Pre-requisite Reading: Identify single bond, double bond, triple bond, saturation, and unsaturation.
The DBE calculation tries to find the presence of unsaturation in a compound from the general molecular formula. The unsaturation is calculated in levels or degrees. The lowest level or degree of unsaturation (DOU) indicates minimum loss of hydrogens to form a pie bond or a cycloalkane ring. The formula for calculating DBE is -
DOU/DBE= (2C + 2 + N -H - X)/2
The formula ignores divalent oxygen and sulfur while doing the calculations. The result will always be a non-negative, nonfractional number.
Steps to calculate DBE- Insert the number of Carbon (C), Hydrogen (H), Nitrogen (N) and Halogen (X) in the formula-
Example: 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
DBE does not give the exact number of the double bond, triple bond or ring present in the molecule but a sum of them is known. Below are the few possible combinations of the DBE levels and the type of unsaturation that could be present in the compound-
DBE Value 1 = one pie bond or a ring
DBE Value 2 = two pie bonds or one triple bond or two rings or one pie bond + one ring (a triple bond has two pie bonds)
DBE Value 3 = three pie bonds or one triple bond + one double bond or three rings or two rings + one double bond or one ring + 2 double bonds
DBE value of 4 = four pie bonds, four rings, three pie bond + one ring (a classic example is benzene), two pie bond + two rings, one pie bond + three rings, two triple bond, one triple bond + two double bond, one triple bond + two rings
DBE values give incomplete information. To deduce the actual structure of the molecule more information is needed in the form of experimental observations after which desired conclusions can be made. Even then, only by using analytical methods such as NMR (nuclear magnetic resonance spectroscopy), IR (Infra-Red spectroscopy) and Mass spectroscopy can the actual structure of the molecule be verified.
Examples wherein the structure of the molecule is predicted from DBE value and experimental observations-
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.