Step 1: Understanding the Concept:
This question asks about the structure of a specific metal carbonyl complex, dimanganese decacarbonyl, [Mn\(_2\)(CO)\(_{10}\)]. We need to know whether the CO ligands are terminal (bonded to only one metal atom) or bridging (bonded to both metal atoms).
Step 2: Detailed Explanation:
The structure of [Mn\(_2\)(CO)\(_{10}\)] is a well-known example in organometallic chemistry.
- The structure consists of two Mn atoms joined by a direct metal-metal (Mn-Mn) bond.
- Each manganese atom is bonded to five terminal CO groups in an approximately octahedral geometry (if we consider the other Mn atom as one of the ligands).
- The two Mn(CO)\(_5\) units are staggered with respect to each other to minimize steric hindrance.
- Crucially, there are no bridging carbonyl groups. All ten CO ligands are terminal.
The structure can be visualized as (CO)\(_5\)Mn-Mn(CO)\(_5\).
Other common metal carbonyls like Fe\(_2\)(CO)\(_9\) and Co\(_2\)(CO)\(_8\) (in solid state) do have bridging carbonyls, but [Mn\(_2\)(CO)\(_{10}\)] does not. The presence of a direct metal-metal bond satisfies the 18-electron rule for each metal center without the need for bridging ligands.
Step 3: Final Answer:
The number of bridging carbonyl groups in [Mn\(_2\)(CO)\(_{10}\)] is 0.