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Ch.2 - Atoms, Molecules, and Ions
All textbooksBrown 15th EditionCh.2 - Atoms, Molecules, and IonsProblem 100b
Chapter 2, Problem 100b

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of molecules, and the mass of a molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of consists of three peaks: m/zRelative Peak Intensity157.836 0.2569 159.834 0.4999 161.832 0.2431
b. What is the mass of each isotope?

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1
The problem involves determining the mass of each isotope of bromine based on the mass spectrum data provided. The mass spectrum shows three peaks, which correspond to the different combinations of the two isotopes in Br2 molecules.
Bromine has two stable isotopes, typically denoted as Br-79 and Br-81. These isotopes combine to form Br2 molecules, resulting in different mass-to-charge (m/z) ratios in the mass spectrum.
The peaks at m/z 157.836, 159.834, and 161.832 correspond to the molecular masses of Br2 molecules formed by different combinations of the isotopes: Br-79/Br-79, Br-79/Br-81, and Br-81/Br-81, respectively.
Let m1 be the mass of Br-79 and m2 be the mass of Br-81. The equations based on the peak data are: m1 + m1 = 157.836, m1 + m2 = 159.834, and m2 + m2 = 161.832.
Use the system of equations to solve for m1 and m2. First, solve the first and third equations to find m1 and m2, then verify with the second equation.>

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For bromine, the two stable isotopes are bromine-79 and bromine-81, which have atomic masses of approximately 78.918 and 80.916, respectively. Understanding isotopes is crucial for interpreting mass spectra and calculating average atomic masses.
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Mass Spectrum

A mass spectrum is a graphical representation of the mass-to-charge ratio (m/z) of ions, which helps identify the composition of a sample. Each peak in the spectrum corresponds to a specific ion, with its height indicating the relative abundance of that ion. Analyzing the peaks allows chemists to determine the isotopic composition and relative abundances of the isotopes present in a sample.
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Average Atomic Mass

The average atomic mass of an element is calculated by taking into account the masses of its isotopes and their relative abundances. This value is often not a whole number due to the presence of multiple isotopes with different masses. For bromine, the average atomic mass can be calculated using the mass and relative intensity of each peak in the mass spectrum, providing insight into the isotopic distribution.
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Related Practice
Textbook Question

The element lead (Pb) consists of four naturally occurring isotopes with atomic masses 203.97302, 205.97444, 206.97587, and 207.97663 amu. The relative abundances of these four isotopes are 1.4, 24.1, 22.1, and 52.4%, respectively. From these data, calculate the atomic weight of lead.

Textbook Question

Gallium (Ga) consists of two naturally occurring isotopes with masses of 68.926 and 70.925 amu. a. How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. b. The average atomic mass of Ga is 69.72 amu. Calculate the abundance of each isotope.

Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of molecules, and the mass of a molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of consists of three peaks: m/zRelative Peak Intensity157.836 0.2569 159.834 0.4999 161.832 0.2431

a. What is the origin of each peak (of what isotopes does each consist)?

Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of molecules, and the mass of a molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of consists of three peaks: m/zRelative Peak Intensity157.836 0.2569 159.834 0.4999 161.832 0.2431

c. Determine the average molecular mass of a molecule.

Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of molecules, and the mass of a molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of consists of three peaks: m/zRelative Peak Intensity157.836 0.2569 159.834 0.4999 161.832 0.2431

d. Determine the average atomic mass of a bromine atom.

Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of molecules, and the mass of a molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of consists of three peaks: m/zRelative Peak Intensity157.836 0.2569 159.834 0.4999 161.832 0.2431

e. Calculate the abundances of the two isotopes.