Question

Both \(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}\) and \(\mathrm{C}_{7} \mathrm{H}_{14}\) have the same nominal mass, namely 98 . Show how these compounds can be distinguished by the \(\mathrm{m} / z\) ratio of their molecular ions in highresolution mass spectrometry.

Short answer

Answer: The compounds C6H10O and C7H14 can be distinguished by the m/z ratio of their molecular ions in high-resolution mass spectrometry due to the small difference in their exact molecular masses. The m/z ratio for C6H10O is 98.16 u, and for C7H14, it is 98.21 u. The difference in their m/z ratios is 0.05 u, which can be detected by high-resolution mass spectrometry, allowing them to be distinguished despite having the same nominal mass.

Step-by-step solution

Calculate the molecular masses of the compounds

First, we need to calculate the exact molecular masses of both \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\) and \(\mathrm{C}_7\mathrm{H}_{14}\). To do this, we multiply the number of each element by its atomic mass and then sum it up. Using the atomic masses: C (12.01 u), H (1.01 u), and O (16.00 u): - Exact molecular mass of \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\): \((6 \times 12.01) + (10 \times 1.01) + (1 \times 16.00) = 72.06 + 10.10 + 16.00 = 98.16 \,\text{u}\) - Exact molecular mass of \(\mathrm{C}_7\mathrm{H}_{14}\): \((7 \times 12.01) + (14 \times 1.01) = 84.07 + 14.14 = 98.21 \,\text{u}\)

Explain the concept of the \(\mathrm{m}/z\) ratio in mass spectrometry

The \(\mathrm{m}/z\) ratio in mass spectrometry refers to the mass-to-charge ratio of ions. It's used to identify and differentiate compounds based on their molecular weights/ sizes. In high-resolution mass spectrometry, the \(\mathrm{m}/z\) ratio is measured with higher accuracy and precision, allowing the distinction of compounds with even very small differences in their molecular masses.

Compare the \(\mathrm{m}/z\) ratios of the compounds

Since both compounds have a molecular ion with a single positive charge, their \(\mathrm{m}/z\) ratios are equal to their exact molecular masses. The difference in the \(\mathrm{m}/z\) ratios for the two compounds can be calculated as follows: - \(\Delta\mathrm{m}/z = \mathrm{m}/z(\mathrm{C}_7\mathrm{H}_{14}) - \mathrm{m}/z(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}) = 98.21 - 98.16 = 0.05 \,\text{u}\) As there is a difference of 0.05 u in the \(\mathrm{m}/z\) ratios of the two compounds, high-resolution mass spectrometry can distinguish between \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\) and \(\mathrm{C}_7\mathrm{H}_{14}\) despite their having the same nominal mass.