Use the standard reduction potentials to find the...

Use the standard reduction potentials to find the equilibrium constant for each of the following reactions at $25^{\circ} \mathrm{C}$ : (a) $\mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)$ (b) $2 \mathrm{Ce}^{4+}(a q)+2 \mathrm{Cl}^{-}(a q) \underset{\mathrm{Cl}_{2}(g)+2 \mathrm{Ce}^{3+}(a q)}{\rightleftharpoons}$ (c) $5 \mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q) \rightleftharpoons$ $\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)+5 \mathrm{Fe}^{3+}(a q)$

Use the standard reduction potentials to find the equilibrium constant for each of the following reactions at $25^{\circ} \mathrm{C}$ :
(a) $\mathrm{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)$
(b) $2 \mathrm{Ce}^{4+}(a q)+2 \mathrm{Cl}^{-}(a q) \underset{\mathrm{Cl}_{2}(g)+2 \mathrm{Ce}^{3+}(a q)}{\rightleftharpoons}$
(c) $5 \mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q) \rightleftharpoons$
$\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)+5 \mathrm{Fe}^{3+}(a q)$

Key Concepts

Relationship Between Cell Potential, Free Energy, and Equilibrium Constant

The net cell potential (E°cell) of a reaction is directly related to the standard free energy change (?G°) by the equation ?G° = -nFE°. Furthermore, the free energy change is linked to the equilibrium constant (K) through the expression ?G° = -RT ln K. These relationships make it possible to calculate the equilibrium constant of a redox reaction from the measured or calculated standard cell potential.

Electrochemical Thermodynamics

Electrochemical thermodynamics connects electrical measurements with chemical equilibria. Using constants such as Faraday's constant (F) and the universal gas constant (R), one can convert the cell potential into free energy changes, and subsequently into equilibrium constants, thereby providing a thermodynamic basis for understanding redox processes.

Standard Reduction Potentials

Standard reduction potentials quantify the tendency of a chemical species to gain electrons under standard conditions (25°C, 1 M concentration, 1 atm pressure). They are essential for determining which half-reactions occur as reductions and which as oxidations, and are used to calculate the overall cell potential in an electrochemical reaction.

Redox Half-Reactions and Balancing

In a redox reaction, the overall process is split into two half-reactions: one for oxidation and one for reduction. Proper balancing of these half-reactions, including the electrons transferred, is crucial to accurately determine the net change in potential and to ensure that the total number of electrons lost equals the electrons gained.

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