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Question: What is the standard reduction potential \(\left( {{E^0}} \right)\) for \(F{e^{3 + }} \to Fe\) Gi...

What is the standard reduction potential (E0)\left( {{E^0}} \right) for Fe3+→FeF{e^{3 + }} \to Fe
Given that:
Fe2++2e−→Fe;EFe2+Fe=−0.47VFe^{2+} + 2e^{-} \to Fe; E_{Fe^{2+}{Fe}} = -0.47V
Fe3++e−→Fe2+;EFe3+Fe2+=+0.77VFe^{3+} + e^{-} \to Fe^{2+}; E_{Fe^{3+}{Fe^{2+}}} = +0.77V
A) −0.057V - 0.057V
B) +0.30V + 0.30V
C) −0.30V - 0.30V
D) +0.057V + 0.057V

Explanation

Solution

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 Fe+3+3e−→FeF{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:
Fe2++2e−→FeF{e^{2 + }} + 2{e^ - } \to Fe
Fe3++e−→Fe2+F{e^{3 + }} + {e^ - } \to F{e^{2 + }}
Let us now, add up these two reactions. Now the reaction becomes Fe2++2e−+Fe3++e−→Fe+Fe2+F{e^{2 + }} + 2{e^ - } + F{e^{3 + }} + {e^ - } \to Fe + F{e^{2 + }}
We have Fe2+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 Fe3++3e−→FeF{e^{3 + }} + 3{e^ - } \to Fe which is our initial or main reaction.

Since the reaction Fe3++3e−→FeF{e^{3 + }} + 3{e^ - } \to Fe can be attained by adding the reactions Fe2++2e−→FeF{e^{2 + }} + 2{e^ - } \to Fe and Fe3++e−→Fe2+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 Fe3++3e−→FeF{e^{3 + }} + 3{e^ - } \to Fe
Hence, the standard reduction potential of the give reaction is −0.47V+0.77V=+0.30V - 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.