Step 1: Identify the central metal and oxidation state

The central metal is Cobalt (Co) with an oxidation state of +3. This is indicated by (III) in the name.

Step 2: Identify the ligands and their charges

The ligands are:

• Tetraammine: 4 $NH_{3}$ (neutral, charge = 0)
• Aqua: 1 $H_{2}O$ (neutral, charge = 0)
• Chlorido: 1 $Cl^{-}$ (anionic, charge = -1)

Step 3: Calculate the charge of the coordination sphere

The total charge of the complex ion is the sum of the metal oxidation state and the charges of the ligands: $$Charge = (+3) + 4(0) + 1(0) + 1(-1) = +2$$ Thus, the coordination sphere is $[Co(NH_{3})_{4}(H_{2}O)Cl]^{2+}$.

Step 4: Balance with counter ions

Since the complex ion has a charge of +2, we need two chloride ions ($Cl^{-}$) outside the coordination sphere to balance the charge. The formula is $[Co(NH_{3})_{4}(H_{2}O)Cl]Cl_{2}$.