The ground state of Co2+ ion in CoSO4.7H2O may be regarded as 4T3/2. T...
Ground State of Co2+ ion in CoSO4.7H2O
The ground state of the Co2+ ion in CoSO4.7H2O can be regarded as 4T3/2. This notation indicates that the ground state electronic configuration of the ion is a triplet state with a total spin quantum number of 3/2.
Entropy Contribution from Electron Spin
The entropy of a substance at temperatures below 1K is derived almost entirely from the electron spin. In the case of the Co2+ ion, the electron spin can have two possible orientations: spin-up and spin-down. Each orientation has a degeneracy of 2. Therefore, the total degeneracy of the electron spin is 2^2 = 4.
Molar Entropy Calculation
To calculate the molar entropy of the solid at temperatures below 1K, we need to consider the degeneracy of the electron spin and the Boltzmann constant.
The formula to calculate the molar entropy is given by:
S = R * ln(W)
Where:
S = molar entropy
R = gas constant (8.314 J/mol-K)
W = degeneracy of the system
In this case, the degeneracy of the electron spin is 4. Therefore, the molar entropy can be calculated as:
S = 8.314 * ln(4)
S = 8.314 * 1.386
Rounding off to two decimal places, the molar entropy of the solid at temperatures below 1K is 19.15 J/mol-K.
Conclusion
The molar entropy of the Co2+ ion in CoSO4.7H2O at temperatures below 1K is 19.15 J/mol-K. This value is calculated based on the degeneracy of the electron spin, which is 4, and the Boltzmann constant. The entropy of the solid at these temperatures is mainly derived from the electron spin contributions.