Calculate the unsaturation number for each of the following compounds:
(a) C3H4Cl4
(b) C4H7Cl
The Correct Answer and Explanation is :
Unsaturation Number Calculation & Explanation
The unsaturation number (also called the degree of unsaturation or double bond equivalent, DBE) helps determine the presence of double bonds, rings, or triple bonds in a molecular formula.
Formula for Unsaturation Number:
[
DBE = \frac{2C + 2 – H – X + N}{2}
]
where:
- C = number of carbon atoms
- H = number of hydrogen atoms
- X = number of halogens (F, Cl, Br, I)
- N = number of nitrogen atoms
(a) C₃H₄Cl₄
Using the formula:
[
DBE = \frac{2(3) + 2 – 4 – 4 + 0}{2}
]
[
DBE = \frac{6 + 2 – 4 – 4}{2} = \frac{0}{2} = 0
]
Answer: 0 (Saturated compound, no rings or multiple bonds)
Explanation: Since DBE = 0, the molecule has no rings, double bonds, or triple bonds. It is a fully saturated structure with single bonds only.
(b) C₄H₇Cl
Using the formula:
[
DBE = \frac{2(4) + 2 – 7 – 1 + 0}{2}
]
[
DBE = \frac{8 + 2 – 7 – 1}{2} = \frac{2}{2} = 1
]
Answer: 1 (One ring or one double bond present)
Explanation: Since DBE = 1, the molecule has either one double bond or one ring. It cannot have a triple bond (which would require DBE = 2).
Conclusion
- C₃H₄Cl₄ (DBE = 0): Fully saturated compound with no rings or double bonds.
- C₄H₇Cl (DBE = 1): One ring or one double bond present in the structure.
Now, I’ll generate an image representing these molecular structures.
Here is the molecular diagram illustrating the degrees of unsaturation for the given compounds. Let me know if you need further explanations or modifications!