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Ch.2 - Atoms, Molecules, and Ions
All textbooksBrown 14th EditionCh.2 - Atoms, Molecules, and IonsProblem 98e
Chapter 2, Problem 98e

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of Br2 molecules, and the mass of a Br2 molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of Br2 consists of three peaks: Mass (u) Relative Size 157.836 0.2569 159.834 0.4999 161.832 0.2431 (e) Calculate the abundances of the two isotopes. Calculate the abundance of the heavier isotope.

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Step 1: Understand that the mass spectrum of Br2 is a result of the combinations of the two isotopes of bromine. The three peaks correspond to the combinations of Br-79 and Br-79, Br-79 and Br-81, and Br-81 and Br-81.
Step 2: Let's denote the abundance of Br-79 as x and the abundance of Br-81 as y. Since these are the only two isotopes and their abundances must add up to 1, we can write the first equation as x + y = 1.
Step 3: The relative sizes of the peaks in the mass spectrum correspond to the probabilities of the combinations. Therefore, the second equation can be written as x^2 = 0.2569 (for Br-79 and Br-79), 2xy = 0.4999 (for Br-79 and Br-81), and y^2 = 0.2431 (for Br-81 and Br-81).
Step 4: Solve these equations to find the values of x and y. You can start by adding the equations for x^2, 2xy, and y^2 together. This will give you the equation x^2 + 2xy + y^2 = 1, which is the same as (x + y)^2 = 1. Since we know that x + y = 1, this equation is already satisfied.
Step 5: Next, solve the equation 2xy = 0.4999 for y. This will give you y = 0.4999 / (2x). Substitute this into the equation x + y = 1 to solve for x. Once you have the value of x, you can find the value of y by substituting x into the equation y = 0.4999 / (2x).

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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 isotopes are typically Br-79 and Br-81. Understanding isotopes is crucial for analyzing mass spectra, as the relative abundance of each isotope affects the overall mass of the molecule.
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Mass Spectrum

A mass spectrum is a graphical representation of the mass-to-charge ratio of ions, which helps identify the composition of a sample. In the case of Br<sub>2</sub>, the peaks in the mass spectrum correspond to the different isotopic combinations of bromine atoms. The height of each peak indicates the relative abundance of each isotope, which is essential for calculating their proportions.
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Weighted Average

The weighted average is a calculation that takes into account the relative abundances of different isotopes to determine the average atomic mass of an element. In this context, the average mass of Br<sub>2</sub> can be calculated using the masses of the isotopes and their respective abundances. This concept is vital for solving the problem, as it allows for the determination of the abundance of the heavier isotope based on the mass spectrum data.
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Related Practice
Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of Br2 molecules, and the mass of a Br2 molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of Br2 consists of three peaks: Mass (u) Relative Size 157.836 0.2569 159.834 0.4999 161.832 0.2431 (b) What is the mass of each isotope?

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Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of Br2 molecules, and the mass of a Br2 molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of Br2 consists of three peaks: Mass (u) Relative Size 157.836 0.2569 159.834 0.4999 161.832 0.2431 (c) Determine the average molecular mass of a Br2 molecule.

Textbook Question

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of Br2 molecules, and the mass of a Br2 molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of Br2 consists of three peaks: Mass (u) Relative Size 157.836 0.2569 159.834 0.4999 161.832 0.2431 (d) Determine the average atomic mass of a bromine atom

Textbook Question

It is common in mass spectrometry to assume that the mass of a cation is the same as that of its parent atom. (b) What percentage of the mass of an 1H atom does the electron represent?

Textbook Question

From the following list of elements—Mg, Li, Tl, Pb, Se, Cl, Xe, Si, C—pick the one that best fits each description. Use each element only once: (a) an alkali metal, (b) an alkaline earth metal, (c) a noble gas, (d) a halogen, (e) a metalloidin group 14, (f) a nonmetal listed in group 14, (g) a metal that forms a 3+ ion, (h) a nonmetal that forms a 2- ion, (i) an element that is used as radiation shielding.

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Textbook Question

The first atoms of seaborgium (Sg) were identified in 1974. The longest-lived isotope of Sg has a mass number of 266. (a) How many protons, electrons, and neutrons are in an 266Sg atom?

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