The difference between spin only magnetic moment values of $$[Co(H_2O)_6]Cl_2$$ and $$[Cr(H_2O)_6]Cl_3$$ is ______.

We need to find the difference between the spin-only magnetic moment values of $$[Co(H_2O)_6]Cl_2$$ and $$[Cr(H_2O)_6]Cl_3$$.

In $$[Co(H_2O)_6]Cl_2$$ cobalt is in the +2 oxidation state so $$Co^{2+}$$ has the configuration $$[Ar]3d^7$$. Water is a weak field ligand giving a high-spin octahedral complex with configuration $$t_{2g}^5\,e_g^2$$ and 3 unpaired electrons.

In $$[Cr(H_2O)_6]Cl_3$$ chromium is in the +3 oxidation state so $$Cr^{3+}$$ has the configuration $$[Ar]3d^3$$. The octahedral $$d^3$$ configuration is $$t_{2g}^3\,e_g^0$$ with 3 unpaired electrons.

The spin-only magnetic moment formula is

For $$Co^{2+}$$

For $$Cr^{3+}$$

The difference between the two magnetic moments is

Therefore, the correct answer is 0.