Formula from precise nuclidic mass

FORMULA FROM PRECISE NUCLIDIC MOLECULAR MASS... 

Column (2) lists the mass numbers of the (C, O, N) skeletons. Column (3) lists the number of hydrogen atoms needed to bring the mass number of the molecule to 44. Column (4) lists the maximum number of H atoms consistent with rules for molecular structure as discussed in Chapters 9 and 15. One such rule is that (H, max) is equal to twice the number of carbon atoms plus the number of nitrogen atoms plus 2. Column (5) lists the allowed formulas consistent with the total mass number and with all the assumptions and rules. Note that all skeletons for which the number in column (3) (the mass shortage to be made up by hydrogen) exceeds the number in column (4) (the amount of hydrogen allowable for the skeleton by the rules of valence) are rejected. Column (6) tabulates the nuclidic molecular masses for the allowed formulas, computed from the nuclidic masses in Table 2-1. When the computed molecular masses are compared with the experimental value, 44.025, it is seen that C2OH4 is the only allowable formula that fits the data within the claimed precision therefore this must be the formula of the substance. 

A mass spectrometer is an instrument that separates particles by mass and measures their individual relative masses. If a nuclidic mass of an unknown compound is known with great precision from mass spectrometry, the exact molecular formula can often be deduced directly from this information without resort to a quantitative chemical analysis. 

An alkaloid was extracted from the seed of a plant and purified. The molecule was known to contain I atom of nitrogen, no more than 4 atoms of oxygen, and no other elements besides C and H. The mass-spectrometrically determined nuclidic molecular mass was found to be 297.138. a) How many molecular formulas are consistent with mass number 297 and with the other known facts except the precise molecular weight (b) What is the probable molecular formula ... 

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