The value of Ecell ^∘ at 25^∘ C for the equation Pb(s)+Cu^2 *(a q) ⇋Pb^2+(a q)+Cu(s) is 0.47 V.

step 1 Here in this problem, given the cell reaction and the E0 of cell at 25 degrees centigrade, given

The value of Ecell ^∘ at 25^∘ C for the equation Pb(s)+Cu^2...

The value of $E_{\text {cell }}^{\circ}$ at $25^{\circ} \mathrm{C}$ for the equation $$ \mathrm{Pb}(s)+\mathrm{Cu}^{2 *}(a q) \leftrightharpoons \mathrm{Pb}^{2+}(a q)+\mathrm{Cu}(s) $$ is $0.47 \mathrm{~V}$. Calculate the value of the equilibrium constant at $25^{\circ} \mathrm{C}$ for this equation.

The value of $E_{\text {cell }}^{\circ}$ at $25^{\circ} \mathrm{C}$ for the equation
$$
\mathrm{Pb}(s)+\mathrm{Cu}^{2 *}(a q) \leftrightharpoons \mathrm{Pb}^{2+}(a q)+\mathrm{Cu}(s)
$$ is $0.47 \mathrm{~V}$. Calculate the value of the equilibrium constant at $25^{\circ} \mathrm{C}$ for this equation.

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Key Concepts

Equilibrium Constant Calculation

The equilibrium constant (K) for a redox reaction can be determined from the standard cell potential by connecting it to Gibbs free energy, using the relationship ?G = ?RT ln K. This, combined with ?G = ?nFE°, results in the expression K = exp(nFE°/RT), which allows the calculation of K under standard conditions.

Nernst Equation

The Nernst equation relates the cell potential under any conditions to the standard cell potential, temperature, and the reaction quotient (Q). At equilibrium, the cell potential is zero and the Nernst equation leads to the relationship between the standard cell potential and the equilibrium constant.

Standard Electrode Potential

Standard electrode potentials are measured under standard conditions and represent the intrinsic tendency of a half-cell to be reduced. They are used to calculate the overall cell potential for a redox reaction by combining the potentials of the oxidation and reduction half-reactions.

Gibbs Free Energy

Gibbs free energy change (?G) is directly related to the spontaneity of a reaction. In electrochemistry, it is calculated as ?G = ?nFE°, linking the electric work obtainable from an electrochemical cell to the cell potential, where n is the number of moles of electrons transferred and F is Faraday’s constant.

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