Ch.2 - Atoms, Molecules, and Ions

Problem 33b

Chapter 2, Problem 33b

(b) The atomic weight of boron is reported as 10.81, yet no atom of boron has the mass of 10.81 u. Explain.

Verified step by step guidance

Understand that the atomic weight of an element is a weighted average of the masses of its isotopes, not the mass of a single atom.

Identify the isotopes of boron: Boron has two stable isotopes, Boron-10 and Boron-11.

Recognize that each isotope has a different mass: Boron-10 has a mass of approximately 10 u, and Boron-11 has a mass of approximately 11 u.

Consider the natural abundance of each isotope: Boron-10 and Boron-11 occur in nature in different proportions, with Boron-11 being more abundant.

Calculate the weighted average: The atomic weight of boron (10.81 u) is calculated by multiplying the mass of each isotope by its relative abundance and summing these values. This results in a value that does not correspond to the mass of any single boron atom but represents the average mass of boron atoms as they occur naturally.

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Key Concepts

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

Atomic Weight vs. Atomic Mass

Atomic weight is a weighted average of the masses of an element's isotopes, reflecting their relative abundances in nature. In contrast, atomic mass refers to the mass of a specific isotope, measured in atomic mass units (u). Since boron has isotopes with different masses, the atomic weight of 10.81 u does not correspond to any single boron atom.

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. Boron has two stable isotopes: boron-10 (10 u) and boron-11 (11 u). The presence of these isotopes contributes to the average atomic weight of boron being 10.81 u, as it accounts for their relative abundances.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element found in a natural sample. For boron, the atomic weight of 10.81 u is calculated based on the relative abundances of its isotopes, boron-10 and boron-11. This average reflects the typical composition of boron in nature, rather than the mass of any individual atom.

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