Index of Hydrogen Deficiency (IHD)

Saturday 12 March 2016

The Index of Hydrogen Deficiency applies to organic compounds and is part of sub-topic 11.3 Spectroscopic identification of organic compounds in the IB programme. Most books and websites that deal with this give a formula which can be applied, for example IHD = ½ x (2x + 2 - y) where x = the number of carbon atoms and y = the number of hydrogen atoms. However in an exam students may well not remember this or may apply it incorrectly, particularly when atoms other than C and H are involved, so it seems much better to me if they can always work it out from first principles which avoids the use of any formula. This is particularly relevant as the specimen papers have the wrong answer to a question that asks for the IHD of C19H20N2O2.

The Index of Hydrogen Deficiency used to be known as the degree of unsaturation. In many ways it would be better if the shortened version was IH2D rather than IHD as it is equal to the number of units of H2 that need to be added to make the organic compound in question fully saturated. To work out the IHD all that needs to be known is the molecular formula of the compound.

For hydrocarbons just calculate the number of units of H2 that need to be added to make it into an alkane, i.e. to give it the formula CnH(2n+2). Thus C6H12 has an IHD of one. Note that all isomers of the same compound have the same IHD so whether C6H12 refers to an alkene (e.g. hex-1-ene or hex-2-ene) or to a cyclic compound (e.g. cyclohexane or methylcyclopentane) makes no difference to the IHD.

If elements other than carbon and hydrogen are present then it depends upon which group in the periodic table they come from. In each case, rather than just remembering what to do without any understanding, it can be useful to work it out simply by substituting the element into a simple compound such as ethane.

Group 17 (F, Cl, Br, I). In chloroethane each carbon atom is surrounded by four single bonds so for any halogen just exchange the halogen atom for a hydrogen atom so that C2H5Cl becomes C2H6 with an IHD or zero and C2H2Br2 becomes C2H4 with an IHD of 1.

Group 16 (O, S). In ethanol the two carbon atoms still have four single bonds so the insertion of an oxygen atom into ethane to make either ethanol or methoxymethane has no effect on the IHD so oxygen atoms can simply be ignored when calculating the IHD. For example C2H6O becomes C2H6 with an IHD of zero and C3H6O becomes C3H6 with an IHD of 1.

Group 15 (N, P). Adding amine groups to a compound will not alter the IHD . Consider dimethylamine, (CH3)2NH, which is saturated. To calculate the IHD either remove all the nitrogen atoms and deduct one hydrogen atom for each nitrogen removed so that (CH3)2NH becomes C2H6 with an IHD of zero, or change the nitrogen atoms into carbon atoms and add one hydrogen atom for each nitrogen atom changed so that (CH3)2NH becomes C3H8 which of course also has an IHD of zero.

Now to apply the theory to two real examples.

1. A topical example is mildronate, otherwise known as meldonium, which the tennis player Maria Sharapova has admitted to using.


Maria Sharapova (Image from Pavel Golovkin/Associated Press) and Mildronate manufactured by Grindex

Mildronate has the molecular formula C6H14N2O2. You should be able to calculate that the IHD is 1. This single degree of unsaturation is due to the carbonyl C=O bond in the molecule.

2. Now for the IB. Look at question Qu. 4(b)(iii) on the SL Paper 2  specimen paper (which is the same as Question 7(b)(iii) on the HL Paper 2). The molecular formula is C19H20N2O2. Removing the oxygen atoms gives C19H20N2 and then removing the two N atoms and also deducting two hydrogen atoms gives C19H18. The saturated hydrocarbon containing 19 carbon atoms has 40 hydrogen atoms (C19H40) so we need to add 11 units of H2 making the IHD 11. (Note that if you change the N atoms into C atoms and add one hydrogen for each N atom changed you get C21H22 which also give an IHD of 11). 11 is the correct answer although currently the IB markscheme uses an unexplained formula wrongly to give 9.


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