Calculating Cobalt Oxidation Number in $[Co(H_2NCH_2CH_2NH_2)_3]_2(SO_4)_3$

To find the oxidation number of Cobalt (Co) in the given complex, follow these steps:

• Identify the components: The complex contains Cobalt (Co), ethylenediamine ($H_2NCH_2CH_2NH_2$), and sulfate ($SO_4$).
• Determine the charge of the ligand: Ethylenediamine ($H_2NCH_2CH_2NH_2$), often abbreviated as 'en', is a neutral molecule. Its oxidation number is 0.
• Determine the charge of the counter ion: The sulfate ion ($SO_4$) carries a charge of -2.
• Analyze the overall formula: The formula is $[Co(H_2NCH_2CH_2NH_2)_3]_2(SO_4)_3$. The overall charge of the compound is neutral (0).
• Calculate the total charge from sulfate ions: There are 3 sulfate ions, so their total charge is $3 \times (-2) = -6$.
• Determine the total charge of the complex cation: Since the overall compound is neutral, the cation part $[Co(H_2NCH_2CH_2NH_2)_3]_2$ must have a total charge of +6 to balance the -6 charge from the sulfates.
• Determine the charge of a single cobalt complex unit: The cation part contains two identical cobalt complexes, $[Co(H_2NCH_2CH_2NH_2)_3]$. Therefore, the charge on each $[Co(H_2NCH_2CH_2NH_2)_3]$ unit is $\frac{+6}{2} = +3$.
• Set up the equation for the cobalt complex unit: Let the oxidation number of Cobalt (Co) be $x$. The charge of the unit is +3. The equation is:

  $x + 3 \times (\text{charge of ethylenediamine}) = +3$

• Solve for $x$: Substitute the charge of ethylenediamine (0):

  $x + 3 \times (0) = +3$

  $x + 0 = +3$

  $x = +3$

The oxidation number of Cobalt (Co) in the complex $[Co(H_2NCH_2CH_2NH_2)_3]_2(SO_4)_3$ is 3.