# Degree of Unsaturation Formula

A compound’s molecular formula is a derivative of its molecular weight (which was determined independently) and elemental analysis. The notion of the degree of unsaturation of an organic compound is derived simply from the tetravalency of carbon. Any compound whose chemical formula has two hydrogens less than the maximum number possible (2n+2) must have one ring or one double bond. The Degree of Unsaturation is the rings plus the total number of multiple bonds. The molecular formula is abridged to CnHm and the Degree of Unsaturation Formula is given by

$\dpi{120}&space;\large&space;Degree&space;of&space;Unsaturation&space;=&space;n-\frac{m}{2}&space;+&space;1$

The degree of unsaturation designates the number of π bonds or rings that the compound is comprised of. For hydrocarbons that are compounds comprising of only hydrogen and carbon, the degree of unsaturation formula is

$Degree&space;of&space;Unsaturation=\frac{Number&space;of&space;H&space;in&space;saturated&space;hydrocarbon&space;-&space;number&space;of&space;H&space;in&space;C_{n}H_{2n}+2}{2}$

Degree of unsaturation = Total number of rings + Total number of double bonds + (2 x total number of triple bonds)

The formula for degree of unsaturation is articulated like this if the molecular formula is given,

$Degree&space;of&space;Unsaturation=\frac{2C+2+N-X-H}{2}$C is the number of carbons

N is the number of nitrogens

X is the number of halogens (F, Cl, Br, I)

H is the number of hydrogens

Solved Examples

Problem: Calculate the degree of unsaturation for benzene.

The molecular formula for benzene is C6H6Thus,C=6, N=0,X=0, and H=6

Substituting the values in the formula

$Degree&space;of&space;Unsaturation=\frac{2C+2+N-X-H}{2}$

Degree of Unsaturation =2(6)+2-6/2

= 4

Therefore, Degree of Unsaturation = 4