First slide

Electrochemical cell

Question

$If E_{{Fe}^{+ 2} / Fe}^{0} = x_{1} V; E_{{Fe}^{+ 3} / {Fe}^{+ 2}}^{0} = x_{2} V, E_{{Fe}^{+ 3} / Fe}^{0} is$

Difficult

A

$\frac{2 x_{1} + x_{2}}{4}$
B

$\frac{2 x_{1} + x_{2}}{3}$
C

$\frac{2 x_{1} + x_{2}}{2}$
D

$2 x_{1} + x_{2}$

Solution

${Fe}^{+ 2} + 2 e^{-} \to Fe; E_{1}^{0} = x_{1} and ∆ G_{1}^{0} = - 2 {FE}_{1}^{0} = - 2 {Fx}_{1} {Fe}^{+ 3} + e^{-} \to {Fe}^{+ 2}; E_{2}^{0} = x_{2} and ∆ G_{2}^{0} = - 1 {FE}_{2}^{0} = - 1 {Fx}_{2} {Fe}^{+ 3} + 3 e^{-} \to Fe; E_{3}^{0} = ?; ∆ G_{3}^{0} = - 3 {FE}_{3}^{0} = ∆ G_{1}^{0} + ∆ G_{2}^{0} - 3 {FE}_{3}^{0} = - F (2 x_{1} + x_{2}) E_{3}^{0} = \frac{2 x_{1} + x_{2}}{3}$

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