Degree of Unsaturation Formula

The degree of unsaturation is defined as the number of numerous bonds or rings in an unknown chemical structure. To put it another way, it determines the total number of rings and links in a compound. It is equal to the number of rings multiplied by the total number of multiple bonds. It aids in the sketching of chemical structures and finding the exact number of rings and/or a double or triple bond.

Formulas

The general formula of the degree of unsaturation for a compound is given by,

D = a + b + 2c

where,

a is the number of rings,

 b is the number of double bonds,

c is the number of triple bonds.

For an organic compound of the form C_nH_m, the degree of unsaturation is given by,

D = n – m/2 + 1

If the molecular formula of a compound is given, then the degree of unsaturation is given by,

D = (2a + b – c – d + 2)/2

where,

a is the number of carbons,

b is the number of nitrogen,

c is the number of hydrogens.

d is the number of halogens such as F, Cl, Br or I.

Examples

• The compound C₇H₈ has 7 carbon atoms and 8 hydrogen atoms. Its degree of saturation is calculated using the formula: D = n – m/2 + 1.

Here, n = 7 and m = 8.

So, using the formula we get

D = 7 – 8/2 + 1

= 7 – 4 + 1

= 4

• The compound C₅H₇Cl has 5 carbon atoms, 7 hydrogen atoms and 1 chlorine atom. Its degree of saturation is calculated using the formula discussed above: D = (2a + b – c – d + 2)/2.

Here, a = 5, b = 0, c = 7 and d = 1.

So, using the formula we get

D = (2(5) + 0 – 7 – 1 + 2)/2

= (10 – 7 – 1 + 2)/2

= 4/2

= 2

Sample Problems

Problem 1. Calculate the degree of unsaturation for the compound C₄H₁₀.

Solution:

The compound C₄H₁₀ has 4 carbon atoms and 10 hydrogen atoms.

Its degree of saturation is calculated using the formula: D = n – m/2 + 1.

Here, n = 4 and m = 10.

So, using the formula we get

D = 4 – 10/2 + 1

= 4 – 5 + 1

= 0

Problem 2. Calculate the degree of unsaturation for the compound C₄H₈.

Solution:

The compound C₄H₈ has 4 carbon atoms and 8 hydrogen atoms.

Its degree of saturation is calculated using the formula: D = n – m/2 + 1.

Here, n = 4 and m = 8.

So, using the formula we get

D = 4 – 8/2 + 1

= 4 – 4 + 1

= 1

Problem 3. Calculate the degree of unsaturation for the compound C₇H₉F.

Solution:

The compound C₇H₉F has 7 carbon atoms, 9 hydrogen atoms and 1 fluorine atom.

Its degree of saturation is calculated using the formula discussed above: D = (2a + b – c – d + 2)/2.

Here, a = 7, b = 0, c = 9 and d = 1.

So, using the formula we get

D = (2(7) + 0 – 9 – 1 + 2)/2

= (14 – 9  – 1 + 2)/2

= 6/2

= 3

Problem 4. Calculate the degree of unsaturation for the compound C₉H₉NO₄.

Solution:

The compound C₉H₉NO₄ has 9 carbon atoms, 9 hydrogen atoms, 1 nitrogen atom and 4 oxygen atoms. 

Its degree of saturation is calculated using the formula discussed above: D = (2a + b – c – d + 2)/2.

Here, a = 9, b = 1, c = 9 and d = 0.

So, using the formula we get

D = (2(9) + 1 – 9 – 0 + 2)/2

= (18 + 1 – 9 + 2)/2

= 12/2

= 6

Problem 5. Calculate the degree of unsaturation for the compound C₁₀H₆N₄.

Solution:

The compound C₁₀H₆N₄ has 10 carbon atoms, 6 hydrogen atoms and 4 nitrogen atoms.

Its degree of saturation is calculated using the formula discussed above: D = (2a + b – c – d + 2)/2.

Here, a = 10, b = 4 , c = 6 and d = 0.

So, using the formula we get

D = (2(10) + 4 – 6 – 0 + 2)/2

= (20 + 4 – 6 + 2)/2

= 20/2

= 10

Problem 6. Calculate the degree of unsaturation for the compound benzene.

Solution:

The molecular formula for benzene is C₆H₆. It has 6 carbon atoms and 6 hydrogen atoms.

Its degree of saturation is calculated using the formula: D = n – m/2 + 1.

Here, n = 6 and m = 6.

So, using the formula we get

D = 6 – 6/2 + 1

= 6 – 3 + 1

= 4

Problem 7. Calculate the degree of unsaturation for the compound propene.

Solution:

The molecular formula for propene is C₃H₆. It has 3 carbon atoms and 6 hydrogen atoms.

Its degree of saturation is calculated using the formula: D = n – m/2 + 1.

Here, n = 3 and m = 6.

So, using the formula we get

D = 3 – 6/2 + 1

= 3 – 3 + 1

= 1