Final answer:
The octahedral crystal-field splitting diagrams for each species are as follows: V(H2O)6^3+: t2g^3 with eg energy levels separated by A, Co(CN)6^3-: high-spin t2g^3↓↑ electron configuration with eg energy levels separated by A, Mn(H2O)6^2+: low-spin t2g^3↓↑ electron configuration with eg energy levels separated by A.
Step-by-step explanation:
The octahedral crystal-field splitting diagram for each species is as follows:
a. V(H2O)6³⁺: Since V(III) has three unpaired d electrons in an octahedral field, the diagram will have a t2g3 electron configuration with the energy levels of eg and t2g separated by the crystal field splitting energy, A.
b. Co(CN)6³⁻: Co(III) has three d electrons in an octahedral field, paired with high-spin (t2g3↓↑) electron configuration. The energy levels of eg and t2g are separated by A.
c. Mn(H2O)6²⁺: Mn(II) has five d electrons in an octahedral field. With a strong-field ligand like H2O, it will adopt a low-spin configuration (t2g3↓↑) where three electrons occupy the t2g energy level and two electrons occupy the eg level separated by A.