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Q5.5 (iv):
Specify the oxidation numbers of the metals: (K_{3}[Fe(CN)_{6}])

Solution :

Step 1: Identification of Oxidation States of Ligands and Counter Ions

To determine the oxidation state of the central metal atom ($Fe$) in the coordination entity $[Fe(CN)_{6}]^{3-}$, we must assign the known oxidation states to the coordinating ligands and the counter ions based on standard IUPAC nomenclature and chemical equilibrium rules.

  • Potassium ($K$): As an alkali metal (Group 1), it consistently exhibits an oxidation state of $+1$.
  • Cyanide ($CN^-$): The cyano ligand carries a formal charge of $-1$ per ion.
  • Central Metal ($Fe$): Let the oxidation state of Iron be denoted by $x$.

Step 2: Algebraic Formulation of the Neutrality Condition

According to the Principle of Electroneutrality, the sum of the oxidation states of all atoms in a neutral coordination compound must equal zero [Per IUPAC coordination rules].

The chemical formula is given as: $K_{3}[Fe(CN)_{6}]$

The equation is constructed as follows:

$3 \times (\text{Oxidation state of } K) + 1 \times (\text{Oxidation state of } Fe) + 6 \times (\text{Oxidation state of } CN) = 0$

Step 3: Solving the Equation

Substituting the known values into the algebraic equation:

$3(+1) + x + 6(-1) = 0$

$3 + x - 6 = 0$ [Applying Arithmetic Associative Law]

$x - 3 = 0$

$x = +3$

Step 4: Verification via Coordination Sphere Charge

The compound dissociates as: $K_{3}[Fe(CN)_{6}] \rightarrow 3K^{+} + [Fe(CN)_{6}]^{3-}$

In the complex ion $[Fe(CN)_{6}]^{3-}$, if $x$ is the oxidation state of Iron:

$x + 6(-1) = -3$

$x - 6 = -3$

$x = +3$

Visual Representation of the Octahedral Complex

Fe³⁺ CN⁻ CN⁻ CN⁻ CN⁻ CN⁻ CN⁻

Final Solution: The oxidation number of Iron ($Fe$) in $K_{3}[Fe(CN)_{6}]$ is $+3$.


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