Final answer:
The preference of a transition metal octahedral complex for high spin or low spin is influenced by the magnitude of crystal field splitting, metal ion charge, the principal quantum number, and the nature of the ligands. Experimentally, this can be determined by measuring the complex's magnetic susceptibility or its electronic absorption spectrum.
Step-by-step explanation:
The factors contributing to the preference of a first row transition metal octahedral complex forming a high spin or low spin complex include the magnitude of crystal field splitting (Δ), metal ion charge, the principal quantum number, and the nature of the ligands. For example, complexes with large values of Δ (greater than the pairing energy P) will form low spin complexes, while those with small values of Δ (less than P) form high spin complexes. In a high spin octahedral complex, electrons are placed in the d orbitals with parallel spins before pairing up, leading to a greater number of unpaired electrons and thus different magnetic properties.
To experimentally determine whether a complex is high spin or low spin, one would measure its magnetic susceptibility to see how many unpaired electrons it has. Additionally, spectroscopic methods such as electronic absorption spectroscopy can provide information on Δ and help deduce the spin state. For instance, a high spin complex [ Fe2+(CN)6 ]4- would be expected to have a relatively small Δ due to the weak field of the CN- ligand, whereas the low spin complex [ Fe3+(CN)6 ]3- would exhibit a large Δ, as CN- acts as a strong field ligand in this context.