Crystal field splitting energy (CFSE) for the complex `[Cr(H_2O)_6]^(2+)` is when `P =20925 cm^(-1)` and `Delta_(o) = 10462.5 cm^(-1) (1 kJ mol^(-1) = 83.7 cm^(-1))`

Options

A. `-75kJ mol^(-1)`
B. `75 kJ mol^(-1)`
C. `750 kJ mol^(-1)`
D. `-750 kJ mol^(-1)`

Answer

A

Explanation

`Delta lt P` (weak field,no pairing, high spin state)
Octahedral complex, CN = 6
`Cr = 3d^5 4s^1, Cr^(+2) = 3d^4` Structure is : `3(t_(2g)^3 e_g^1)`
`P = (20925 cm^(-1))/(83.7)=250 kJ mol^(-1)`
`Delta_0 = (10462.5 cm^(-1))/(83.7) = 125 kJ mol^(-1)`
`CFSE = (-0.4 xx 3 + 0.6) Delta_0 = -0.6 Delta_0 = -0.6 xx 125 = -75kJ mol^(-1)`