3 moles of metal complex with formula Co(en)$$_2$$Cl$$_3$$ gives 3 moles of silver chloride on treatment with excess of silver nitrate. The secondary valency of Co in the complex is _________ (Round off to the nearest integer)

We are told that “3 moles of the metal complex having the empirical formula Co(en)$$_2$$Cl$$_3$$ give 3 moles of AgCl on treatment with excess AgNO$$_3$$.” When silver nitrate is added to a coordination compound, it precipitates only those chloride ions that are present outside the coordination (inner-) sphere, because these chloride ions behave as free, ionisable Cl$$^-$$ ions in solution. The chloride ions that are directly bonded to the metal centre (present inside the square brackets) are not precipitated.

From the experimental observation we have

$$ \text{Moles of complex} : \text{Moles of AgCl} \;=\; 3 : 3 \;=\; 1 : 1 $$

Hence, one mole of the complex liberates one mole of AgCl. Therefore, exactly one chloride ion per formula unit is outside the coordination sphere.

So the correct structural formula must be written as

$$ [\text{Co(en)}_2\text{Cl}_2]\;\text{Cl} $$

Inside the square brackets lie two ethylenediamine ligands and two chloride ligands, whereas the remaining one chloride ion is outside, balancing charge and precipitating as AgCl.

Now we recall the definition: the secondary valency of a metal ion in Werner’s theory equals its coordination number, i.e. the total number of donor atoms that are directly bonded to the metal centre.

In our complex:

• Each ethylenediamine (en) ligand is bidentate; it donates two lone pairs to the metal. Therefore two en ligands furnish $$2 \times 2 = 4$$ donor atoms.
• Two chloride ions inside the bracket each donate one lone pair, supplying $$2$$ further donor atoms.

Adding these contributions we obtain the total number of donor atoms directly attached to Co:

$$ \text{Coordination number} = 4 + 2 = 6 $$

This value, by Werner’s postulates, is the secondary valency.

Hence, the secondary valency of cobalt in this complex is

$$ \boxed{6} $$

Hence, the correct answer is Option 6.