Problem 8 - Chemistry: Principles and Reactions

Question

Oxygen consists of three isotopes with atomic masses \(16.00,17.00\), and \(18.00\) amu. Their abundances are \(99.76 \%, 0.04 \%\), and \(0.20 \%\), respectively. What is the atomic mass of oxygen?

Step-by-Step Solution

Answer

Question: Calculate the atomic mass of oxygen using the given isotopes and their abundance percentages: O-16 (99.76%), O-17 (0.04%), O-18 (0.20%). Answer: The atomic mass of oxygen is approximately 16.00 amu.

Step 1: Calculate the weighted mass for each isotope of oxygen using their abundance percentages

First, we have to find the weighted mass of each isotope of oxygen using the abundance percentages. This can be done by multiplying the atomic mass of the isotope with its abundance percentage. Weighted mass of isotope 1 (O-16) = Atomic mass * Abundance percentage = 16.00 amu * 99.76% Weighted mass of isotope 2 (O-17) = Atomic mass * Abundance percentage = 17.00 amu * 0.04% Weighted mass of isotope 3 (O-18) = Atomic mass * Abundance percentage = 18.00 amu * 0.20%

Step 2: Convert abundance percentages to decimals by dividing by 100

Next, we will convert the abundance percentages to decimal format by dividing each one by 100. Abundance of isotope 1 (O-16) = 99.76% / 100 = 0.9976 Abundance of isotope 2 (O-17) = 0.04% / 100 = 0.0004 Abundance of isotope 3 (O-18) = 0.20% / 100 = 0.0020

Step 3: Calculate the weighted atomic mass for each isotope of oxygen using decimals

Now, we will calculate the weighted atomic mass of each isotope of oxygen using decimal values. Weighted atomic mass of isotope 1 (O-16) = 16.00 amu * 0.9976 ≈ 15.96 amu Weighted atomic mass of isotope 2 (O-17) = 17.00 amu * 0.0004 ≈ 0.0068 amu Weighted atomic mass of isotope 3 (O-18) = 18.00 amu * 0.0020 ≈ 0.0360 amu

Step 4: Calculate the average atomic mass of oxygen by summing up the weighted atomic masses

Finally, we can calculate the average atomic mass of oxygen by summing up the weighted atomic masses of all isotopes. Average atomic mass of oxygen = Weighted atomic mass of O-16 + Weighted atomic mass of O-17 + Weighted atomic mass of O-18 ≈ 15.96 amu + 0.0068 amu + 0.0360 amu Average atomic mass of oxygen ≈ 16.0028 amu The atomic mass of oxygen is approximately 16.00 amu.

Key Concepts

Isotopes of Oxygen

Oxygen, a fundamental element of life, consists of atoms with the same number of protons but a different number of neutrons. These variants are known as isotopes. The most common isotopes of oxygen are O-16, O-17, and O-18, with the number representing the atomic mass of each isotope. This atomic mass is the sum of the protons and neutrons in the nucleus.

While the electrons contribute negligibly to an atom's mass, neutrons contribute significantly, which is why isotopes have different masses. Despite these differences, all isotopes of oxygen chemically behave in almost the same way because their chemical behavior is determined by the number of electrons and protons, which remains consistent across isotopes.

In nature, oxygen predominantly exists as O-16, with O-17 and O-18 present in much smaller quantities. This natural variation in isotopes allows scientists to study environmental conditions of the past by analyzing oxygen isotopic ratios in ice cores and sediment layers.

Abundance Percentage

Abundance percentage refers to the relative amount of each isotope of an element found in nature. For oxygen, the isotope O-16 is vastly more abundant than its heavier counterparts, O-17 and O-18. The abundance percentage is crucial when calculating the average atomic mass of an element because this average considers the mass of all isotopes weighted by their abundance.

The abundance percentage needs to be converted into a decimal to perform calculations involving isotopes. For example, an isotope with an abundance of 99.76% would be represented as 0.9976 in decimal form. This conversion is essential when calculating the weighted mass of each isotope as it aligns with the mathematical conventions used in calculations.

Familiarity with abundance percentages is not only necessary for understanding atomic mass but also for applications such as radiometric dating and studying geochemical cycles.

Weighted Atomic Mass

Weighted atomic mass, often referred to as atomic weight, is a measurement that reflects the average mass of all the isotopes of an element, each one weighted according to its natural abundance. To find the weighted atomic mass of oxygen, you multiply the mass of each isotope by its decimal abundance and then sum these values together.

The calculation is a reflection of the fact that when weighing a large sample of oxygen atoms, the majority will be O-16 due to its higher abundance, impacting the overall average more than the less abundant isotopes. Therefore, despite isotopes O-17 and O-18 having a greater mass, their limited abundance in nature means they contribute less to the average atomic mass of oxygen.

The concept of weighted atomic mass is a cornerstone in the scientific fields of chemistry and physics as it affects the interpretation of molecular weights, reaction stoichiometry, and the calculation of molar masses in quantitative analyses.