Step 1: Understanding the Question:
A chiral carbon atom is a carbon atom that is bonded to four different groups or atoms.
To find the number of chiral carbons, we must first determine the structural formula of 2-chloro-3,4,5-trimethylhexane.
Step 2: Key Formula or Approach:
Draw the structure:
The parent chain is hexane ($C_{6}$).
Substituents are at positions 2 (chloro), 3 (methyl), 4 (methyl), and 5 (methyl).
Structure: \( CH_{3} - CH(Cl) - CH(CH_{3}) - CH(CH_{3}) - CH(CH_{3}) - CH_{3} \).
Step 3: Detailed Explanation:
Let's analyze each carbon atom in the chain:
1. \( C_{1} \): Part of a methyl group (\( -CH_{3} \)), has three identical hydrogen atoms. Not chiral.
2. \( C_{2} \): Bonded to H, Cl, \( CH_{3} \), and the rest of the chain \( -CH(CH_{3})CH(CH_{3})CH(CH_{3})CH_{3} \). All four groups are different. Chiral.
3. \( C_{3} \): Bonded to H, \( CH_{3} \), \( -CH(Cl)CH_{3} \), and \( -CH(CH_{3})CH(CH_{3})CH_{3} \). All four groups are different. Chiral.
4. \( C_{4} \): Bonded to H, \( CH_{3} \), \( -CH(CH_{3})CH(Cl)CH_{3} \), and \( -CH(CH_{3})_{2} \). All four groups are different. Chiral.
5. \( C_{5} \): Bonded to H, \( CH_{3} \), \( -CH(CH_{3})CH(CH_{3})CH(Cl)CH_{3} \), and another \( CH_{3} \) (the \( C_{6} \) atom). Since it has two methyl groups, it is not chiral.
6. \( C_{6} \): Part of a methyl group. Not chiral.
Total chiral carbons = 3 (at positions 2, 3, and 4).
Step 4: Final Answer:
There are 3 chiral carbon atoms present in 2-chloro-3,4,5-trimethylhexane.