Degree of Unsaturation Formula

What is the Degree of Unsaturation?

There are multiple methods for determining the structure of an organic compound and for knowing about the structural properties of the compound. Determining the degree of saturation is one way to identify the structure of the organic compound. It helps you also to double check the number of 𝜋 bonds and/or presence of any cyclic rings. Typically, sturatino is considered as the point when a solution can dissolve no more of the substance which is added to it. In terms of degree of unsaturation, as mentioned above, it gives information about the bonding of molecules i.e. it tells you whether a molecule has a single bond, double bond, triple bond or a cyclic ring structure. 


Formula of Degree of Unsaturation

From this definition, the degree of unsaturation, organic compounds can be classified into two types: saturated and unsaturated. Saturated compounds are the ones having a single bond. This single bond in a saturated compound should not be part of any cyclic or ring structure. On the other hand, an unsaturated compound is the one that has a double bond(s), triple bond(s), and/or ring(s). The alkanes having single bonds are classified as saturated whereas the alkenes and alkynes having double and triple bonds respectively are classified as unsaturated hydrocarbons. 

To know how to find the degree of unsaturation of a given compound a formula is thus given which includes these characteristics as part of the formula. Hence, the degree of unsaturation formula helps you in determining whether a compound is saturated or unsaturated. 

Calculating the degree of unsaturation gives you information about the total number of pi bonds and rings that can be present within a molecule which can help you in determining the molecular structure instead of using expensive spectroscopic techniques. The degree of unsaturation formula is given below in simplest terms as:

DU = Degree of Unsaturation = number of pi bonds + number of rings


How to Find Degree of Unsaturation

The degree of unsaturation formula takes the number of carbon atoms (C), number of nitrogen atoms (N), number of halogen atoms (X), and the number of hydrogen atoms (H) as input values. These values can be easily obtained from the molecular formula of the compound. For how to calculate the degree of unsaturation, the formula is given as:

DU = ((2C + 2)+ N - X - H)/2

The input values are an indication of the number of hydrogen atoms that should be present for the given compound to be classified as saturated. A saturated molecule contains only single bonds and no rings. In other words, a saturated form of a hydrocarbon will have the maximum number of hydrogen atoms in an acyclic alkane form. Hence, the 2C + 2, in the formula is the total number of hydrogen atoms that should be bound to the saturated carbon atoms and H is the number of hydrogen atoms that are actually present in the compound. The reason that the value of halogen atoms (X) is subtracted is because it replaces an equal number of hydrogen i.e. one halogen atom for one hydrogen atom. Apart from that, nitrogen brings in more hydrogen atoms and because of that the value is added. Oxygen and Sulphur do not seem to have any effect in changing the saturation status of a compound. 

The information obtained from the degree of unsaturation can be characterized as: 1 value of DU gives 1 ring or 1 double bond. For a triple bond, 2 is the minimum DU value. 

The following two simple examples will illustrate the use and understanding of how to find the degree of unsaturation and the degree of unsaturation formula.

Example 1: For a compound having the molecular formula C3H4, find the degree of unsaturation. 

Solution: The given formula is C3H4. Since there is no nitrogen or halogen the degree of unsaturation formula is reduced to:

     DU = (2C + 2 - H)/2

For a compound with the given molecular formula the elongated saturated form will have a total of 2C + 2 hydrogen atoms. Hence, this number is 8.

The difference between the expected number of hydrogens and the observed number of hydrogen atoms = 8 - 4. Thus, the molecule needs 4 more hydrogen atoms to be saturated. From the degree of unsaturation formula for this compound, the value obtained as degree of unsaturation is: 

     DU = 4/2 = 2.

Thus, the given compound can either have 1 ring and 1 double bond; 2 rings and 0 double bonds; 0 rings and 2 double bonds; or only 1 triple bond. 

     

Example 2: What is the Degree of Unsaturation of Benzene?

Solution: The molecular formula for benzene is C6H6. From the above formula, the formula for degree of unsaturation is reduced to:

    DU = (2C + 2 - H)/2

    DU = (2*6 + 2 - 6)/2

    DU = 8/2 = 4.      

Now, 1 value of DU can give either one ring or one double bond. In the case of benzene, the value 4 gives one ring and three double bonds. 

FAQs (Frequently Asked Questions)

1. How to Find the Degree of Unsaturation?

Ans: The degree of unsaturation is equal to 2 or half the total number of hydrogen that  a molecule needs to be classified as saturated. Hence, the degree of unsaturation formula divides the value by 2. The formula includes the number of hydrogen atoms added because of addition of nitrogen and subtracts the number of halogen atoms because they displace an equal number of hydrogen atoms. 

2. What is Meant By Degree of Unsaturation?

Ans: While analysing the molecular formula, the degree of unsaturation helps to gain some information regarding the possible structure of the compound. The degree of unsaturation provides information about the total number of rings and pi bonds in a given molecule. 

3. What is the Degree of Unsaturation of Benzene?

Ans: The molecular formula of benzene is C6H6. Thus, it has six carbon atoms and it needs 8 more hydrogen atoms in order to be classified as saturated. Therefore, the degree of unsaturation of benzene is 4, which gives one ring and three double bonds.