The Index of Hydrogen Deficiency (IHD), is a count of how many molecules of H2 need to be added to a structure in order to obtain the corresponding saturated, acyclic species.
Hence it takes a count of how many rings and care present in the structure, so IHD can also be thought of as (multiple bonds + rings) or (p + r).
The degree of unsaturation (also known as the index of hydrogen deficiency (IHD) or rings plus double bonds[1]) formula is used in organic chemistry to help draw chemical structures. The formula lets the user determine how many rings, double bonds, and triple bonds are present in the compound to be drawn. It does not give the exact number of rings or double or triple bonds, but rather the sum of the number of rings and double bonds plus twice the number of triple bonds. The final structure is verified with use of NMR, mass spectrometry and IR spectroscopy, as well as inspection.
The formula for degree of unsaturation is
DU = 1 + \frac{1}{2} \sum n_i(v_i-2)
where ni is the number of atoms with valence vi.[2]
That is, an atom that has a valence of x contributes a total of x-2 to the degree of unsaturation. The result is then halved and increased by 2.
[edit] Rings plus double bonds formulation
For molecules containing only carbon, hydrogen, monovalent halogens, nitrogen, and oxygen, the formula
R+DB = C - \frac{H}{2} - \frac{X}{2} + \frac{N}{2}+1\,
where C = number of carbons, H = number of hydrogens, X= number of halogens and N = number of nitrogens[3], gives an equivalent result. Oxygen and other divalent atoms do not contribute to the degree of unsaturation, as (2-2) = 0.
The degree of unsaturation is used to calculate the number of rings and pi bonds, where
* Rings count as one degree of unsaturation
* Double bonds count as one degree of unsaturation
* Triple bonds count as two degrees of unsaturation
Once the molecular formula of an unknown compound is known, structural information can be elucidated (for example, what functional groups are probably present, is the compound cyclic or linear...). The first step involves the calculation of the index of hydrogen deficiency, or IHD. The IHD tells us the number of p bonds and/or rings a molecule contains. This information is based on the following general molecular formulas:
alkane CnH2n+2
cycloalkane or alkene CnH2n
alkyne CnH2n-2
Notice that each time a ring or p bond is introduced into a molecule, the number of hydrogens is reduced by two. Therefore, if the molecular formula of an unknown compound has two less hydrogens than a straight chain alkane with the same number of carbon atoms would have, then the IHD is 1 and the unknown compound must have one p bond or one ring. Note that interesting structural information has been gleaned from just knowing the molecular formula of the compound in question.
There are two methods for calculating the index of hydrogen deficiency in a molecule as described below.
A. Determination of IHD - Painful Method
There are several steps to determining the IHD for a molecule.
1. Determine the formula for the saturated, acyclic hydrocarbon containing the same number of carbon atoms as the unknown substance.
2. Correct the formula for the nonhydrocarbon elements present in the unknown. Add one hydrogen atom for each Group V element present, and subtract one hydrogen atom for each Group VII element present.
3. Compare this formula with the molecular formula of the unknown. Determine the number of hydrogens by which the two formulas differ.
4. Divide the difference in the number of hydrogens by two to obtain the index of hydrogen deficiency. This equals the number of p bonds and/or rings in the structural formula of the unknown substance.
Example:
1. Question:
An unknown substance has the molecular formula C2H3Cl3O2. What is the IHD for this unknown?
Answer:
1. The formula for the two-carbon saturated, acyclic hydrocarbon is C2H6.
2. Correction for oxygens in the formula: C2H6O2
Correction for chlorines: C2H3Cl3O2
3. Difference in hydrogens between two formulas: 0
4. Divide by two: 0
Therefore, IHD = 0 and the unknown substance has no p bonds and/or rings.
2. Question:
Nicotine has the molecular formula C10H14N2. What is the IHD for nicotine?
Answer:
1. The formula for the ten-carbon saturated, acyclic hydrocarbon is C10H22.
2. Correction for nitrogens in the formula: C10H24N2
3. Difference in hydrogens between two formulas: 10
4. Divide by two: 5
Therefore, IHD = 5 and the unknown substance has 5 p bonds and/or rings.
B. Determination of IHD - Best Method
A much simpler method for obtaining the IHD of a molecule involves the use of the following equation:
IHD = n + 1 - [(m - t) / 2]
where:
n = # of tetravalent atoms in formula (usually Carbon, Silicon, and Sulfur in the +6 oxidation state)
m = # monovalent atoms in formula (usually hydrogen and the halogens)
t = # trivalent atoms in formula (usually nitrogen and phosphorus)
Example:
1. Question:
An unknown chemical compound has the molecular formula C7H10. What is the IHD for the molecule?
Answer:
IHD = 7 + 1 - [(10 - 0) / 2] = 8 - 5 = 3
Therefore, IHD = 3 and the unknown substance has 3 p bonds and/or rings.
2. Question:
An unknown chemical compound has the molecular formula C8H6ClNO4. What is the IHD for the molecule?
Answer:
IHD = 8 + 1 - [(7 - 1) / 2] = 9 - 3 = 6
Therefore, IHD = 6 and the unknown substance has 6 p bonds and/or rings.
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