JEE Chemistry 2023 Question with Solution

Given: The ratio of spin-only magnetic moment values for $[Cr(CN)_6]^{3-}$ and $[Cr(H_2O)_6]^{3+}$ is required.

Find: $\mu_{eff}[Cr(CN)_6]^{3-}/\mu_{eff}[Cr(H_2O)_6]^{3+}$.

For transition metal complexes, the spin-only magnetic moment depends on the number of unpaired electrons.

The formula is

$$\mu_{\text{eff}} = \sqrt{n(n+2)} \, \text{BM}$$

For $[Cr(CN)_6]^{3-}$, chromium is in the $+3$ oxidation state, so it is $d^3$. Hence,

$$\mu_1 = \sqrt{3(3+2)} = \sqrt{15} \, \text{BM}$$

For $[Cr(H_2O)_6]^{3+}$, chromium is also in the $+3$ oxidation state, so it is again $d^3$. Hence,

$$\mu_2 = \sqrt{3(3+2)} = \sqrt{15} \, \text{BM}$$

Therefore,

$$\frac{\mu_1}{\mu_2} = \frac{\sqrt{15}}{\sqrt{15}} = 1$$

Thus, the ratio of magnetic moments is $1$. The correct option is A.