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My textbook (NCERT Chemistry Part 1) gives this question as an example:

Why is $\ce{Cr^2+}$ reducing and $\ce{Mn^3+}$ oxidising when both have $d^4$ configuration?

And the solution given along with it says the following:

$\ce{Cr^2+}$ is reducing as its configuration changes from $d^4$ to $d^3$, the latter having a half-filled $t_{2\text{g}}$ level. On the other hand, the change from $\ce{Mn^3+}$ to $\ce{Mn^2+}$ results in the half-filled $d^5$ configuration which has extra stability.


Now my question is: why do they consider octahedral crystal field splitting, even though we don't know anything about the complex formed? If $\ce{Cr}$ underwent tetrahedral or square-planar splitting, it would have a different configuration which may not justify its reducing ability.

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