Calculating a Degree of Unsaturation

Because of its double bond, an alkene has fewer hydrogens than an alkane with the same number of carbons—C H2n for an alkene versus C, H2i7+2 for an alkane—and is therefore referred to as unsaturated. Ethylene, for example, has the formula C2H4, whereas ethane has the formula C2He- 

In general, each ring or double bond in a molecule corresponds to a loss of two hydrogens from the related alkane formula Cj,H2n+2. Knowing this relationship, it s possible to work backward from a molecular formula to calculate a molecule s degree of unsaturation—the number of rings and/or multiple bonds present in the molecule. 

Let s assume that we want to find the structure of an unknown hydrocarbon. A molecular weight determination on the unknown yields a value of 82 amu, which corresponds to a molecular formula of CeHio- Since the saturated Ce alkane (hexane) has the formula C6H14, the unknown compound has two fewer pairs of hydrogens (H14 Hjo = H4 = 2 H2), and its degree of unsaturation is two. The unknown therefore contains two double bonds, one ring and one double bond, two rings, or one triple bond. There s still a long way to go to establish structure, but the simple calculation has told us a lot about the molecule. 

Similar calculations can be carried out for compounds containing elements other than just carbon and hydrogen. 

Subtract the number of nitrogens from the number of hydrogens. 

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