How many distinct constitutional isomers are possible for the molecular formula ?
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Identify the molecular formula given: C\_2Cl\_3F\_3. This means the molecule contains 2 carbon atoms, 3 chlorine atoms, and 3 fluorine atoms.
Determine the possible carbon skeletons. With only 2 carbons, the only possible backbone is an ethane (C\_2) structure, since no other connectivity is possible for two carbons.
Consider the substitution pattern on the ethane backbone. Each carbon can have up to 4 bonds. Since the carbons are bonded to each other, each carbon has 3 remaining positions for substituents (Cl or F).
Enumerate all distinct ways to arrange 3 chlorines and 3 fluorines on the two carbons, keeping in mind that swapping identical groups on equivalent carbons may lead to identical isomers. Use the concept of constitutional isomers, which differ in connectivity, not just spatial arrangement.
Count the number of unique substitution patterns that cannot be interconverted by rotation or swapping carbons. This will give the total number of distinct constitutional isomers for C\_2Cl\_3F\_3.