Ch.2 - Atoms & Elements

Problem 121

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Chapter 2, Problem 121

Silver is composed of two naturally occurring isotopes: Ag-107 (51.839%) and Ag-109. The ratio of the masses of the two isotopes is 1.0187. What is the mass of Ag-107?

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First, let's denote the mass of Ag-107 as x. The mass of Ag-109 will then be 1.0187x, according to the given ratio.

Next, we need to use the formula for calculating the average atomic mass. The average atomic mass is the sum of the masses of the isotopes, each multiplied by its natural abundance. In this case, the average atomic mass of silver is the sum of the mass of Ag-107 times its abundance and the mass of Ag-109 times its abundance.

Set up the equation: 107.87 = 0.51839x + 0.48161(1.0187x), where 107.87 is the average atomic mass of silver, 0.51839 is the abundance of Ag-107, and 0.48161 is the abundance of Ag-109 (calculated as 1 - 0.51839).

Solve the equation for x, which represents the mass of Ag-107.

Finally, check your answer by substituting the value of x back into the equation to ensure that it balances.

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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 example, silver has two isotopes, Ag-107 and Ag-109, which differ in their neutron count and thus their mass, but both are chemically identical.

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 reflects the weighted average of all isotopes present in nature, allowing for a more accurate representation of the element's mass as it occurs in nature.

Mass Ratio

The mass ratio of isotopes refers to the relationship between the masses of two isotopes of the same element. In this case, the mass ratio of Ag-107 to Ag-109 is given as 1.0187, indicating that Ag-109 is slightly heavier than Ag-107. This ratio is crucial for calculating the mass of Ag-107 when combined with the known abundance of the isotopes.

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Related Practice

Common brass is a copper and zinc alloy containing 37.0% zinc by mass and having a density of 8.48 g/cm³. A fitting composed of common brass has a total volume of 112.5 cm³. How many atoms (copper and zinc) does the fitting contain?

A 67.2 g sample of a gold and palladium alloy contains 2.49×10²³ atoms. What is the composition (by mass) of the alloy?

Naturally occurring chlorine is composed of two isotopes: 75.76% Cl-35 (mass 34.9688 amu) and 24.24% Cl-37 (mass 36.9659 amu). Naturally occurring oxygen is composed of three isotopes: 99.757% O-16 (mass 15.9949 amu), 0.038% O-17 (mass 16.9991 amu), and 0.205% O-18 (mass 17.9991 amu). The compound dichlorine monoxide is composed of two chlorine atoms and one oxygen atom bonded together to form the Cl₂O molecule. How many Cl₂O molecules of different masses naturally exist? Give the masses of the three most abundant Cl₂O molecules.

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Textbook Question

The U.S. Environmental Protection Agency (EPA) sets limits on healthful levels of air pollutants. The maximum level that the EPA considers safe for lead air pollution is 1.5 µg/m³. If your lungs were filled with air containing this level of lead, how many lead atoms would be in your lungs? (Assume a total lung volume of 5.50 L.)

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Textbook Question

Pure gold is usually too soft for jewelry, so it is often alloyed with other metals. How many gold atoms are in an 0.255-ounce, 18 K gold bracelet? (18 K gold is 75% gold by mass.)

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Textbook Question

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