This online Degree of Unsaturation Calculator performs calculations using a formula that relates the atomic composition of an organic molecule to its degree of unsaturation or the number of rings and pi bonds found in that molecule. You can enter the values of any four parameters in the fields of this calculator and find the missing parameter.
Degree of Unsaturation Formula
Determining the structure of an organic compound and thus obtaining information about the structural properties of the compound is an important task in chemistry. Among the existing methods of structure analysis, one of the simplest and most accessible is finding the degree of unsaturation of an organic compound.
By definition, saturated compounds are those that have only single bonds and no rings. Unsaturated compounds are those that have double bonds, triple bonds, and/or rings.
For example, alkanes having single bonds are classified as saturated, while alkenes and alkynes having double and triple bonds, respectively, are classified as unsaturated hydrocarbons.
The degree of unsaturation in its simplest form is expressed as the following formula:
$$DoU = Degree \ of \ Unsaturation = number \ of \ \pi – bonds \ + \ number \ of \ rings.$$
Calculating the degree of unsaturation gives you information about the total number of pi bonds and rings that may be present in a molecule, which can help you determine the molecular structure instead of using expensive spectroscopic methods.
The general formula for the degree of unsaturation can be rewritten in the following form suitable for practical use:
$$DoU = \frac {2C+2+N-H-X}{2},$$
where
• \(C \:\) is the number of carbon atoms,
• \(N \:\) is the number of nitrogen atoms,
• \(H \:\) is the number of hydrogen atoms,
• \(X \:\) is the number of halogens atoms.
The above degree of unsaturation formula has a clear explanation. To understand it, note that the degree of unsaturation is equal to the number of hydrogen pairs that must be added to a chemical structure in order to make it saturated.
As we know, a saturated molecule contains only single bonds and no rings. So, a saturated form of a hydrocarbon will have the maximum number of hydrogen atoms. Each carbon atom in a straight chain (except the terminal carbons) requires a pair of hydrogen atoms attached to it. Two terminal carbons require one extra hydrogen atom each. Thus we come to the term \(2C + 2\) in the formula. The same is also valid in the case of branched (but not cyclic) alkanes.
Except the terminal nitrogen atoms, each nitrogen in the chain only requires one hydrogen atom attached to it. This is also true if a nitrogen is added into the structure, whether it is inserted to a backbone chain, attached to a terminal to replace a hydrogen, or branched out from a carbon to replace a hydrogen. So we have the term \(N\) in our degree of unsaturation formula.
The term \(H\) in the formula is the number of hydrogen atoms that are actually present in the compound. So this term is subtracted from the total number of hydrogen atoms required for the molecule to be saturated.
The reason that the number of halogens atoms \(X\) is subtracted is because it replaces an equal number of hydrogen i.e. one halogen atom for one hydrogen atom.
Oxygen or sulfur in the structure requires no hydrogen added, which is why the number of oxygen and sulfur atoms do not appears in the formula.
Thus, the numerator in the fraction of the formula is the number of hydrogen atoms missing for the compound to be saturated. Dividing this value by two, we get the number of missing pairs of hydrogen atoms.
The degree of unsaturation can be interpreted as follows. The value of \(DoU\) equal to 1 means that the molecule has 1 ring or 1 double bond. For a triple bond, the minimum \(DoU\) value is equal to 2.
The following examples will illustrate the use and interpretation of the degree of unsaturation formula.
Example 1
Find the degree of unsaturation for a compound having the molecular formula C3H4.
Solution.
Let’s enter the input data into our Degree of Unsaturation Calculator. From the molecular formula we obtain the following data: C = 3, H = 4, N = 0, X = 0. As a result of using our calculator, we immediately get: DoU = 2.
Based on the result, we conclude that this compound can have either 1 ring and 1 double bond, 2 rings and 0 double bonds, 0 rings and 2 double bonds, or only 1 triple bond.
Due to the presence of only three carbon atoms, a structure with 2 rings is obviously impossible. A structure with 1 ring and 1 double bond exists. It is cyclopropene which is the simplest cycloalkene. A structure with 1 triple bond also exists. It is propyne. A structure with 2 double bonds exists and is known as propadiene or allene. It is the simplest allene i.e. a compound with two adjacent carbon double bonds, and it exists in equilibrium with methylacetylene (propyne).
Example 2
What is the degree of unsaturation of benzene?
Solution.
The molecular formula for benzene is C6H6. Acting similarly to the previous example, we obtain using our Degree of Unsaturation Calculator: DoU = 4.
In the case of benzene, it is clear that the DoU value of 4 corresponds to one ring and three double bonds.
Example 3
What is the degree of unsaturation of cubane?
Solution.
It is known that cubane (C8H8) is a hydrocarbon with rings corresponding to six faces of the cube. Using our Degree of Unsaturation Calculator we can get DoU = 5. It means that cubane has 5 rings.
But how does this result correspond to the fact that cubane has a 3D form of cube with six faces?
Imagine a cube. Let us first remove all four edges of the cube, which are related to the face of the cube that is frontal with respect to the observer. After that, we remove only one edge of the cube related to the rear face of the cube. As a result, we get a linear structure instead of a cyclic one. Now remember that each vertex of the cube is a carbon atom and each edge is a bond. And instead of each removed edge, we add a hydrogen atom to each carbon atom in the two vertices of the cube, between which there was a removed edge. Thus, we come to the conclusion that by adding 5 pairs of hydrogen atoms to cubane, we get a saturated compound. And this means that the degree of unsaturation of cubane is 5.
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