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Q5.5 (ii):
Specify the oxidation numbers of the metals: ([CoBr_{2}(en)_{2}]^{+})

Solution :

Step 1: Identification of Coordination Sphere Components

To determine the oxidation state of the central metal atom Cobalt ($Co$) in the coordination complex $[CoBr_{2}(en)_{2}]^{+}$, we must first identify the oxidation states of the individual ligands bonded to the metal center.

  • Metal ($M$): Cobalt ($Co$), whose oxidation state $x$ is unknown.
  • Ligand 1: Bromido ($Br^{-}$). This is an anionic ligand with a charge of $-1$ [Per IUPAC nomenclature rules for anionic ligands].
  • Ligand 2: Ethylenediamine ($en$). This is a neutral bidentate ligand with a charge of $0$ [Per standard coordination chemistry tables].
  • Overall Complex Charge: $+1$ [Given by the superscript outside the square brackets].

Step 2: Algebraic Formulation

The sum of the oxidation states of the metal and all ligands within the coordination sphere must equal the total charge of the complex. The equation is represented as:

$x + (2 \times \text{charge of } Br^{-}) + (2 \times \text{charge of } en) = \text{Total Charge}$

Step 3: Execution of Calculation

Substituting the known values into the algebraic expression:

$x + (2 \times -1) + (2 \times 0) = +1$

$x - 2 + 0 = +1$

$x = +1 + 2$

$x = +3$

Visual Representation of Coordination Geometry

Co Br⁻ Br⁻ en en

Step 4: Verification

The calculated oxidation state of $Co$ is $+3$. In the complex $[CoBr_{2}(en)_{2}]^{+}$, the contribution of $+3$ from Cobalt, $-2$ from two bromide ions, and $0$ from two neutral ethylenediamine ligands results in a net charge of $+1$, which satisfies the electroneutrality principle for the coordination sphere [Per the definition of oxidation state in complex compounds].

Final Solution: The oxidation number of Cobalt (Co) is +3.


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