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What is Degree/Level of Unsaturation (LU) or Double Bond Equivalent (DBE)? How to find and interpret DBE values?

The DBE calculation uses the general molecular formula to find the presence of unsaturation in a compound. The unsaturation is calculated in levels or degrees. 

The lowest degree of unsaturation (DOU) indicates minimum unsaturation, where there is the least loss of hydrogens to form a pie bond or a cyclic ring, like in cycloalkanes.

 

General Molecular Formula

CnH2n+2               CnH2n and CnH2n-2

saturated                     unsaturated

 

The formula for calculating DBE is -

 

DOU/DBE= (2C + 2 + N -H - X)/2

 

The calculation ignores heteroatoms like oxygen and sulfur from the molecular formula; however, it considers halogen and nitrogen. 

 

Steps to calculate DBE

Calculate using the number of Carbon (C), Hydrogen (H), Nitrogen (N), and Halogen (X) from the molecular formula as shown below- 

 

a) For Molecular formula C5H10 = (2C + 2 + N -H - X)/2 = (2 x 5 + 2 - 10)/2 = (12-10)/2 = 1

b) For Molecular formula C2H3OCl = (2C + 2 + N -H - X)/2 = (2 x 2 + 2 - 3 - 1)/2 = (6-4)/2 = 1

c) For Molecular formula C9H10O = (2C + 2 + N -H - X)/2 = (2 x 9 + 2 - 10)/2 = (20-10)/2 = 5

 

The DBE calculation does not give the exact number of the molecule’s double bond, triple bond, or ring present but offers possibilities.

For instance, a few possible combinations of the DBE values and the type of unsaturation that could be present in the compound are- 

 

DBE Value 1 = It could come from one pie bond or from a ring in the structure

 

DBE Value 2 = Possible combinations:

  • two double bonds or 

  • one triple bond or 

  • two rings or 

  • one double bond + one ring   

    Remember that a triple bond has two pie bonds.

     

DBE Value 3 = Possible combinations:

  • three double bonds or 

  • one triple bond + one double bond or 

  • three rings or 

  • two rings + one double bond or 

  • one ring + two double bonds

 

DBE value of 4 = Possible combinations:

  • four pie bonds or

  • four rings or 

  • three pie bonds + one ring (a classic example is benzene) or 

  • two pie bonds + two rings or 

  • one pie bond + three rings or

  • two triple bonds or

  • one triple bond + two double bond or 

  • one triple bond + two rings.

 

 

Example of DBE calculation from a molecule structure

 

 

Therefore, the DBE value provides incomplete information. 

More information is needed to deduce the actual structure of the molecule, which can be obtained from laboratory experiments and analytical techniques like NMR (nuclear magnetic resonance spectroscopy), IR (infrared spectroscopy), and Mass spectroscopy.

 

A few examples wherein the structure of the molecule is predicted from DBE value and laboratory experiments are-

1) An Organic Compound 'A' molecular formula C8H16O2 was hydrolyzed with dilute H2SO4 to give a carboxylic acid 'B' and an alcohol 'C.' Oxidation of 'C' with chromic acid also produced 'B.' On dehydration 'C' gives 1-but-ene. Write the equations for the reaction involved.

2) A and B are two functional isomers of compound C3H6O. On heating with NaOH and I2, Isomer B forms a yellow precipitate of Iodoform whereas Isomer A does not form any precipitate. Write the formulae for A and B.

Practice Problems

a) Calculate the Double Bond Unsaturation from the Molecular Formula (quiz)

b) Predict the Value of Double Bond Unsaturation from the Structure (quiz)

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