The electromotive force of the cell Pb(s)|PbSO4(s)| Na2SO4· 10 H2O(sat)|Hg2SO4(s)| Hg(1) i

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The electromotive force of the cell Pb(s)|PbSO4(s)|...

The electromotive force of the cell \[ \mathrm{Pb}(\mathrm{s})\left|\mathrm{PbSO}_{4}(\mathrm{s})\right| \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{sat})\left|\mathrm{Hg}_{2} \mathrm{SO}_{4}(\mathrm{s})\right| \mathrm{Hg}(1) \] is $0.9647 \mathrm{V}$ at $25^{\circ} \mathrm{C}$. The temperature coefficient is $1.74 \times$ $10^{-4} \mathrm{V} \mathrm{K}^{-1} .(a)$ What is the cell reaction? $(b)$ What are the values of $\Delta_{\mathrm{r}} G, \Delta_{\mathrm{r}} S,$ and $\Delta_{\mathrm{r}} H ?$

The electromotive force of the cell
\[
\mathrm{Pb}(\mathrm{s})\left|\mathrm{PbSO}_{4}(\mathrm{s})\right| \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}(\mathrm{sat})\left|\mathrm{Hg}_{2} \mathrm{SO}_{4}(\mathrm{s})\right| \mathrm{Hg}(1)
\]
is $0.9647 \mathrm{V}$ at $25^{\circ} \mathrm{C}$. The temperature coefficient is $1.74 \times$ $10^{-4} \mathrm{V} \mathrm{K}^{-1} .(a)$ What is the cell reaction?
$(b)$ What are the values of $\Delta_{\mathrm{r}} G, \Delta_{\mathrm{r}} S,$ and $\Delta_{\mathrm{r}} H ?$

Key Concepts

Enthalpy and Entropy Determination in Electrochemical Systems

Thermodynamic properties such as enthalpy (?H) and entropy (?S) can be extracted from the electrical data by combining the relationships ?G = ?H - T?S and the temperature dependence of the cell potential. This allows one to calculate both the enthalpy change and the entropy change for the reaction, providing a complete thermodynamic profile that explains the temperature effects on the electrochemical cell’s performance.

Temperature Dependence of Electromotive Force and Reaction Entropy

The temperature coefficient of the cell potential indicates how the emf changes with temperature. This variation is directly related to the reaction entropy through the temperature derivative of the Gibbs free energy. Understanding this dependence is key for determining the entropy change, ?S, of the reaction, which in turn gives insights into the degree of disorder and spontaneity at different temperatures.

Standard Cell Potential and Faraday’s Constant

The standard cell potential (emf) is the driving force behind an electrochemical reaction; it is defined as the difference between the reduction potentials of the cathode and anode under standard conditions. Faraday’s constant connects the transfer of electrons in the reaction to electrical charge, making it possible to relate cell potential directly to the Gibbs free energy change of the reaction.

Electrochemical Cell Reaction

This concept refers to the overall chemical reaction occurring in an electrochemical cell, where oxidation and reduction processes take place at separate electrodes. In such reactions, it is crucial to identify the half?reactions at the anode and cathode and then combine them to form the balanced overall cell reaction. Understanding this helps in determining which species are oxidized or reduced and in quantifying the number of electrons transferred during the reaction.

Gibbs Free Energy Change in Electrochemistry

Gibbs free energy, ?G, is a thermodynamic function that predicts the spontaneity of the electrochemical reaction. In the context of electrochemistry, the relationship ?G = -nFE is used to directly calculate the free energy change from the measured cell potential, where n is the number of electrons transferred and F is Faraday’s constant. This concept bridges the gap between electrical measurements and chemical thermodynamics.

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