ChemistryIsomerismJEE · NEET

Isomerism · Part 6 of 14

Degree of Unsaturation and Counting Isomers

Before counting isomers, find out what the formula allows. The double bond equivalent tells you how many rings and π bonds to place; a systematic method does the rest.

Builds on: Part 2 · Functional Isomerism, Part 3 · Metamerism.

Double bond equivalent

$D.B.E. = \frac{\sum n ( v - 2 )}{2} + 1$

Each D.B.E. is one ring or one π bond (a triple bond counts two). Divalent O and S add nothing; halogens count like H.

D.B.E. formula and valency table. — v − 2 for each kind of atom.

Four C4H6 structures. — Buta-1,3-diene, but-1-yne, cyclobutene, bicyclobutane.

C₄H₆

Four ways to spend 2 D.B.E.

$\frac{4 ( 2 ) + 6 ( - 1 )}{2} + 1 = 2$ : two C=C, one C≡C, a ring + a C=C, or two rings.

C₃H₆O

7 isomers, 9 with enols

Acetone, propanal, allyl alcohol, methyl vinyl ether, oxetane, 2-methyloxirane, cyclopropanol; plus the enols prop-1-en-2-ol and prop-1-en-1-ol if tautomers are counted.

Nine C3H6O structures. — The two enols are tinted.

Nine C5H8 structures. — All nine constitutional isomers.

C₅H₈

Nine without rings

Three alkynes, four straight-chain dienes and two branched dienes. 2-Methylbuta-1,2-diene can't exist: the central allene carbon has no room for a substituent.

Summary

Key formulas

D.B.E. = \frac{\sum n ( v - 2 )}{2} + 1

Double bond equivalent

Worked examples

From the video

1. Write all structural isomers of C₄H₉Br.

4: 1-bromobutane, 2-bromobutane, 1-bromo-2-methylpropane, 2-bromo-2-methylpropane.

2. Isomeric pentyl alcohols?

8: three on the straight chain, four on the 2-methylbutane skeleton, one on neopentane.

JEE-style question

Your turn

Constitutional isomers of C₅H₈ (excluding ring-chain isomers):

(a)5

(b)6

(c)7

(d)9

Show the answer and the traps

Three alkynes plus six dienes: 9. Option (d).

7 forgets the two branched dienes. 6 counts only the dienes. 5 misses whole families.

Watch out

Common mistakes

Giving oxygen a contribution in D.B.E.For divalent atoms v − 2 = 0.

Counting the same skeleton numbered from the other end.Name every structure and compare names.

Practice

Try these

1. The number of isomeric pentyl alcohols possible is: (a) two (b) four (c) six (d) eight

(d) eight (GRB Ch 4, Illustration Q13).

2. Find the D.B.E. of C₆H₆.

[6(2) + 6(−1)]/2 + 1 = 4.

3. Find the D.B.E. of C₄H₉N.

[4(2) + 9(−1) + 1(1)]/2 + 1 = 1.

4. How many structurally isomeric alkenes have the formula C₄H₈?

3: but-1-ene, but-2-ene, 2-methylpropene.