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 \(m / z\) ratio of their molecular ions in highresolution mass spectrometry.

Short answer

Answer: The molecular compounds C6H10O and C7H14 can be distinguished using their high-resolution mass spectrometry m/z ratios by comparing their exact masses. For C6H10O, the high-resolution m/z ratio is approximately 98.1434, while for C7H14, the high-resolution m/z ratio is approximately 98.1868. Since these two m/z ratios are different, the compounds can be distinguished.

Step-by-step solution

Calculate the exact mass of each compound

In high-resolution mass spectrometry, the molecular masses are measured with higher accuracy (more decimal places). So, to compute exact masses, we'll need to use accurate atomic masses for carbon (C), hydrogen (H), and oxygen (O). Let's calculate the exact mass for each compound: For C6H10O, we use 6 atoms of carbon, 10 atoms of hydrogen, and 1 atom of oxygen: Exact mass = (6 * 12.011) + (10 * 1.00784) + (15.999) Exact mass = 72.066 + 10.0784 + 15.999 Exact mass ≈ 98.1434 For C7H14, we use 7 atoms of carbon and 14 atoms of hydrogen: Exact mass = (7 * 12.011) + (14 * 1.00784) Exact mass = 84.077 + 14.10976 Exact mass ≈ 98.1868

Compare the mass-to-charge (m/z) ratios

Now that we have the exact mass for each compound, we can compare their m/z ratios in high-resolution mass spectrometry to distinguish between them. Since their charge will be the same and not affect the comparison, we just consider their masses: For C6H10O, the high-resolution m/z ratio is approximately 98.1434. For C7H14, the high-resolution m/z ratio is approximately 98.1868. These two m/z ratios are different, and thus, these compounds can be distinguished by their m/z ratios in high-resolution mass spectrometry.

Key concepts

Exact Mass Calculation

Understanding exact mass calculation is crucial when working with high-resolution mass spectrometry. Unlike nominal mass—which rounds atomic masses to the nearest whole number—exact mass uses precise atomic masses for each element.
This allows us to achieve greater accuracy when identifying molecular formulas.

For example, when calculating the exact mass of a compound like \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\), the exact atomic masses of carbon (\(12.011\)), hydrogen (\(1.00784\)), and oxygen (\(15.999\)) are used.
This provides a more precise measurement than nominal mass. Here's how it works:

• Multiply the number of each type of atom by its exact atomic mass.
• Sum these values to get the compound's exact mass.

For \(\mathrm{C}_7\mathrm{H}_{14}\), the process is similar, using the same exact atomic mass values. In both cases, this detailed method helps in distinguishing compounds that might otherwise appear identical with nominal mass calculations.

Mass-to-Charge Ratio (m/z)

The mass-to-charge ratio, denoted as \(m/z\), is essential for analyzing compounds in mass spectrometry.
It describes how the mass of an ion relates to its charge, typically simplifying to just mass because the charge \(z\) is usually one. This simplification allows us to focus primarily on the mass differences between molecular ions.

In high-resolution mass spectrometry, these differences can become apparent even when compounds have the same nominal mass. For our example compounds \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\) and \(\mathrm{C}_7\mathrm{H}_{14}\), their \(m/z\) ratios are determined by their exact masses:

• For \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\), the \(m/z\) is about \(98.1434\).
• For \(\mathrm{C}_7\mathrm{H}_{14}\), the \(m/z\) is about \(98.1868\).

Despite being close, these values are distinct enough to differentiate the compounds in high-resolution mass spectrometry.
The reflection of exact mass in the \(m/z\) ratio is key to analyzing and identifying substances in a precise manner.

Molecular Ion Differentiation

Differentiating molecular ions in mass spectrometry is often challenging, especially with compounds that share a nominal mass.
This is where high-resolution mass spectrometry excels, offering precise measurements that reveal subtle differences between ions.

Understanding how molecular ions vary is pivotal. For instance, \(\mathrm{C}_6\mathrm{H}_{10}\mathrm{O}\) and \(\mathrm{C}_7\mathrm{H}_{14}\) share a nominal mass of \(98\), but their actual masses differ due to the unique elemental composition:

• Their molecular ion peaks show different \(m/z\) ratios, which helps in distinguishing them.

These differences assist scientists in identifying and confirming the presence of specific compounds, even with minute variances.
This technique enhances the accuracy of substance identification in complex mixtures, making it a vital tool in chemical analysis.