Calculate the value of Ecell ^∘ and the equilibrium constant at 25^∘ C for the cell reaction des

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Calculate the value of Ecell ^∘ and the equilibrium constant...

Calculate the value of $E_{\text {cell }}^{\circ}$ and the equilibrium constant at $25^{\circ} \mathrm{C}$ for the cell reaction described by $$ \mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q) \leftrightharpoons 2 \mathrm{Ag}(s)+\mathrm{Cu}^{2+}(a q) $$ Predict whether the reaction is spontaneous when $\left[\mathrm{Ag}^{4}\right]=0.10 \mathrm{M}$ and $\left[\mathrm{Cu}^{2 \cdot}\right]=1.00 \times 10^{-4} \mathrm{M}$. See Appendix $\mathrm{G}$ for the necessary $E^{\circ}$ data.

Calculate the value of $E_{\text {cell }}^{\circ}$ and the equilibrium constant at $25^{\circ} \mathrm{C}$ for the cell reaction described by
$$
\mathrm{Cu}(s)+2 \mathrm{Ag}^{+}(a q) \leftrightharpoons 2 \mathrm{Ag}(s)+\mathrm{Cu}^{2+}(a q)
$$
Predict whether the reaction is spontaneous when $\left[\mathrm{Ag}^{4}\right]=0.10 \mathrm{M}$ and $\left[\mathrm{Cu}^{2 \cdot}\right]=1.00 \times 10^{-4} \mathrm{M}$. See Appendix
$\mathrm{G}$ for the necessary $E^{\circ}$ data.

Key Concepts

Gibbs Free Energy Change

Gibbs free energy change (?G°) is a thermodynamic quantity that relates to the maximum work obtainable from a reaction at constant temperature and pressure. In electrochemistry, it is directly connected to the cell potential by the equation ?G° = -nFE°, providing insight into reaction spontaneity.

Equilibrium Constant

The equilibrium constant (K) quantifies the ratio of product concentrations to reactant concentrations at equilibrium. It is linked to the Gibbs free energy change by the relation ?G° = -RT ln K, and consequently to the cell potential through the relation K = exp(nFE°/RT), allowing one to predict the extent of a reaction.

Standard Electrode Potential

This concept refers to the voltage associated with a half-reaction under standard conditions (1 M concentration for aqueous species, 1 atm pressure for gases, pure solids or liquids). It provides a measure of the tendency of a chemical species to be reduced and is the basis for predicting electron flow in an electrochemical cell.

Standard Cell Potential

The standard cell potential is calculated as the difference between the standard reduction potentials of the cathode and the anode. It represents the driving force of the electrochemical cell under standard conditions, and a positive value indicates a spontaneous reaction.

Nernst Equation

The Nernst equation is used to determine the cell potential under non-standard conditions by incorporating the reaction quotient. It adjusts the standard cell potential to account for variations in concentration or pressure, helping to predict the direction and spontaneity of the reaction in real-world scenarios.

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