Calculation of Total CFSE for K3[CoF6] with Magnetic Moment of 5.0 B.M

Step 1: Identification of the Oxidation State of the Central Metal Ion
The complex ion K3[CoF6] contains Co as the central metal ion. From the formula, we can infer that the oxidation state of Co is +3. This is because the charge on K is +1, and there are three K ions, making a total of +3. The charge on [CoF6] is -3, which balances the charge on K.

Step 2: Determination of the Number of Electrons in the Complex
The complex ion [CoF6] contains six fluoride ions, each with a charge of -1. Therefore, the total charge on the ligands is -6. The charge on the complex ion is -3, which means that the central metal ion has a net charge of +3. From the oxidation state of Co, we know that it has lost three electrons. Hence, the total number of electrons in the complex is 3 x 6 = 18.

Step 3: Calculation of the Spin-Only Magnetic Moment
The spin-only magnetic moment is given by the formula µ = √n(n+2)BM, where n is the number of unpaired electrons and BM is the Bohr magneton. Since Co3+ has lost three electrons, we need to determine the number of unpaired electrons in the d-orbitals of Co2+. The electronic configuration of Co2+ is [Ar] 3d7. According to Hund’s rule, we can distribute the seven electrons in the five d-orbitals in the following manner:
↑ ↓
↑ ↓
↑
↑
↑
The number of unpaired electrons is therefore 3. Substituting this value in the formula, we get µ = √3(3+2)BM = 3.87 BM.

Step 4: Calculation of the CFSE
The CFSE is given by the formula CFSE = -0.4nΔo, where n is the number of unpaired electrons and Δo is the crystal field splitting energy. From the electronic configuration of Co2+, we know that there are three unpaired electrons. To calculate Δo, we need to refer to the spectrochemical series. F- is a weak-field ligand, and its crystal field splitting energy is around 8000 cm-1. Substituting the values in the formula, we get CFSE = -0.4 x 3 x 8000 = -9600 cm-1.

Step 5: Calculation of the Total CFSE
The total CFSE is the sum of the CFSE due to the ligand field and the spin pairing energy. The spin pairing energy is given by the formula E = -0.5µBHS, where µB is the Bohr magneton, H is the external magnetic field, and S is the total spin quantum number. For Co2+, S = 3/2. We know that the magnetic moment of the complex is 5.0 BM. Substituting the values in the formula, we get E = -0.5 x 5.0 x 9