I know the formula for the DOU, but don't really understand why the formula works. Could someone elaborate that to me?
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2$\begingroup$ Simple things first. Is it clear why $2n+2$ works in alkanes? $\endgroup$– Ivan NeretinCommented Mar 28, 2023 at 6:27
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$\begingroup$ @IvanNeretin Yes. $\endgroup$– BlueInfinite1729Commented Mar 28, 2023 at 6:33
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$\begingroup$ The rest is simple. How many hydrogens do you need to remove to turn a single bond into double? $\endgroup$– Ivan NeretinCommented Mar 28, 2023 at 6:39
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$\begingroup$ @IvanNeretin 2 hydrogens. $\endgroup$– BlueInfinite1729Commented Mar 28, 2023 at 10:33
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2$\begingroup$ Well, that's it. What else is left to understand? $\endgroup$– Ivan NeretinCommented Mar 28, 2023 at 11:28
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1 Answer
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The formula for calculating the Degree of Unsaturation (DU) is awkward. The derivation will come later. There is a better way to address this issue by what I shall call the Atom Replacement Method (ARM). The gist of the method is to replace all heteroatoms with C and/or H. This revised formula is compared with the most saturated hydrocarbon bearing the same number of carbon atoms. As an example, consider the molecular formula of the marine dye Tyrian purple: $\ce{C16H8Br2N2O2}$.
Replace halogens with the same number of hydrogens and ignore divalent atoms: $\ce{C16H8Br2N2O2}$ --> $\ce{C16H10N2}$
Replace each nitrogen with one carbon and one hydrogen: $\ce{C16H10N2}$ --> $\ce{C18H12}$ (1)
The most saturated $\ce{C18}$ hydrocarbon is $\ce{C18H38}$ (2)
Subtracting 1 from 2 gives 26.
DU=26/2=13. There are 4 rings and 9 double bonds in Tyrian purple.
The following derivation of the formula is located here. Here is a synopsis.
Let c=#C, h=#H, n=#N and x=#Br, where "x" is the number of halogens.
Ignoring divalent atoms and replacing xX with xH in CcHhNnXx
gives CcHh+xNn
Replacing nN with nC and nH yields Cc+nHh+x+n (1)
The most saturated hydrocarbon is Cc+nH2(c+n)+2 (2)
Subtracting 1 from 2 and simplifying gives 2c+2n+2-h-n-x
Further simplification affords 2c+n+2-h-x
Division by 2 gives
DU = c+1+(n-h-x)/2
Q.E.D.
For a related discussions on ChemSE, see this link and this one.
answered Mar 28, 2023 at 19:51
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$\begingroup$ Aah! Got it after reading your answer and the derivation. Thank you so much! $\endgroup$ Commented Mar 29, 2023 at 4:49
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$\begingroup$ This method is godly! No need to bend the brains. $\endgroup$ Commented Mar 2 at 6:43
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$\begingroup$ @Laxmi Narayan Bhandari: This method may not work when N or S is at an oxidation state greater than -3 and -2, respectively. Compare nitrobenzene with aniline. $\endgroup$ Commented Mar 2 at 20:21
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$\begingroup$ @user55119 so basically, for simple looking compounds right? with the usual covalent bonds, that is $\endgroup$ Commented Mar 3 at 10:42