Question #45037

Consider the solid polynuclear carbonyl complex $\ce{Fe2(CO)9 (s)}$ at $298\text{ K}$. Let $P$ be the true formal oxidation state of each iron atom. Let $Q$ be the number of bridging carbonyl ligands in the most stable structure of this complex. Let $R$ be the actual number of unpaired electrons in the entire molecule. A student incorrectly attempts to apply simple Crystal Field Theory (CFT) by assigning a fractional oxidation state of $+0.5$ to each iron atom due to the $\ce{Fe-Fe}$ bond. To evaluate the magnetic properties, the student models the complex as a mixture of one isolated high-spin octahedral $d^7$ center and one isolated high-spin octahedral $d^8$ center. Let $S^2$ be the sum of the squares of the spin-only magnetic moments (in $\text{BM}^2$) of these two hypothetical isolated centers. Calculate the value of $(P + Q + R + S^2)$.