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?

Short Answer

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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 by step solution

01

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%
02

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
03

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
04

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Oxygen masks for producing \(\mathrm{O}_{2}\) in emergency situations contain potassium superoxide, \(\mathrm{KO}_{2}\). It reacts with \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) in exhaled air to produce oxygen: $$ 4 \mathrm{KO}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)+4 \mathrm{CO}_{2}(g) \longrightarrow 4 \mathrm{KHCO}_{3}(s)+3 \mathrm{O}_{2}(g) $$

Determine whether the statements given below are true or false. (a) The mass of an atom can have the unit mole. (b) In \(\mathrm{N}_{2} \mathrm{O}_{4}\), the mass of the oxygen is twice that of the nitrogen. (c) One mole of chlorine atoms has a mass of \(35.45 \mathrm{~g}\). (d) Boron has an average atomic mass of \(10.81\) amu. It has two isotopes, \(\mathrm{B}-10(10.01\) amu \()\) and \(\mathrm{B}-11(11.01 \mathrm{amu}) .\) There is more naturally occurring B-10 than B-11. (e) The compound \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{2} \mathrm{~N}\) has for its simplest formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{ON}_{1 / 2}\). (f) A 558.5-g sample of iron contains ten times as many atoms as \(0.5200 \mathrm{~g}\) of chromium. (g) If \(1.00\) mol of ammonia is mixed with \(1.00\) mol of oxygen the following reaction occurs, $$ 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ All the oxygen is consumed. (h) When balancing an equation, the total number of moles of reactant molecules must equal the total number of moles of product molecules.

The combustion of liquid chloroethylene, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}\), yields carbon dioxide, steam, and hydrogen chloride gas. (a) Write a balanced equation for the reaction. (b) How many moles of oxygen are required to react with \(35.00 \mathrm{~g}\) of chloroethylene? (c) If \(25.00 \mathrm{~g}\) of chloroethylene reacts with an excess of oxygen, how many grams of each product are formed?

Phosphorus reacts with oxygen to produce different kinds of oxides. One of these oxides is formed when \(1.347 \mathrm{~g}\) of phosphorus reacts with \(1.744 \mathrm{~g}\) of oxygen. What is the simplest formula of this oxide? Name the oxide.

Epsom salts are hydrates of magnesium sulfate. The formula for Epsom salts is \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\). A \(7.834\) -g sample is heated until a constant mass is obtained indicating that all the water has been evaporated off. What is the mass of the anhydrous magnesium sulfate? What percentage of the hydrate is water?

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