In the analysis of the
molecular formula
In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, ...
of
organic molecule
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. The s ...
s, the degree of unsaturation (also known as the index of hydrogen deficiency (IHD), double bond equivalents, or unsaturation index
) is a calculation that determines the total number of rings and
π bonds
In chemistry, pi bonds (π bonds) are covalent bond, covalent chemical chemical bond, bonds, in each of which two lobes of an atomic orbital, orbital on one atom overlap with two lobes of an orbital on another atom, and in which this overlap oc ...
. A formula is used in
organic chemistry
Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.Clayden, J.; ...
to help draw chemical structures. It does not give any information about those components individually—the specific number of rings, or of
double bond
In chemistry, a double bond is a covalent bond between two atoms involving four bonding electrons as opposed to two in a single bond. Double bonds occur most commonly between two carbon atoms, for example in alkenes. Many double bonds exist betw ...
s (one π bond each), or of
triple bond
A triple bond in chemistry is a chemical bond between two atoms involving six bonding electrons instead of the usual two in a covalent single bond. Triple bonds are stronger than the equivalent single bonds or double bonds, with a bond order o ...
s (two π bonds each). The final structure is verified with use of
NMR
Nuclear magnetic resonance (NMR) is a physical phenomenon in which nuclei in a strong constant magnetic field are perturbed by a weak oscillating magnetic field (in the near field) and respond by producing an electromagnetic signal with ...
,
mass spectrometry
Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is use ...
and
IR spectroscopy
Infrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or function ...
, as well as qualitative inspection. It is based on comparing the actual molecular formula to what would be a possible formula if the structure were
saturated
Saturation, saturated, unsaturation or unsaturated may refer to:
Chemistry
* Saturation, a property of organic compounds referring to carbon-carbon bonds
** Saturated and unsaturated compounds
**Degree of unsaturation
** Saturated fat or fatty ac ...
—having no rings and containing only
σ bonds—with all atoms having their standard
valence.
General formula
The formula for degree of unsaturation is:
:
where ''n
i'' is the number of atoms with
valence ''v
i''.
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 1.
Simplified formulae
For certain classes of molecules, the general formula can be simplified or rewritten more clearly. For example:
:
where
:''a'' = number of carbon atoms in the compound
:''b'' = number of hydrogen atoms in the compound
:''c'' = number of nitrogen atoms in the compound
:''f'' = number of halogen atoms in the compound
or
:
where ''C'' = number of carbons, ''H'' = number of hydrogens, ''X'' = number of halogens and ''N'' = number of nitrogens,
[''Organic structural spectroscopy'', chapter 1.] gives an equivalent result.
In either case, oxygen and other
divalent
In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with other atoms when it forms chemical compounds or molecules.
Description
The combining capacity, or affinity of an ...
atoms do not contribute to the degree of unsaturation, as 2 − 2 = 0.
Explanation
For hydrocarbons, the DBE (or IHD) tells us the number of rings and/or extra bonds in a non-saturated structure, which equals to the number of hydrogen pairs that are required to make the structure saturated, simply because joining two elements to form a ring or adding one extra bond in a structure reduces the need for two H's. For non-hydrocarbons, the elements in a pair can include any elements in the lithium family and the fluorine family in the periodic table, not necessary all H's.
A popular form of the formula is as follows:
:
where , , and represent the number of
carbon
Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent
In chemistry, the valence (US spelling) or valency (British spelling) of an element is the measure of its combining capacity with o ...
,
nitrogen
Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...
,
hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
and
halogen
The halogens () are a group in the periodic table consisting of five or six chemically related elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), astatine (At), and tennessine (Ts). In the modern IUPAC nomenclature, this group is ...
atoms, respectively. Each of the terms on the RHS can be explained, respectively, as follows:
*Except the terminal carbons, each of the carbon chained to the structure with a single bond requires a pair of hydrogen atoms attached to it -- that is why the number is in the formula, which actually represents the number of hydrogen pairs requires for that number of carbons in a saturated structure. (This is also true if a carbon 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.)
*Each of the two terminal carbons needs one extra hydrogen – that is why 1 is added to the formula. (A branch’s terminal doesn’t need an extra hydrogen added in the calculation because an hydrogen at where the branch attached to must have been replaced, which is true for a branch terminated with any element.)
*Except the terminal nitrogens, each nitrogen in the chain only requires one H attached to it, which is half a pair of hydrogens -- that is why is in the formula, which gives a value of 1 for every two nitrogens. (This is also true if nitrogen is added into the structure, whether it is inserted to a backbone chain, attached to a terminal to replace an hydrogen, or branched out from a carbon to replace a hydrogen.)
*The represents the number of hydrogen pairs because it gives a value of 1 for every two hydrogen atoms. It is subtracted in the formula to count how many pairs of hydrogen atoms are missing in the unsaturated structure, which tells us the degree of hydrogen deficiency. (No hydrogen pair is missing if , which corresponds to no H-deficiency.)
*The presence of is for a reason similar to .
Adding an oxygen atom in the structure requires no hydrogen added, which is why the number of oxygen atoms does not appears in the formula.
Furthermore, the formula can be generalised to include all elements of
Group I Group 1 may refer to:
* Alkali metal, a chemical element classification for Alkali metal
* Group 1 (racing), a historic (until 1981) classification for Touring car racing, applied to standard touring cars. Comparable to modern FIA Group N
* Group ...
(the hydrogen and lithium family),
Group IV
The carbon group is a periodic table group consisting of carbon (C), silicon (Si), germanium (Ge), tin (Sn), lead (Pb), and flerovium (Fl). It lies within the p-block.
In modern IUPAC notation, it is called group 14. In the field of semicon ...
(the carbon family),
Group V
A pnictogen ( or ; from grc, πνῑ́γω "to choke" and -gen, "generator") is any of the chemical elements in group 15 of the periodic table. Group 15 is also known as the nitrogen group or nitrogen family. Group 15 consists of the el ...
(the nitrogen family) and
Group VII (the fluorine family) of CAS A group in the
periodic table
The periodic table, also known as the periodic table of the (chemical) elements, is a rows and columns arrangement of the chemical elements. It is widely used in chemistry, physics, and other sciences, and is generally seen as an icon of ch ...
as follows:
:
Or simply,
:
See also
*
Iodine number
Iodine is a chemical element with the symbol I and atomic number 53. The heaviest of the stable halogens, it exists as a semi-lustrous, non-metallic solid at standard conditions that melts to form a deep violet liquid at , and boils to a vio ...
- practical measure of number of double bonds in a sample
References
External links
Molecular weight and degree of unsaturation calculator
{{DEFAULTSORT:Degree Of Unsaturation
Organic chemistry