free energy change of a reaction using the measured or given electrode potential.

Standard Enthalpy and Standard Entropy

The standard enthalpy (?H°) and standard entropy (?S°) of a reaction are interrelated with Gibbs free energy through the equation ?G° = ?H° - T?S°. This relationship allows one to derive enthalpy and entropy changes by analyzing the temperature dependence of the free energy. Differentiating with respect to temperature can provide insights into the reaction’s energy and disorder changes.

Reaction Heat Capacity

The reaction heat capacity (?_r C_p°) represents the change in the heat capacity during a reaction and is connected to the temperature dependence of the reaction enthalpy. It reflects how the reaction’s enthalpy changes with temperature and can be extracted from the curvature in the temperature dependence of the electrode potential, highlighting the role of temperature in modifying reaction energetics.

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