Show how the compounds with the molecular formulas \(\mathrm{C}_{6} \mathrm{H}_{9} \mathrm{~N}\) and \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{NO}\) can be distinguished by the \(m / z\) ratio of their molecular ions in high- resolution mass spectrometry.

Understanding the molecular weight of a compound is critical for numerous scientific studies, including high-resolution mass spectrometry. To calculate the molecular weight, each atom's atomic weight is multiplied by the number of times it appears in the molecular formula and then summed up. For instance, taking the compound with the molecular formula \(\mathrm{C}_{6}\mathrm{H}_{9}\mathrm{N}\), we multiply the atomic weights of Carbon (C), Hydrogen (H), and Nitrogen (N) by their respective counts in the formula.

To find the total molecular weight, simply add these individual weights together:\[\text{Molecular weight of } \mathrm{C}_{6}\mathrm{H}_{9}\mathrm{N} = (6 \times 12.011) + (9 \times 1.008) + (14.007)\].

The precise values of the atomic weights used in these calculations often come from standards set by IUPAC, ensuring consistency across different analyses and industries. It is the sum of these accurate measurements that allows us to confidently compare the molecular weights of different compounds and proceed to further analysis in mass spectrometry.

In mass spectrometry, the \(m/z\) ratio is a crucial metric used for identifying and quantifying molecules. It represents the ratio of the mass of an ion (\(m\)) to its charge number (\(z\)). High-resolution mass spectrometry, in particular, can distinguish between compounds that have very similar molecular weights by measuring their \(m/z\) ratios with great precision.

Most molecules in organic mass spectrometry have a charge of +1, which means their \(m/z\) ratio is simply equivalent to their molecular weight. Taking high-resolution mass spectrometry into account, it’s important to understand that even the tiniest difference in molecular weight can be detected due to their highly accurate mass analyzers. This precision allows researchers to tell apart compounds—like the example compounds \(\mathrm{C}_{6}\mathrm{H}_{9}\mathrm{N}\) and \(\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NO}\)—based on slight variances in mass.

Molecular formula analysis expands upon molecular weight calculation by providing not just the weight but also the composition of the molecule in terms of the types and numbers of atoms present. It is the detailed breakdown of a molecule that can be crucial in characterizing a compound.

In the context of mass spectrometry, understanding the exact molecular formula of a substance allows scientists to deduce structural information. This is particularly valuable when assessing fragmentation patterns in mass spectra. When compounds like \(\mathrm{C}_{6}\mathrm{H}_{9}\mathrm{N}\) and \(\mathrm{C}_{5}\mathrm{H}_{5}\mathrm{NO}\) give close molecular weights, their true differentiation comes only after thorough molecular formula analysis. Such analysis often involves comparing theoretical isotopic patterns with the observed spectrum – a step that is vital for accurate compound identification in advanced applications including pharmacology, environmental analysis, and biochemistry.