Problem 128 - Chemistry An Atoms First Approach

Question

Boron consists of two isotopes, \(^{10} \mathbf{B}\) and \(^{11} \mathbf{B}\). Chlorine also has two isotopes, \(^{35} \mathrm{Cl}\) and \(^{37} \mathrm{Cl}\). Consider the mass spectrum of \(\mathrm{BCl}_{3}\) How many peaks would be present, and what approximate mass would each peak correspond to in the \(\mathrm{BCl}_{3}\) mass spectrum?

Step-by-Step Solution

Answer

The mass spectrum of BCl₃ will have 6 peaks, corresponding to the approximate masses of 115, 116, 117, 118, 119, and 120 amu. This results from the unique combinations of isotopes in each BCl₃ molecular ion: B¹⁰Cl³⁵Cl³⁵Cl³⁵, B¹⁰Cl³⁵Cl³⁵Cl³⁷, B¹⁰Cl³⁵Cl³⁷Cl³⁷, B¹¹Cl³⁵Cl³⁵Cl³⁵, B¹¹Cl³⁵Cl³⁵Cl³⁷, and B¹¹Cl³⁵Cl³⁷Cl³⁷.

Step 1: Isotope combinations

First, we must identify all the possible combinations of isotopes in BCl3. Since we have two isotopes each of Boron and Chlorine, the following combinations can be formed: 1. B¹⁰Cl³⁵Cl³⁵Cl³⁵ 2. B¹⁰Cl³⁵Cl³⁵Cl³⁷ 3. B¹⁰Cl³⁵Cl³⁷Cl³⁷ 4. B¹¹Cl³⁵Cl³⁵Cl³⁵ 5. B¹¹Cl³⁵Cl³⁵Cl³⁷ 6. B¹¹Cl³⁵Cl³⁷Cl³⁷

Step 2: Mass calculation

Now that we have identified the unique combinations of isotopes in BCl3, we can sum the mass numbers in each combination to find the approximate mass of each peak: 1. B¹⁰Cl³⁵Cl³⁵Cl³⁵: \( 10 + 35 + 35 + 35 = 115 \) amu 2. B¹⁰Cl³⁵Cl³⁵Cl³⁷: \( 10 + 35 + 35 + 37 = 117 \) amu 3. B¹⁰Cl³⁵Cl³⁷Cl³⁷: \( 10 + 35 + 37 + 37 = 119 \) amu 4. B¹¹Cl³⁵Cl³⁵Cl³⁵: \( 11 + 35 + 35 + 35 = 116 \) amu 5. B¹¹Cl³⁵Cl³⁵Cl³⁷: \( 11 + 35 + 35 + 37 = 118 \) amu 6. B¹¹Cl³⁵Cl³⁷Cl³⁷: \( 11 + 35 + 37 + 37 = 120 \) amu

Step 3: Counting peaks and summarizing results

Based on the calculations, each unique combination gives us a distinct peak, resulting in a total of 6 peaks. Therefore, the mass spectrum of BCl3 will have 6 peaks with approximate masses of 115, 116, 117, 118, 119, and 120 amu.

Key Concepts

Understanding Isotopes

Isotopes are variations of the same element that have different numbers of neutrons. This means that isotopes have the same number of protons but differ in their atomic masses. For example, boron has two naturally occurring isotopes:

• Boron-10
• Boron-11

These isotopes have atomic masses of 10 and 11 respectively. Similarly, chlorine also exhibits isotopic variation with

• Chlorine-35
• Chlorine-37

Understanding isotopes is crucial when studying mass spectrometry, as it helps identify the different possible masses a compound might have due to these variations.

The Significance of Mass Spectrum

A mass spectrum is a plot that represents the masses of molecules in a sample, typically provided by mass spectrometry analysis. It shows the intensity of each ion plotted against the mass-to-charge ratio. Each peak in a mass spectrum corresponds to a different set of isotopic compositions within the molecules being analyzed.
For a compound like \(\text{BCl}_3\), the peaks indicate the presence of different isotopic combinations. Understanding how to interpret these peaks allows chemists to determine the distribution of isotopic combinations in a compound, offering insight into its molecular composition.

Boron in Mass Spectrometry

Boron is an essential element analyzed via mass spectrometry due to its isotopic nature. With two main isotopes, \(^{10} \text{B}\) and \(^{11} \text{B}\), boron behaves uniquely in spectrometric studies.
During mass spectrometric analysis, each isotope of boron will contribute differently to the mass spectrum of a compound like \(\text{BCl}_3\).
For instance, \(^{10} \text{B}\) and \(^{11} \text{B}\) create different peaks because they have different mass numbers, thus resulting in distinct spectra appearances when combined with other elements, such as chlorine isotopes.

Chlorine's Isotopic Impact

Chlorine, like boron, also exhibits isotopic characteristics critical in mass spectrometry analysis. Both \(^{35} \text{Cl}\) and \(^{37} \text{Cl}\) are naturally occurring isotopes that influence the mass spectrum of compounds such as \(\text{BCl}_3\).
Due to their different atomic masses (35 and 37), these isotopes of chlorine contribute to an array of possible mass combinations, reflecting as different peaks in a mass spectrum examination. By analyzing these peaks, scientists can infer the isotopic distribution of chlorine within the sample. This helps in understanding the structure and composition specifics of the compound in question.