Devise a cell for which the cell reaction is H2O(l)=H^+(ao)+OH^-(ao) Calculate Δr G^∘ at 2

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Devise a cell for which the cell reaction is ...

Devise a cell for which the cell reaction is \[ \mathrm{H}_{2} \mathrm{O}(\mathrm{l})=\mathrm{H}^{+}(\mathrm{ao})+\mathrm{OH}^{-}(\mathrm{ao}) \] Calculate $\Delta_{\mathrm{r}} G^{\circ}$ at $25^{\circ} \mathrm{C}$ from electrode potentials. What is the value of the equilibrium constant at this temperature?

Devise a cell for which the cell reaction is
\[
\mathrm{H}_{2} \mathrm{O}(\mathrm{l})=\mathrm{H}^{+}(\mathrm{ao})+\mathrm{OH}^{-}(\mathrm{ao})
\]
Calculate $\Delta_{\mathrm{r}} G^{\circ}$ at $25^{\circ} \mathrm{C}$ from electrode potentials. What is the value of the equilibrium constant at this temperature?

Key Concepts

Electrode Potentials

Electrode potentials represent the ability of a half-cell to gain or lose electrons at a standard state, and they are measured relative to a standard reference, often the Standard Hydrogen Electrode. They are essential in constructing electrochemical cells as they allow the calculation of the overall cell potential when two half-cell reactions are combined, with the difference between the cathodic and anodic potentials determining the spontaneous direction of electron flow.

Standard Free Energy Change (?rG°)

The standard free energy change is a thermodynamic quantity that indicates the amount of reversible work obtainable from a process at constant temperature and pressure. In electrochemistry, it is closely related to the cell potential by the relation ?rG° = -nFE°, where n is the number of electrons transferred, F is Faraday's constant, and E° is the standard cell potential. This connection bridges electrical measurements with chemical thermodynamics.

Equilibrium Constant (K)

The equilibrium constant quantifies the ratio of the activities (or concentrations) of products to reactants at equilibrium. In the context of a chemical reaction, it provides insights into the position of equilibrium, with a large constant indicating that the reaction strongly favors products. The relationship ?rG° = -RT ln K connects the thermodynamic driving force of a reaction with its equilibrium position.

Relationship Between Thermodynamics and Electrochemistry

The analysis of chemical reactions via both thermodynamics and electrochemistry involves understanding how electrical measurements, like electrode potentials, can be translated into thermodynamic quantities such as ?rG° and the equilibrium constant. The equations ?rG° = -nFE° and ?rG° = -RT ln K establish a direct link between the energetic and equilibrium properties of a chemical reaction, allowing predictions of reaction spontaneity and extent under standard conditions.

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