Question

For an octahedral complex, which of the following d-electron configurations will give maximum CFSE?

(A) High spin $d^6,-0.4{\mathrm{\Delta }}_o$ $d^6,-0.4{\mathrm{\Delta }}_o$
(B) Low spin $d^4,-1.6{\mathrm{\Delta }}_o$ $d^4,-1.6{\mathrm{\Delta }}_o$
(C) Low spin $d^5,-2.0{\mathrm{\Delta }}_o$
(D) High spin $d^7,-0.8{\mathrm{\Delta }}_o$

Answer 1

Hint: The value of CFSE is more in the given options for the option (C). However it can be understood from the calculation.

Complete step by step answer:
Crystal field splitting energy, CFSE for octahedral complexes is calculated from the following formula,
$[(-0.4\times 5)+(+0.6\times 2)]{\mathrm{\Delta }}_o$
Let us calculate the CFSE for all the given electronic configurations. Let us consider,
- Option (A), in the high spin $d^6$ configuration, there will be 4 $t_{2g}$ electrons and 2 $e_g$ electrons. The CFSE is $[(-0.4\times 4)+(+0.6\times 2)]{\mathrm{\Delta }}_o$
=$[-1.6+1.2]{\mathrm{\Delta }}_o$
=$-0.4{\mathrm{\Delta }}_o$
- Option (B), in low spin $d^4$ configuration, there will be 4 $t_{2g}$ electrons and 0 $e_g$ electrons and its CFSE is = $[-0.4\times 4]{\mathrm{\Delta }}_o$
 = $-1.6{\mathrm{\Delta }}_o$
- Option (C), for low spin $d^5$ configuration, the number of $t_{2g}$ electrons are 5 and $e_g$ are 0, its CFSE is,$[-0.4\times 5]{\mathrm{\Delta }}_o$=$-2.0{\mathrm{\Delta }}_o$
- Option (D), in the high spin $d^7$ configuration, the number of $t_{2g}$ electrons are 5 and $e_g$ are 2, its CFSE is,
=$[(-0.4\times 5)+(+0.6\times 2)]{\mathrm{\Delta }}_o$
=$[-2.0+1.2]{\mathrm{\Delta }}_o$
=$-0.8{\mathrm{\Delta }}_o$
From the above obtained values of Crystal field stabilization energies, the value for low spin $d^5$ configuration is maximum which is, $-2.0{\mathrm{\Delta }}_o$.
The correct answer is option “C” .

Additional Information : The stabilization energy gained by the complex by filling electrons in lower energy $t_{2g}$ orbitals of octahedral complexes is known as crystal field stabilization energy of octahedral complexes. $t_{2g}$ and $e_g$ orbitals are sets of orbitals resulting from splitting of the degenerate d-orbitals. The d-orbitals in which their lobes are oriented along x and y axes are named as $e_g$ orbitals; these are also called double degenerate orbitals. The d-orbitals whose lobes are oriented in between x, y, z axes are named as $t_{2g}$ orbitals. These are also called triple degenerate orbitals. These two sets of orbitals have differences in their energies.

Note: The electrons are filled in the orbitals for calculating CFSE by considering whether the given complex is a low spin complex or a high spin complex. In a low spin complex pairing of electrons takes place whereas in a high spin complex, all the degenerate orbitals are filled by one electron each and then pairing occurs.