JEE Chemistry 2026 Question with Solution

Given: The crystal field splitting energy of $[Co(oxalate)_3]^{3-}$ is to be compared with that of $[Cr(oxalate)_3]^{3-}$, with the assumption $\Delta_0 \gg P$.

Find: The value of $n$ such that the splitting energy of the cobalt complex is $n$ times that of the chromium complex.

From the solution, both complexes have the same ligand, oxalate, and the metal ions are in the same oxidation state $+3$. The explanation states that although $Co^{3+}$ generally has slightly higher splitting than $Cr^{3+}$, for this comparison it is treated as approximately equal.

The extracted working gives approximate values:

$$\Delta_0\big([Cr(ox)_3]^{3-}\big) \approx 17400 \, \text{cm}^{-1}$$ $$\Delta_0\big([Co(ox)_3]^{3-}\big) \approx 18000 \, \text{cm}^{-1}$$

These are very close, so the ratio is taken as approximately:

$$n = \frac{\Delta_0\big([Co(ox)_3]^{3-}\big)}{\Delta_0\big([Cr(ox)_3]^{3-}\big)} \approx 1$$

Therefore, the value of $n$ is $1$.

Note: The answer key shows $3$, but the solution explicitly concludes that the value of $n$ is $1$. The solution is taken.