Ch.2 - Atoms, Molecules, and Ions

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.2 - Atoms, Molecules, and Ions

Problem 100e

Chapter 2, Problem 100e

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.

Verified step by step guidance

Determine the molecular composition of bromine: Bromine exists as diatomic molecules (Br2), so each molecule consists of two bromine atoms.

Identify the isotopes: The mass spectrum peaks correspond to different combinations of the two isotopes of bromine. The peaks at m/z 157.836, 159.834, and 161.832 suggest the presence of two isotopes, Br-79 and Br-81.

Assign the peaks to isotopic combinations: The peak at m/z 157.836 corresponds to Br-79/Br-79, the peak at m/z 159.834 corresponds to Br-79/Br-81 or Br-81/Br-79, and the peak at m/z 161.832 corresponds to Br-81/Br-81.

Use the relative peak intensities to set up equations: Let x be the abundance of Br-79 and y be the abundance of Br-81. The relative intensities give us the equations: x^2 = 0.2569, 2xy = 0.4999, and y^2 = 0.2431.

Solve the system of equations: Use the equations to solve for x and y, which represent the fractional abundances of Br-79 and Br-81, respectively.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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. Understanding isotopes is crucial for analyzing mass spectra, as the relative abundance of each isotope affects the overall mass of the elemental sample.

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. In the case of bromine, the peaks represent the isotopes and their respective abundances, which can be calculated from the peak intensities.

Relative Abundance Calculation

Relative abundance refers to the proportion of each isotope present in a sample compared to the total amount of isotopes. To calculate the abundances of bromine isotopes from the mass spectrum, one can use the peak intensities to determine the ratio of each isotope's contribution to the total intensity. This involves setting up equations based on the peak heights and solving for the unknown abundances.

Recommended video:

Guided course

5:42

Calculating Abundance Example

Related Practice

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?

views

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

b. What is the mass of each isotope?

Textbook Question

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

Textbook Question

From the following list of elements—Ar, H, Ga, Al, Ca, Br, Ge, K, O—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 metalloid, (f) a nonmetal listed in group 1A, (g) a metal that forms a 3+ ion, (h) a nonmetal that forms a 2- ion, (i) an element that resembles aluminum.

Textbook Question

c. Determine the average molecular mass of a molecule.

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?