Determination of a Molecular Formula

TABLE 1.3 Relative Isotope Abundances of Common Elements. 

Elements Isotope Abundance Isotope Abundance Isotope Abundance 

If these isotope peaks are intense enough to be measured accurately, the above calculations may be useful in determining the molecular formula.  

If sulfur or silicon is present, the M + 2 will be more intense. In the case of a single sulfur atom, 34S contributes approximately 4.40% to the M + 2 peak for a single silicon in the molecule, 30Si contributes about 3.35% to the M + 2 peak (see Section 1.6.15).The effect of several bromine and chlorine atoms is described in Section 1.6.16. Note the appearance of additional isotope peaks in the case of multiple bromine and chlorine atoms. Obviously the mass spectrum should be routinely scanned for the relative intensities of the M + 2, M + 4, and higher isotope peaks, and the relative intensities should be carefully measured. Since F, P, and I are monoisotopic, they can be difficult to spot. 

For most of the Problems in this text, the unit-resolution molecular ion, used in conjunction with IR and NMR, will suffice for determining the molecular formula by browsing in Appendix A. For several more difficult Problems, the high-resolution formula masses—for use with Appendix A (see Section 1.5.2.2)—have been supplied. 

Element Crams Moles Mole Ratio Formula Empirical Ratio Formula 

Multiplying the mole ratio numbers by 2 yields 1.00 X 2 whole numbers without a common divisor. = 2 and 1.5 X 2 = 3, both 

Usually a mole ratio that is not a ratio of whole numbers can be made into one by multiplying all ratio numbers by the same integer. In Example 7.15, the multiplier was 2. If 2 doesn t work, try 3. If that fails, try 4, and, if necessary, 5. Remember, however, that your final ratio of whole numbers must not have a common divisor. 

The procedure is the same for compounds containing more than two elements. 

Fe Oj is a source of iron in an ore called hematite. The compound is used to polish glass, precious metals, and diamonds. Hence another of its names is jeweler s rouge. 

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An empirical formula shows the simplest ratio of atoms in a molecule (or an ionic compound). For a molecular substance, the empirical formula only tells you the ratio of atoms, so it may not be very helpful at identifying the nature of a substance. For example, take any of the group of hydrocarbons known as the alkenes. All of the different compounds have a l-to-2 ratio of carbon to hydrogen. Ethene is C2H4, propene is C H, and butene is C,Hj. If you reduce all of the subscripts, they each come out to CH2. Knowing the empirical formula helps to tell you that this substance is an alkene, but it doesn t tell you which one. How can you determine what a compound is from the empirical formula The molecular weight will solve your problem. If you know the empirical formula and the molecular weight, you can determine the molecular formula for a compound. The first type of calculation we will look at is the determination of the empirical formula. The second type is the determination of a molecular formula. 

The example of ethane can illustrate the determination of a molecular formula from a comparison of the intensities of mass spectral peaks of the molecular ion and the ions bearing heavier isotopes. Ethane, C2H6, has a molecular weight of 30 when it contains the most common isotopes of carbon and hydrogen. Its molecular ion peak should appear at a position in the spectrum corresponding to a mass of 30. Occasionally, however, a sample of ethane yields a molecule in which one of the carbon atoms is a heavy isotope of carbon, This molecule would appear in the mass spectrum at a mass of 31. The relative abundance of in nature is 1.08% of the atoms. In the tremendous number of molecules in a sample of ethane gas, either of the carbon atoms of ethane will turn out to be a atom 1.08% of the time. Since there are two carbon atoms in ethane, a molecule of mass 31 will turn up (2 x 1.08) or 2.16% of the time. Thus, we would expect to observe a peak of mass 31 with an intensity of 2.16% of the molecular ion peak intensity. This mass 31 peak is called the M+ peak, since its mass is one unit higher than that of the molecular ion. 

The determination of a molecular formula by an accurate measurement of a molecular weight is possible because the actual masses of atomic particles (nuclides) are not integers (see Table 9.5). Consider, as examples, the three molecules O2, N2H4, and CH3OH. 

Figures 8.43 and 8.45 show scatter plots of the number of candidates versus the molecular mass. Let us consider, for example, the precisions of d = 0 and 2 decimal places. The exponential increase of candidate formulas with increasing mass is clearly visible, as is the lower candidate count for d = 2 compared with 0 decimal places. In real life it will not be possible to restrict oneself to the elements from 4, but it will not always be necessary to consider all molecular formulas containing all the elements of 11. Rather, the atom count of each element can be restricted using additional knowledge. Then, the necessary measurement precision for unambiguous determination of a molecular formula from a molecular mass using additional restrictions can be estimated essentially as demonstrated above.

