Find the hydrogen deficiency index (HDI) of each molecular formula given below (5 points): a. C12H18 b. C5H5Br2NO
The correct answer and explanation is:
Hydrogen Deficiency Index (HDI) / Degree of Unsaturation
The Hydrogen Deficiency Index (HDI) tells us how many rings or multiple bonds (double or triple) are present in a molecule. Each degree of unsaturation corresponds to:
- 1 ring
- 1 double bond
- 1 triple bond = 2 degrees
HDI Formula:
For a molecular formula CₓHᵧN𝓏OₐXᵦ, where:
- C = carbon atoms
- H = hydrogen atoms
- N = nitrogen atoms
- O = oxygen atoms
- X = halogens (F, Cl, Br, I)
The formula is: HDI=2C+2+N−H−X2\text{HDI} = \frac{2C + 2 + N – H – X}{2}
Note: Oxygen does not affect the HDI and is ignored in the calculation.
a. C₁₂H₁₈
HDI=2(12)+2−182=24+2−182=82=4\text{HDI} = \frac{2(12) + 2 – 18}{2} = \frac{24 + 2 – 18}{2} = \frac{8}{2} = \boxed{4}
Explanation:
This molecule has 4 degrees of unsaturation. That means it could have:
- 4 double bonds, or
- 2 double bonds and 2 rings, or
- 1 ring and 3 double bonds, etc.
The actual structure would tell us which combination is present.
b. C₅H₅Br₂NO
Bromine (Br) is a halogen, so we treat it as X = 2, and N = 1. HDI=2(5)+2+1−5−22=10+2+1−5−22=62=3\text{HDI} = \frac{2(5) + 2 + 1 – 5 – 2}{2} = \frac{10 + 2 + 1 – 5 – 2}{2} = \frac{6}{2} = \boxed{3}
Explanation:
This compound has 3 degrees of unsaturation. This could mean:
- A benzene ring (which is 4), but since this is only 3, maybe
- 1 ring and 1 double bond, or
- 1 triple bond, or
- 3 double bonds.
The presence of nitrogen and halogens hints it could be an aromatic or substituted ring structure.
✅ Final Answers:
- a. C₁₂H₁₈ → HDI = 4
- b. C₅H₅Br₂NO → HDI = 3