Related Formula
Degrees of Unsaturation (Double Bond Equivalents, DBE):
DBE = C + 1 - (H)/(2) + (N)/(2)$$\mathrm{DBE} = C + 1 - \frac{H}{2} + \frac{N}{2}$$
For formula C₉H₁₂$\mathrm{C_9H_{12}}$:
DBE = 9 + 1 - (12)/(2) = 4$$\mathrm{DBE} = 9 + 1 - \frac{12}{2} = 4$$
These 4 degrees of unsaturation match a benzene ring exactly (one ring + three double bonds).
Core Logic
Since the question specifies 'substituted benzene derivatives', we must keep the benzene core (C₆H₅-$\mathrm{C_6H_5-}$ or similar) intact. This leaves 3 carbon atoms to be distributed as alkyl substituents.
Step 1: Categorize by substitution patterns
- Mono-substituted benzene (one propyl group containing 3 carbons):
- n-Propylbenzene: C₆H₅-CH₂-CH₂-CH₃$\mathrm{C_6H_5-CH_2-CH_2-CH_3}$ (Isomer 1)
- Isopropylbenzene (Cumene): C₆H₅-CH(CH₃)₂$\mathrm{C_6H_5-CH(CH_3)_2}$ (Isomer 2)
- Di-substituted benzene (one ethyl group and one methyl group):
- 1-Ethyl-2-methylbenzene (ortho-ethylmethylbenzene) (Isomer 3)
- 1-Ethyl-3-methylbenzene (meta-ethylmethylbenzene) (Isomer 4)
- 1-Ethyl-4-methylbenzene (para-ethylmethylbenzene) (Isomer 5)
Step 2: Tri-substituted benzenes
- Tri-substituted benzene (three methyl groups):
- 1,2,3-Trimethylbenzene (Hemimellitene) (Isomer 6)
- 1,2,4-Trimethylbenzene (Pseudocumene) (Isomer 7)
- 1,3,5-Trimethylbenzene (Mesitylene) (Isomer 8)
Step 3: Total Count
Summing all options:
Total structural isomers = 2 + 3 + 3 = 8$$\text{Total structural isomers} = 2 + 3 + 3 = 8$$
Pattern Recognition
For alkyl benzenes with N$N$ extra carbons, systematically group them as single chain substituents down to multiple methyl substituents. This hierarchical sorting prevents duplicates or missing patterns.
Chapter Mix
Class 11 Chemistry: Organic Chemistry - Some Basic Principles and Techniques
Class 11 Chemistry: Hydrocarbons