Question #44576

An aqueous solution of a coordination compound with the empirical formula \ce{M(en)2Cl3} (where \ce{M^{3+}} is a $d^6$ transition metal) is treated with excess \ce{AgNO3(aq)} at $298\text{ K}$, yielding exactly $1\text{ mol}$ of \ce{AgCl(s)} precipitate per mole of the compound. The complex cation exists in multiple stereoisomeric forms. Due to the anisotropic ligand field, the crystal field splitting energy ($\Delta_o$) is highly sensitive to the geometry. In the \textit{trans}-isomer, the weaker axial field results in $\Delta_o < P$ (where $P$ is the spin-pairing energy). Conversely, in the \textit{cis}-isomer, the synergistic ligand field yields $\Delta_o > P$.

Calculate the sum of the numerical values of: (i) The total number of stereoisomers of the complex cation. (ii) The number of unpaired electrons in the high-spin isomer. (iii) The spin-only magnetic moment (in BM) of the optically active isomer(s).