Double bond equivalence is also known as the degree of unsaturation (DU), index of hydrogen deficiency (IHD), double bond equivalents (DBE), or unsaturation index.
- The general formula for DBE= 1+ 1/2 Σ Ni (Vi-2)
where Ni is the number of atoms with valency Vi.
Suppose, we take a hetero-organic compound having nitrogen, oxygen, halogen, carbon, and hydrogen having N, O, X, C, and H number of atoms. According to the general formula, DBE will be:
DBE= 1+ 1/2 [ C(4–2)+N(3–2)+ X(1–2)+ O(2–2)+H(1–2)]
= 1+C+(N/2-X/2-H/2 +0)= (1+C)+ (N-X-H)/2
Finally, we have derived another formula. I recommend you remember this derived formula instead of the general formula as it will be easier to calculate DBE.
During derivation, we observed one thing in case oxygen becomes zero (2–2) after cancellation. Hence, we can conclude that oxygen and other divalent atoms do not contribute to the degree of unsaturation.
2. DBE= no of Ring + No of pi bond= No of ring+ No of double bond + 2 x (No of triple bond)
3. Till now, I have talked about 2-D compounds in two points above, now let's proceed to the 3-D structure.
Method 1: Simply DU (or DBE) of 3-D structure is equal to the number of bonds required to be broken for a complete opening of that structure. In the case of cubane (example), you can see in the figure that 5 bonds are required to be broken for an open structure.
Method 2: If you find this method hectic and boring, then no need to worry as I have another method for you. Just use a simple formula which is (N-1) whereas N is no of the face of that solid (For eg, DU of Cubane is 5 as the cube has 6 faces (5–1). Not only this, this applies to any kind of 3-D solid.
Method 3: You can also DU of 3-D solid by method 1. Cubane has 8 carbon and 8 hydrogens, so
DBE= (C+1)-H/2= (8+1)-8/2 = 5. All three methods give the same result. At your convenience, you can choose any of these methods.
I am leaving some brain teaser questions related to DBE that can make you think about this deeply.
a) Will carboxylate anion and carboxylic acid have the same DU? If yes/no, justify your answer.
b) The degree of unsaturation (D.U.) of a saturated aliphatic compound is zero while D.U. of the saturated cyclic compound is One. Why does It happen and how it's possible?
c) Evaluate the D.U. of the prism (C6H6) by three methods. This is one easy!!
Thank you so much for reading. If you find our post interesting, knowledgeable, and enjoyable, then share our post with max people and follow us for more conceptual knowledge related to chemistry.