Question

What is the standard reduction potential $\left( {{E^0}} \right)$ for $F{e^{3 + }} \to Fe$
Given that:
$Fe^{2+} + 2e^{-} \to Fe; E_{Fe^{2+}{Fe}} = -0.47V$
$Fe^{3+} + e^{-} \to Fe^{2+}; E_{Fe^{3+}{Fe^{2+}}} = +0.77V$
A) $ - 0.057V$
B) $ + 0.30V$
C) $ - 0.30V$
D) $ + 0.057V$

Answer 1

Hint: In the given reaction, Ferric ion is being reduced to form Iron. This process involves the addition of three electrons to Ferric ions for the formation of Iron. The other two reactions show the reduction of Ferrous ion to Iron and Ferric ion to Ferrous ion. Add these two reactions to get our main reaction.

Complete step by step solution:
Given to us is a reaction involving the reduction of Ferric ions to form Iron. The equation for this reaction can be written as $F{e^{ + 3}} + 3{e^ - } \to Fe$
We are asked to calculate the standard reduction potential for this reaction.
Given to us are two more reactions:
 $F{e^{2 + }} + 2{e^ - } \to Fe$
$F{e^{3 + }} + {e^ - } \to F{e^{2 + }}$
Let us now, add up these two reactions. Now the reaction becomes $F{e^{2 + }} + 2{e^ - } + F{e^{3 + }} + {e^ - } \to Fe + F{e^{2 + }}$
We have $F{e^{2 + }}$ common on both sides of the reaction so that can be cancelled. Also the electrons can be added up. So now the reaction can be written as $F{e^{3 + }} + 3{e^ - } \to Fe$ which is our initial or main reaction.

Since the reaction $F{e^{3 + }} + 3{e^ - } \to Fe$ can be attained by adding the reactions $F{e^{2 + }} + 2{e^ - } \to Fe$ and $F{e^{3 + }} + {e^ - } \to F{e^{2 + }}$ we can add up the standard reduction potentials of both the reactions to attain standard reduction potential of the reaction $F{e^{3 + }} + 3{e^ - } \to Fe$
Hence, the standard reduction potential of the give reaction is $ - 0.47V + 0.77V = + 0.30V$

Therefore the correct answer is option B.


Note: It is to be noted that when writing an equation for a reduction or oxidation reaction, the electrons lost or gained should always be mentioned in the equation. This makes it easier for one to understand the reactions when adding or subtracting them.