First slide

Standard EMF of a cell

Question

Standard electrode potentials of $\large F{e^{2 + }} + \,2e\, \to \,Fe$ and $\large F{e^{3 + }} + \,3e\, \to \,Fe$ are – 0.440V and – 0.036V respectively. The standard electrode potential (E°) for $\large F{e^{3 + }} + \,e\, \to \,F{e^{2 + }}$ is

Moderate

Solution

Electrode potentials are intensive properties. Their magnitude remains same on doing mathematical operation.
Extensive properties like Gibbs energy is used to find Electrode potential values.
$\begin{gathered} F{e^{ + 2}} + 2{e^ - } \to Fe\,\,\,;\Delta {G_1} = - 2F{E_1} \ \\ \underline {F{e^{ + 3}} + 3{e^ - } \to Fe\,\,\,;\Delta {G_2} = - 3F{E_2}} \\ \\ \underline {F{e^{ + 3}} + {e^ - } \to F{e^{ + 2}}\,\,\,\,\,\,\,\,\,\,;\Delta G = - FE} \ \\ \end{gathered}$
Required equation is obtained bysubstracting eq.1 from eq.2
$\Delta G = \Delta {G_2} - \Delta {G_1}$
$- FE = - 3F\left( { - 0.036} \right) - \left( { - 2F\left( { - 0.44} \right)} \right) = 0.108F - 0.88F = - 0.772F$
$E = 0.772V$

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