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

Solution :

Step 1: Identification of Coordination Entity Components

To determine the oxidation state of the central metal atom, we must analyze the charges of all ligands present within the coordination entity $[CoBr_{2}(en)_{2}]^{+}$.

  • Central Metal Atom: Cobalt ($Co$), let its oxidation state be represented by the variable $x$.
  • Ligand 1: Bromide ($Br^{-}$), which carries a charge of $-1$. There are $2$ such ligands.
  • Ligand 2: Ethylenediamine ($en$), which is a neutral bidentate ligand. Its charge is $0$. There are $2$ such ligands.
  • Overall Charge: The entire coordination entity carries a net charge of $+1$.

Step 2: Algebraic Formulation

According to the fundamental principle of coordination chemistry, the algebraic sum of the oxidation states of the central metal atom and the charges contributed by all ligands must equal the total charge on the coordination entity [Per the Stock Notation IUPAC nomenclature rules].

The equation is established as follows:

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

Step 3: Execution of Mathematical Calculation

Substitute the known values into the equation derived in Step 2:

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

Perform the arithmetic operations:

$x - 2 + 0 = +1$

Isolate the variable $x$:

$x = 1 + 2$

$x = +3$

Step 4: Visual Representation of the Coordination Geometry

Co Br⁻ Br⁻ en en

Step 5: Theoretical Justification

The calculation confirms that Cobalt is in the $+3$ oxidation state, denoted as $Co(III)$. This is consistent with the stability of the $d^{6}$ electronic configuration in an octahedral field, which is common for $Co^{3+}$ complexes when coordinated with nitrogen-donor ligands like ethylenediamine [By Crystal Field Theory].

Final Solution: The oxidation number of the metal Cobalt ($Co$) in the complex $[CoBr_{2}(en)_{2}]^{+}$ is $+3$.


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