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 CnHm, 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