Question
Among the following complexes, the one which shows zero crystal field stabilisation energy $$(CFSE)$$ is
A.
$${\left[ {Mn{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
B.
$${\left[ {Fe{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
C.
$${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{2 + }}$$
D.
$${\left[ {Co{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
Answer :
$${\left[ {Fe{{\left( {{H_2}O} \right)}_6}} \right]^{3 + }}$$
Solution :
The $$CFSE$$ for octahedral complex is given by
$$\eqalign{
& CFSE = \left[ { - 0.4\,{t_{2g}}{e^ - } + 0.6\,{e_g}{e^ - }} \right] \cr
& {\text{For}}\,\,M{n^{3 + }},\left[ {3{d^4}} \right] \to t_{2g}^3e_g^1 \cr
& \therefore \,\,CFSE = \left[ {\left( { - 0.4 \times 3} \right) + \left( {0.6 \times 1} \right)} \right] = - 0.6 \cr
& {\text{For}}\,\,F{e^{3 + }},\left[ {3{d^5}} \right] \to t_{2g}^3e_g^2 \cr
& CFSE = \left[ { - \left( {0.4 \times 3} \right) + \left( {0.6 \times 2} \right)} \right] = 0 \cr
& {\text{For}}\,\,{\text{C}}{{\text{o}}^{2 + }},\left[ {3{d^7}} \right] \to t_{2g}^5e_g^2 \cr
& CFSE = \left[ {\left( { - 0.4 \times 5} \right) + \left( {2 \times 0.6} \right)} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 0.8 \cr
& {\text{For}}\,\,C{o^{3 + }},\left[ {3{d^6}} \right] \to t_{2g}^4e_g^2 \cr
& CFSE = \left[ {\left( { - 0.4 \times 4} \right) + \left( {2 \times 0.6} \right)} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = - 0.4 \cr} $$