Question

Number of carbon atoms connected to the metal center in [W(C\(_{60}\))(CO)\(_5\)] is _________ (rounded off to the nearest integer). 
(Given: atomic number of W = 74)

Hint:

In organometallic complexes, each CO ligand donates its {carbon} atom. C\(_{60}\) typically coordinates in an \(\eta^2\) fashion through a double bond (2 carbons to the metal). Always include both CO carbons and fullerene carbons when asked for “number of carbons connected to the metal.”

Answer 1

Step 1: Nature of the complex.
The complex is \([W(C_{60})(CO)_5]\), where tungsten is coordinated to 5 terminal carbonyls and the fullerene (C\(_{60}\)). Each CO contributes one carbon donor. The question is about the number of carbon atoms of the fullerene directly bonded to W.
Step 2: Electron-counting perspective.
W has atomic number 74; in zero oxidation state it has 6 valence electrons (group 6). The five CO ligands donate \(5 \times 2 = 10\) electrons. For the stable 18-electron configuration, the metal must receive 2 additional electrons from the C\(_{60}\).
Thus, C\(_{60}\) as a ligand provides \(\eta^2\)-type coordination (a C=C double bond). Hence, W is connected to two adjacent carbon atoms of C\(_{60}\).
Step 3: Interpretation of “number of carbon atoms connected.”
In such \(\eta\)\(^2\)-binding, the metal simultaneously bonds to both carbons of the C=C bond. Therefore, the number of C atoms directly connected to W = 5 (from CO) + 2 (from C\(_{60}\)) = 7.
However, the question asks only for the number of carbon atoms (not counting O of CO), i.e., the carbon donors:
- 5 carbons from the CO ligands
- 2 carbons from the \(\eta\)\(^2\)-C\(_{60}\) bond
Total = \(\mathbf{7}\).
Rounded off to the nearest integer → \(\mathbf{7}\). \[ \boxed{7} \]