The primary and secondary valencies of cobalt respectively in [Co(NH3)5Cl]Cl2 are:

🧠 Werner's Dictionary

Werner's two valencies translate cleanly into modern terms:

• Primary valency = oxidation state of the metal.
• Secondary valency = coordination number (number of donor atoms directly bonded to the metal).

So this is two separate one-line calculations.

🗺️ Compute Both

The complex is $[\mathrm{Co(NH_3)_5Cl}]\mathrm{Cl_2}$ — the coordination sphere is $[\mathrm{Co(NH_3)_5Cl}]^{2+}$ and two chlorides sit outside.

Primary valency (oxidation state of Co). Inside the bracket: $x + 5(0) + (-1) = +2 \Rightarrow x = +3$. Primary = 3.

Secondary valency (coordination number). Donor atoms inside the bracket: 5 from $\mathrm{NH_3}$ + 1 from $\mathrm{Cl^-}$ = 6.

So (3, 6).

⚡ The 30-Second Read

For any $[\mathrm{M(L)_a(X)_b}]\mathrm{Y_n}$:

• Primary valency = sum of charges on ligands inside the bracket (with sign flipped) plus the bracket's overall charge.
• Secondary valency = total ligand-donor count inside the bracket ($a + b$).

This sentence solves nearly every Werner-valency question on the JEE.

⚠️ Counting Outer-Sphere Chlorides

The two $\mathrm{Cl^-}$ outside the bracket do not contribute to either valency — they're free counter-ions. Including them inflates the coordination number to 8 and the oxidation state to +5, both wrong. Only atoms inside the square brackets count toward secondary valency.

$\boxed{\text{Answer: (4) 3 and 6}}$