Rationalization of known compounds provides a level of usefulness that justifies the rule. But the rule also permits observed molecular stoichiometries of newly synthesized compounds to be translated into acluster shape. For example, [Al Bu ]2-has eve = 50 or sep =13 consistent with n = 12 and a deltahedral structure. The compound has been synthesized and an X-ray diffraction study reveals an icosahe-dral shape. The ability to suggest reasonable structures based on knowledge of a molecular formula generated by a technique like mass spectrometry accelerated the development of cluster chemistry simply because rapid spectroscopic methods can be more productively applied. Although efficient X-ray crystallographic structure determination reduces its importance for compounds that can be isolated in pure crystalline forms, transient intermediates detected in a reaction mixture can now be given reasonable structures. 

Alkynes and dienes respond to characterization tests in the same way as alkenes they decolorize bromine in carbon tetrachloride without evolution of hydrogen bromide, and they decolorize cold, neutral, dilute permanganate they are not oxidized by chromic anhydride. They are, however, more unsaturated than alkenes. This property can be detected by determination of their molecular formulas (CnH2n-2) and by a quantitative hydrogenation (two moles of hydrogen are taken up per mole of hydrocarbon). 

Elemental Analysis The carbon, hydrogen, and nitrogen contents of reference standards may be determined by combustion analysis. Combustion analysis thus provides an orthogonal determination of the molecular formula and the purity of the reference standard. Poor agreement between the theoretical and experimental elemental compositions is generally an indication of an impure substance or a discrepancy between the theoretical and actual molecular formulas. Elemental analysis may also identify the presence of solvates and inorganic contaminants. Elemental analysis is typically performed in specialized laboratories under blinded conditions. 

As an aside, the determination of the molecular formula does not end the problem for a chemist. As is sometimes the case, the formula GeHi4 is appropriate for several distinctly different molecules. Two of the five molecules having this formula are shown here ... 

This only expresses the relative number of atoms of each element in a compound. Nevertheless, it is the first step in the experimental determination of the molecular formula of a compound from its percentage composition. 

In a modem, state-of-the-art mass spectrometry laboratory, the determination of the molecular formula of an unknown substance is done using exact masses. The spectroscopist must be careful, however, as the method cannot be used if the molecular ion peak is very weak or absent. 

We noted earlier that mass spectrometry had not been used to any extent in speciation studies of organic phosphorus in natural environments. Here we define phosphorus speciation as the determination of actual molecular formulas and structures of molecules containing phosphorus, and not the more commonly accepted, broad classes of phosphorus such as filterable reactive phosphorus, total filterable phosphorus, filterable organic phosphorus, etc. While a few studies have focused on particular classes of organic phosphorus, such as the inositol phosphates, we are not aware of any attempt to broadly speciate... 

Mass spectra have long been used (a) as fingerprints for organic compounds (previous section) and (b) for the determination of accurate molecular weights (well within one mass unit). More recently, they have been exploited (c) for the determination of exact molecular formulas. The emphasis in this section is on applications (b) and (c). 

In some cases, the identification of chemical agents with GC-MS may be difficult. In those cases, analysis with GC-AED (atomic emission detector) may be of assistance. This device makes elemental analysis of chemical agents separated in the chromatographic column possible. The quantitative assay of elements in a given chemical compound allows determination of its molecular formula. Analysis of the same samples with GC-MS and GC-AED allows much more certain identification of chemical agents than the utilization of any of those instruments separately. 

The quantiles assist us in determining the acceptance (or rejection) of a molecular formula candidate, given a prescribed probability. If all molecular formulas p of correct mass m = trip are generated for our data set with a prescribed probability and all p whose match value is MV(7, P) > qi p are selected, then the correct molecular formula is contained in our selection with probability p. 

The next step in calculation of match values is the determination of fragment molecular formulas. Table 8.8 Usts all such molecular formulas where there is a peak in the spectrum corresponding to the mass of highest intensity, f(m ) > 0. The solution Xj of the optimization problem is given in the last column. We obtain a match value... 

What do the calculations above tell us about the relationship between the number of candidates for the molecular formula and the precision of the mass spectrometer If the mass resolution, or better the measurement error for the exact mass of a molecular formula of mass mj, is smaller than half the distance to the neighboring mass of other candidates of masses mj i and m,4i, then the molecular formula can be determined... 

The work presented in the previous sections demonstrates clearly that HR-MS provides much more information for the determination of the molecular formula when compared with LR-MS data. Exact masses alone already assist in the limitation of candidate molecular formulas, but the combination with MS/MS data (where available) clearly adds a significant improvement in eliminating false candidate formulas fiom consideration, for example through the use of combined match value. 

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