Molecular Formula Determination
(Compiled from Dr. N. Glagovich’s (CCSU) work.)
The molecular ion gives the nominal molecular weight of the substance. To
determine the chemical formula (or a series of possible chemical formulas), one
can use the Rule of 13.
The Rule of Thirteen is so named because, to generate a base formula
(containing only carbon and hydrogen); the molar mass of the substance is
divided by 13. The numerator from division gives the number of carbon atoms in
the base formula. The remainder, when added to the numerator, gives the
number of hydrogens in the base formula.
MW / 13 = n + r / 13
The base formula becomes CnHn+r that is a combination of carbons and
hydrogens having the desired molecular weight, MW. One can then calculate the
Index of Hydrogen Deficiency (IHD), which we have called degree of
unsaturation (DU), for this formula using 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)
Special attention should be paid to the IHD (DU) calculation, because impossible
IHDs (negative or fractional) can lead to the rejection of one or more possible
chemical formulas. Of course, the compound may contain other elements
besides carbon and hydrogen. To account for other elements present, the
appropriate number of carbons and hydrogens that equals the molar mass of the
desired element is subtracted from the base formula to account for the added
element(s). Table 1 shows the carbon/hydrogen equivalents for some of the
more common elements.
Table 1. Carbon/Hydrogen equivalents for some of the more
common elements found in organic compounds.
Add Element
Subtract Element
IHD
C
H12
7
H12
C
-7
O
CH4
1
O2
C2H8
2
O3
C3H12
3
N
CH2
½
N2
C2H4
1
S
C2H8
2
35Cl
C2H11
3
79Br
C6H7
-3
79Br
C5H19
4
F
CH7
2
Si
C2H4
1
P
C2H7
2
I
C9H19
0
I
C10H7
7
As an example, benzamide has a mass (from mass spectrum) of 121, which is
odd. Applying the rule of thirteen results in a base formula of C9H13 (IHD = 3.5).
Since this formula has an impossible IHD (degree of unsaturation cannot be a
fraction) and the M+ is shown to have an odd mass, it is reasonable to add
nitrogen to the formula (subtracting CH2) resulting in a new formula of C8H11N
(IHD = 4). Other possible formulas (involving nitrogen and oxygen are C 6H7N3
(IHD = 5) and C7H7NO (IHD = 5). Other spectral evidence (for instance IR and
NMR data) can be very useful in identifying specific elements to include in this
analysis. Further analysis of the mass spectrum, the accurate mass, or isotope
ratio data is required to settle upon the correct formula. Benzamide has formula
C6H5CONH2) and structure:
O
NH2