(a) Calculate ΔG^∘ for the following cell reaction: Tl(s)|Tl^+(a q) Pb^2+(a q)| Pb(s) The ΔGf^∘

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(a) Calculate ΔG^∘ for the following cell reaction:...

(a) Calculate $\Delta G^{\circ}$ for the following cell reaction: $$ \mathrm{Tl}(s)\left|\mathrm{Tl}^{+}(a q) \| \mathrm{Pb}^{2+}(a q)\right| \mathrm{Pb}(s) $$ The $\Delta G_{f}^{\circ}$ for $\mathrm{Tl}^{+}(a q)$ is $-32.4 \mathrm{~kJ} / \mathrm{mol}$. (b) From $\Delta G^{\circ}$, calculate the standard cell potential for the cell reaction and from this, determine the standard potential for $\mathrm{Tl}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Tl}(s)$

(a) Calculate $\Delta G^{\circ}$ for the following cell reaction:
$$
\mathrm{Tl}(s)\left|\mathrm{Tl}^{+}(a q) \| \mathrm{Pb}^{2+}(a q)\right| \mathrm{Pb}(s)
$$
The $\Delta G_{f}^{\circ}$ for $\mathrm{Tl}^{+}(a q)$ is $-32.4 \mathrm{~kJ} / \mathrm{mol}$.
(b) From $\Delta G^{\circ}$, calculate the standard cell potential for the cell reaction and from this, determine the standard potential for $\mathrm{Tl}^{+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{Tl}(s)$

Key Concepts

Gibbs Free Energy

Gibbs free energy (?G) is the thermodynamic potential that indicates the maximum reversible work of a reaction at constant temperature and pressure. It determines the spontaneity of a reaction—negative ?G suggests that a reaction can occur spontaneously, whereas a positive value indicates that the reaction is nonspontaneous under given conditions.

Electrochemical Cells

Electrochemical cells are systems that convert chemical energy into electrical energy through redox (reduction-oxidation) reactions. These cells typically consist of two half-cells, each containing an electrode and an electrolyte, where oxidation happens at one electrode and reduction at the other, driving the flow of electrons in the circuit.

Standard Electrode Potentials

Standard electrode potentials (E°) are measures of the tendency of a chemical species to be reduced, recorded under standard conditions. They are essential for predicting the direction of electron flow in an electrochemical cell and in calculating the overall cell potential by combining the standard potentials of the half-cell reactions.

Relationship between Gibbs Free Energy and Cell Potential

The relationship between the Gibbs free energy change (?G°) and the cell potential (E°) is given by the equation ?G° = -nFE°, where n is the number of moles of electrons transferred in the reaction and F is Faraday's constant. This equation links the thermodynamic feasibility of a reaction to its electrochemical characteristics, allowing for quantitative analysis of energy changes in redox reactions.

Faraday’s Constant

Faraday's constant (F) is the amount of electric charge carried by one mole of electrons, approximately equal to 96485 coulombs per mole. It serves as a vital conversion factor that connects the microscopic transfer of electrons in chemical reactions with the macroscopic measurement of electrical energy.

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