An aqueous solution of NiCl$$_2$$ was heated with excess sodium cyanide in presence of strong oxidizing agent to form [Ni(CN)$$_6$$]$$^{2-}$$. The total change in number of unpaired electrons on metal centre is ___.

In aqueous NiCl$$_2$$, nickel exists as $$\text{Ni}^{2+}$$. The electronic configuration of $$\text{Ni}^{2+}$$ is [Ar] $$3d^8$$. In an octahedral aqua complex, $$\text{Ni}^{2+}$$ ($$d^8$$) has the configuration:

$$t_{2g}^6 \, e_g^2$$

This gives 2 unpaired electrons.

When heated with excess sodium cyanide in the presence of a strong oxidising agent, $$\text{Ni}^{2+}$$ is oxidised to $$\text{Ni}^{4+}$$ and forms the complex $$[\text{Ni(CN)}_6]^{2-}$$. The charge balance: $$-2 = +\text{Ni}_{ox} + 6(-1)$$, giving $$\text{Ni}_{ox} = +4$$. The configuration of $$\text{Ni}^{4+}$$ is [Ar] $$3d^6$$.

Since CN$$^-$$ is a strong-field ligand, in the octahedral $$[\text{Ni(CN)}_6]^{2-}$$ complex, the $$d^6$$ configuration is in low-spin state:

$$t_{2g}^6 \, e_g^0$$

This gives 0 unpaired electrons.

The total change in the number of unpaired electrons at the metal centre:

$$\Delta n = |2 - 0| = \mathbf{2}$$