Problem 115 - Chemistry Matter and Change

Question

Infer Sulfur’s average atomic mass is close to the whole number 32. Chlorine’s average atomic mass is 35.453, which is not a whole number. Suggest a possible reason for this difference.

Step-by-Step Solution

Answer

The difference between the average atomic masses of sulfur and chlorine may be attributed to their isotopic compositions and relative abundances. Sulfur's isotopes likely have atomic masses close to 32, resulting in an average atomic mass approximately equal to 32. In contrast, chlorine's isotopes have atomic masses that differ significantly from whole numbers, or a more considerable difference between the isotopic masses, and their relative abundances result in an average atomic mass that is not a whole number (35.453).

Step 1: Revisit the concept of average atomic mass

Average atomic mass is obtained by calculating the weighted average of the atomic masses of an element's isotopes, considering their relative abundance in nature. The formula for average atomic mass is: Average atomic mass = Σ (fraction of isotope × atomic mass of isotope)

Step 2: Analyze sulfur's average atomic mass

Sulfur has an average atomic mass close to the whole number 32. This suggests that sulfur's most abundant isotope has an atomic mass close to 32, and its other isotopes either have relatively low abundance or atomic masses very close to 32, which yield an average atomic mass close to 32 after the calculation.

Step 3: Analyze chlorine's average atomic mass

Chlorine has an average atomic mass of 35.453, which is not a whole number. This implies that there's a significant abundance of chlorine isotopes with atomic masses that differ from whole numbers or have a substantial difference from the most abundant isotope's atomic mass. This results in an average atomic mass that is not a whole number.

Step 4: Suggest a possible reason for the difference

The difference between the average atomic masses of sulfur and chlorine may be attributed to the isotopic compositions and their relative abundances. Sulfur's isotopes likely have atomic masses close to 32, which results in an average atomic mass approximately equal to 32. In contrast, chlorine's isotopes have atomic masses that differ significantly from whole numbers, or a more considerable difference between the isotopic masses, and their relative abundances result in an average atomic mass that is not a whole number (35.453).

Key Concepts

Understanding Isotopes

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This difference in neutron count causes each isotope to have a distinct atomic mass. Imagine atoms as building blocks. Even if they're built on the same foundation (same element), the number of extra pieces (neutrons) can vary. Here are some essential points about isotopes:

• Because isotopes belong to the same element, their chemical properties are mostly the same. It's their physical properties, like atomic mass, that differ.
• Most elements naturally occur as a mix of different isotopes.
• The atomic mass of these isotopes is expressed in atomic mass units (amu), which reflects the mass based on the atomic nucleus.

Understanding isotopes is key to grasping why the average atomic mass of an element is not always a whole number. Consider sulfur, most of its isotopes have masses close to 32, making its average atomic mass almost a whole number. On the other hand, chlorine has isotopes that vary more in mass, contributing to a non-whole number average atomic mass.

Relative Abundance: Making Sense of Isotope Impact

Relative abundance refers to how common or prevalent a particular isotope of an element is in nature compared to other isotopes of the same element. Imagine a bag full of candies, where different colors represent different isotopes. The relative abundance indicates how many candies of each color are present.

• An isotope's impact on the average atomic mass is weighted by its relative abundance. This means more prevalent isotopes have a larger effect on the average.
• If one isotope is much more abundant than the others, it heavily influences the average atomic mass.
• Relative abundance is usually expressed as a fraction or percentage.

Distinguishing sulfur from chlorine, the relative abundance of sulfur isotopes results in an average atomic mass close to a whole number because one isotope is predominantly present. In contrast, the isotopes of chlorine have more varied abundances and atomic masses, resulting in an average atomic mass that is not a whole number.

Atomic Mass Calculation Demystified

Atomic mass calculation involves taking into account each isotope’s atomic mass and its relative abundance. The average atomic mass is calculated using a weighted mean, considering both of these factors. Here's how the process unfolds:

• Multiply the atomic mass of each isotope by its relative abundance (expressed as a fraction).
• Add all these values together. The sum is the average atomic mass of the element.
• This calculated value explains why the atomic mass isn't a simple average of isotope masses—it accounts for abundance.

This method explains the atomic mass results in decimals, rather than whole numbers. A practical example: For sulfur, with most isotopes having a mass near 32, the calculation yields about 32 for its atomic mass. In contrast, chlorine’s isotopes significantly differ, resulting in an average atomic mass of 35.453. Knowing how to calculate and interpret the atomic mass allows for better comprehension of isotopic variations and their significance in chemical science.