Question

The mass spectrum of bromine \(\left(\mathrm{Br}_{2}\right)\) consists of three peaks with the following characteristics: $$ \begin{array}{|cc|} \hline \text { Mass (amu) } & \text { Relative Size } \\ \hline 157.84 & 0.2534 \\ 159.84 & 0.5000 \\ 161.84 & 0.2466 \\ \hline \end{array} $$ How do you interpret these data?

Short answer

In conclusion, the mass spectrum data of bromine Br₂ shows that Br₂ molecules are made up of a mixture of stable isotopes \(\mathrm{^{79}Br}\) and \(\mathrm{^{81}Br}\) with relative abundances of 25.34%, 50.00%, and 24.66% for the molecular combinations \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\), \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\), and \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\), respectively.

Step-by-step solution

Identify the isotopes of bromine

In nature, bromine exists as two stable isotopes: \(\mathrm{^{79}Br}\) (mass number 79) and \(\mathrm{^{81}Br}\) (mass number 81). Since bromine naturally pairs up to form Br₂, the peaks in the mass spectrum are representing the combinations of these isotopes.

Find the molecular combinations for each peak

For a Br₂ molecule, there can be the following combinations of the two stable isotopes: 1. \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\): Two \(\mathrm{^{79}Br}\) isotopes combined. 2. \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\): One \(\mathrm{^{79}Br}\) and one \(\mathrm{^{81}Br}\) isotope combined. 3. \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\): Two \(\mathrm{^{81}Br}\) isotopes combined.

Calculate the mass of each combination

Next, determine the molecular mass of each combination: 1. \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\): \( 2 \times 79 = 158 \) 2. \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\): \( 79 + 81 = 160 \) 3. \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\): \( 2 \times 81 = 162 \)

Compare calculated masses to the given mass spectrum

Compare the calculated masses of each combination to the masses given in the mass spectrum: 1. Peak at 157.84 amu: Molecular combination of \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\) which is around 158 amu. 2. Peak at 159.84 amu: Molecular combination of \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\) which is around 160 amu. 3. Peak at 161.84 amu: Molecular combination of \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\) which is around 162 amu.

Interpret the relative size

The relative sizes of each peak represent the relative abundances of the isotopes in the Br₂ molecule: 1. \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\): Relative size 0.2534 indicates that 25.34% of Br₂ molecules are composed of two \(\mathrm{^{79}Br}\) isotopes. 2. \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\): Relative size 0.5000 indicates that 50.00% of Br₂ molecules are composed of one \(\mathrm{^{79}Br}\) and one \(\mathrm{^{81}Br}\) isotope. 3. \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\): Relative size 0.2466 indicates that 24.66% of Br₂ molecules are composed of two \(\mathrm{^{81}Br}\) isotopes. In conclusion, the mass spectrum data of bromine Br₂ shows that Br₂ molecules are made up of a mixture of stable isotopes \(\mathrm{^{79}Br}\) and \(\mathrm{^{81}Br}\) with relative abundances of 25.34%, 50.00%, and 24.66% for the molecular combinations \(\mathrm{^{79}Br}\mathrm{-}^{79}Br\), \(\mathrm{^{79}Br}\mathrm{-}^{81}Br\)/ \(\mathrm{^{81}Br}\mathrm{-}^{79}Br\), and \(\mathrm{^{81}Br}\mathrm{-}^{81}Br\), respectively.

Key concepts

Isotopic Abundance

Isotopic abundance is a measure of how much of each isotope is present in a sample. In chemistry, specifically in mass spectrometry, understanding isotopic abundance helps in determining the distribution of isotopes. The mass spectrum gives peaks that correlate with specific isotopic combinations, showing their relative presence within a molecule.

In the case of bromine, there are two naturally occurring isotopes:

• the lighter \text{\(^{79}\text{Br}\)} isotope and,
• the heavier \text{\(^{81}\text{Br}\)} isotope.

These isotopes pair up in different combinations to form bromine molecules (Br₂), and each combination is represented as a peak in the mass spectrum. The relative size of each peak indicates the percentage of that isotopic combination in the sample. For example, a relative peak size of 0.5000 tells us that this isotopic combination is predominant, making up 50% of the sample.

Understanding isotopic abundance allows chemists to elucidate the natural composition of molecules, quantify elements in mixtures, and perform calculations needed in research and various applications.

Bromine Isotopes

Bromine is an element that exists in the form of stable isotopes. In fact, there are two main stable isotopes that are crucial in understanding its chemical properties:

• \(^{79}Br\), which has a mass number of 79,
• and \(^{81}Br\), with a mass number of 81.

When investigating molecules like \(Br_2\), these isotopes combine to form molecules with specific masses. It's essential to understand that these isotopes do not change in number or properties during chemical reactions, making them stable points of reference.

In a sample of bromine, different pairs of these isotopes come together to form different molecular combinations, and they exhibit specific traits in mass spectrometry. You can find peaks in mass spectra corresponding to the combinations like \(^{79}Br-^{79}Br\), \(^{79}Br-^{81}Br\) or \(^{81}Br-^{79}Br\), and \(^{81}Br-^{81}Br\). Recognizing the mass of these combinations helps scientists distinguish and analyze them, gaining insights into their abundance and proportions in various samples. This knowledge plays a vital role in fields like environmental science, pharmacology, and geochemistry.

Molecular Mass Calculation

Calculating the molecular mass of a compound is an integral aspect of chemistry, allowing for detailed analysis and understanding of molecules. The molecular mass of a molecule is determined by summing up the masses of all the atoms that comprise it. When dealing with isotopes, as in the example of bromine, the mass calculation considers the atomic masses of the isotopes involved.

For bromine molecules (\(Br_2\)), three distinct molecular combinations exist due to its isotopes:

• A \(Br_2\) molecule consisting of two \(^{79}Br\) atoms will have a calculated mass of \(2 \times 79 = 158\) amu.
• A molecule with \(^{79}Br\) and \(^{81}Br\) will yield a mass of \(79 + 81 = 160\) amu.
• Finally, a molecule of two \(^{81}Br\) atoms results in a mass of \(2 \times 81 = 162\) amu.

Comparing the calculated molecular masses with experimental mass spectrometry data helps identify and confirm isotope combinations in a sample. This approach is critical for understanding the chemical nature and potential applications of substances in various scientific and industrial processes.