Problem 76 - Chemistry Matter and Change

Question

Gallium, which has an atomic mass of 69.723 amu, has two naturally occurring isotopes, Ga- 69 and Ga- \(71 .\) Which isotope occurs in greater abundance? Explain.

Step-by-Step Solution

Answer

Ga-69 occurs in greater abundance, as the atomic mass (69.723 amu) is closer to 69.

Step 1: Understanding the Isotopes

Gallium has two isotopes, Ga-69 and Ga-71. The atomic mass of these isotopes represents the mass of an average atom of that isotope, usually in atomic mass units (amu). The naturally occurring isotopes contribute to the atomic mass of the element we've observed on the periodic table.

Step 2: Understanding Atomic Mass

The atomic mass of gallium (69.723 amu) listed on the periodic table is a weighted average of the masses of its isotopes. This value suggests the average weight of a gallium atom, based on the relative abundances of each isotope.

Step 3: Comparing Isotopic Mass and Atomic Mass

Ga-69 has a mass number (stands in for the atomic mass in isotopic terms) of 69, while Ga-71 has a mass number of 71. The listed atomic mass of 69.723 is closer to 69 than it is to 71.

Step 4: Conclusion on Greater Abundance

Since the atomic mass of gallium (69.723 amu) is closer to the mass of Ga-69 than to that of Ga-71, Ga-69 contributes more to this average atomic mass. This implies that Ga-69 occurs in greater abundance than Ga-71.

Key Concepts

Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the average mass of atoms of an element, measured in atomic mass units (amu). This average takes into account the masses and relative abundances of all isotopes of a particular element. For instance, the atomic mass of gallium is reported as 69.723 amu, indicating that this is the weighted average of its isotopic masses. Unlike the straight average arithmetic mean, atomic mass is calculated considering the factor of isotopic abundance, which means it reflects which isotopes are present most and least.

• The atomic mass number is what you will typically see on the periodic table.
• This is often not a whole number because it accounts for isotope averages.

When dealing with isotopes, atomic mass becomes crucial, as it helps predict which isotope is more prevalent in nature.

Gallium

Gallium is an intriguing element with the atomic number 31. It is mostly recognized for its distinctive property of melting at slightly above room temperature. Found in group 13 of the periodic table, gallium is not freely found in nature but is usually isolated from sources like bauxite and zinc ores. Its significance comes not just from its unusual properties but most importantly from its isotopic composition.

• Gallium has two stable isotopes: Ga-69 and Ga-71.
• The atomic mass of gallium, 69.723 amu, reflects a mixture of these two isotopes.

Understanding gallium's isotopes helps explain why the observed atomic mass is close to the mass of Ga-69, suggesting its greater natural abundance.

Weighted Average

The concept of a weighted average is pivotal when exploring isotopic compositions. In general, a weighted average gives different weights to different numbers based on their importance or frequency. When applied to isotopes, this process involves multiplying each isotope's mass by its relative abundance (expressed as a fraction of 1) and then summing these products.

• The atomic mass is a form of a weighted average where isotopic masses and their natural abundances determine the final value.
• It helps in understanding why the atomic mass of an element usually isn't a whole number.

For gallium, the atomic mass being closer to 69 than to 71 suggests that Ga-69 is weighted more heavily due to its larger natural occurrence compared to Ga-71.

Abundance of Isotopes

The abundance of isotopes refers to how commonly or rarely an isotope occurs in nature. Different elements have isotopes that exist in varying amounts, impacting the calculated atomic mass.

• Isotopic abundance is often given in percentage or fractional form.
• It is a critical factor in determining the atomic mass of an element.

For gallium, the relative abundance of its isotopes Ga-69 and Ga-71 affects its atomic mass. The atomic mass of gallium (69.723 amu) being much closer to 69 indicates that Ga-69 is more prevalent, constituting a larger proportion naturally compared to Ga-71. This concept not only helps in understanding the atomic mass but also aids in various applications, such as material science and geology, where precise isotopic analysis is required.