Problem 91 - General Chemistry: Principles and Modern Applications

Question

Before \(1961,\) the standard for atomic masses was the isotope \(^{16} \mathrm{O},\) to which physicists assigned a value of exactly \(16 .\) At the same time, chemists assigned a value of exactly 16 to the naturally occurring mixture of the isotopes \(^{16} \mathrm{O},^{17} \mathrm{O},\) and \(^{18} \mathrm{O}\). Would you expect atomic masses listed in a 60 -year-old text to be the same, generally higher, or generally lower than in this text? Explain.

Step-by-Step Solution

Answer

The atomic masses listed in a 60-year-old text should be generally lower than those listed in a more recent text. This is because an isotope with fewer neutrons, like \(^{16}\mathrm{O}\), is lighter than a mixture of isotopes including ones with more neutrons like \(^{17}\mathrm{O}\) and \(^{18}\mathrm{O}\). Therefore, when chemists considered the average mass of naturally occurring isotopes post-1961, the atomic masses would generally be higher compared to when physicists used only \(^{16}\mathrm{O}\) isotope for calibration.

Step 1: Analyzing the atomic masses

Before 1961, physicists considered the atomic mass of \(^{16}\mathrm{O}\) isotope to be exactly 16, whereas chemists used the average mass of the naturally occurring mixture of \(^{16} \mathrm{O},^{17} \mathrm{O},\) and \(^{18}\mathrm{O}\). This implies that the atomic masses provided by chemists were a weighted average of the isotopes, likely resulting in a value greater than 16 given that \(^{17}\mathrm{O}\) and \(^{18}\mathrm{O}\) are heavier than \(^{16}\mathrm{O}\).

Step 2: Predicting the change in atomic masses

Since \(^{16}\mathrm{O}\) is lighter than the average mass of the naturally occurring isotopes, its atomic mass being exactly 16 would be lower than the average atomic mass calculated by the chemists. Therefore, if the atomic mass standard used by chemists was applied universally post-1961, the atomic masses in a 60-year-old text would be generally lower compared to a newer text.

Step 3: Conclusion

Thus, atomic masses listed in a 60-year-old text (which used the physicists' standard of \(^{16}\mathrm{O}\) atomic mass) should generally be lower than those in a more recent text (which uses the average mass of the naturally occurring isotopes).

Key Concepts

Oxygen Isotopes

Isotopes are variants of a particular chemical element that have different numbers of neutrons. This results in different atomic masses. Oxygen, for instance, has three main isotopes:

• ¹⁶O: The most abundant isotope, with eight protons and eight neutrons.
• ¹⁷O: Contains one additional neutron compared to ¹⁶O, making it heavier.
• ¹⁸O: Has two more neutrons than ¹⁶O, so it's even heavier.

Naturally occurring oxygen is a mix of these isotopes. Each isotope contributes to the overall atomic mass of oxygen based on its abundance. This natural mix leads to an average atomic mass that differs from any single isotope's mass. Understanding these differences is key when evaluating how atomic mass standards have evolved over time.

Weighted Average

The concept of a weighted average is crucial in determining the atomic mass of elements with isotopes. Unlike a simple average, a weighted average considers both the mass and the relative abundance of each isotope. For oxygen, the process can be simplified to:

• Multiply each isotope's mass by its relative abundance.
• Sum these values to get the overall atomic mass.

Mathematically, it's expressed as:\[\text{Weighted Average} = \left( \text{mass of } ^{16}\text{O} \times \text{abundance} \right) + \left( \text{mass of } ^{17}\text{O} \times \text{abundance} \right) + \left( \text{mass of } ^{18}\text{O} \times \text{abundance} \right)\]This approach explains why the average atomic mass is often not a whole number. By using a weighted average, chemists provide a more accurate representation of an element's mass as it naturally occurs.

Historical Atomic Mass Standards

Historically, the way atomic masses were measured has evolved. Before 1961, physicists and chemists had different standards for oxygen's atomic mass.

• Physicists set the mass of ¹⁶O as exactly 16, a decision based solely on this single isotope.
• Chemists, on the other hand, considered the mixture of ¹⁶O, ¹⁷O, and ¹⁸O, leading to a higher value due to the inclusion of the heavier isotopes.

This difference meant atomic masses calculated by chemists were generally higher than those by physicists. After 1961, the standards were unified to better reflect the naturally occurring mixtures of isotopes, leading to more consistent atomic masses across the scientific community. Understanding this shift helps clarify why atomic masses in older texts may differ from modern values.