POGIL: Average Atomic Mass

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Name: Date: Period: Chemistry POGIL: Average Atomic Mass WHY? It is assumed that the composition of a sample of an element (in terms of percent natural abundances of each of the element s isotopes) is the same everywhere on Earth. For instance, in any sample containing carbon, be it diamond or coal, 98.89% of the carbon atoms in that sample will be carbon-12, and the remaining 1.11% will be carbon-13. If you take samples in Africa or Canada, the natural abundance will have the same percentages for each isotope. The majority of the elements that are encountered in the chemistry lab have two or more naturally-occurring isotopes. If an element has more than one naturally occurring isotope, then a random sample of the element should be assumed to exist as a mixture of these isotopes that are found in Nature. Success Criteria Explain how isotopes differ and why the atomic masses of elements are not whole numbers. Calculate the average atomic mass of an element from isotope data. Prerequisites Distinguish among protons, electrons, and neutrons in terms of relative mass and charge. Describe the structure of an atom, including the location of the protons, electrons, and neutrons with respect to the nucleus. Explain how atomic number identifies an element. Use atomic number, mass number, and charge of an atom to find the numbers of protons, electrons, and neutrons. Vocabulary Isotopes = atoms of the same element that have the same atomic number but different atomic masses due to a different number of neutrons Atomic Mass Unit (amu) = a unit of mass equal to 1/12 the mass of a carbon-12 atom Percent Natural Abundance = the number of isotopes out of 100 that exist in nature Relative Natural Abundance = the ratio of isotopes that exist in a sample (% Abundance / 100) Relative Atomic Mass = weighted average mass of the atoms of the element as they occur in nature Model 1: The Weight of an Atom and AMUs A single atom is extremely small. The typical atom will have a mass of approximately 3 x 10-23 g. This is 0.000000000000000000000003 g. The smallest mass that the standard analytical balance can weigh reliably is 0.0001 g, which corresponds to roughly 3 quintillion (3,000,000,000,000,000,000) atoms. These numbers become quite complicated and confusing. To make it convenient to discuss the mass of very small particles, we use the term atomic mass unit (amu) rather than very tiny fractions of what can be weighed out on a balance. 1 amu = 1.6606 x 10-24 g 1. A carbon-12 atom has a mass of 12.000 amu. What would be the mass of this in grams? 2. What would be the mass of 1 million carbon atoms? 1 trillion carbon atoms?

P O G I L : A v e r a g e A t o m i c M a s s Page 2 MODEL 2 A Strip of Magnesium Metal 3. What is the atomic number for each magnesium atom in Model 2? 4. What are the mass numbers of the naturally occurring isotopes of magnesium shown in Model 2? 5. Will all of the atoms of magnesium have the same atomic mass? Explain. 6. For the sample of 20 atoms of magnesium shown in Model 2, complete the table for each isotope. Isotope 24 Mg 25 Mg 26 Mg Number of Atoms 7. Which isotope of magnesium is the most common in Model 2? 8. Based on Model 2 and the table in Question 6, for every 100 atoms of magnesium: Isotope 24 Mg 25 Mg 26 Mg % Abundance

Model 3 Natural Abundance Information for Magnesium P O G I L : A v e r a g e A t o m i c M a s s Page 3 Isotope Natural Abundance (%) Atomic Mass (amu) magnesium 24 78.99 23.9850 magnesium 25 10.00 24.9858 magnesium 26 11.01 25.9826 9. Consider the natural abundance information in Model 3. a. Calculate the expected number of atoms of each isotope that will be found in a sample of 20 atoms of magnesium. (Please make it a whole number. We can t have partial atoms.) b. Is Model 2 (Magnesium Strip Picture) accurate in its representation of magnesium at the atomic level? Explain. 10. If you could pick a single atom of magnesium and put it on a balance, the mass of that atom would most likely be amu. Explain your reasoning. 11. Refer to the Periodic Table and find the box for magnesium. a. Write down the decimal number shown in that box. amu b. Does the decimal number shown on the Periodic Table match any of the atomic masses listed in Model 3? 12. The periodic table does not show the atomic mass of every isotope for an element. a. Explain why this would be an impractical goal for the Periodic Table. b. Is it important to the average scientist to have information about a particular isotope of an element. Explain. (Hint: Do scientists work with individual atoms?)

P O G I L : A v e r a g e A t o m i c M a s s Page 4 13. What would be a practical way of showing the mass of magnesium atoms on the Periodic Table given that most elements occur as mixtures of isotopes? 14. Propose a possible way to calculate the average atomic mass of 100 magnesium atoms. Your answer may include a mathematical equation, but it is not required. Model 4 Proposed Average Atomic Mass Calculations 15. Complete the three proposed calculations for the average atomic mass of magnesium in Model 4. 16. Consider the calculation in Model 4. a. Which method(s) shown in Model 4 give an answer for average atomic mass that matches the mass of magnesium on the Periodic Table? b. Explain why the mathematical reasoning was incorrect for any method(s) in Model 4 that did not give the correct answer for the Periodic Table average atomic mass. c. For the methods in Model 4 that give the correct answer for average atomic mass, show that they are mathematically equivalent methods.

P O G I L : A v e r a g e A t o m i c M a s s Page 5 17. Use one of the methods in Model 4 (that gave a correct answer) to calculate the average atomic mass for oxygen. Isotope Natural Abundance (%) Atomic Mass (amu) Oxygen 16 99.76 15.9949 Oxygen 17 0.04 16.991 Oxygen 18 0.20 17.992 Exercises 18. Germanium has several naturally occurring isotopes. What is the average atomic mass? Isotope Natural Abundance (%) Atomic Mass (amu) Germanium 70 20.5 69.924 Germanium 72 27.4 71.992 Germanium 73 7.8 72.923 Germanium 74 36.5 73.921 Germanium 76 7.8 75.921

P O G I L : A v e r a g e A t o m i c M a s s Page 6 19. 98.89% of all carbon is carbon-12 (12.0000 amu), and 1.11% is carbon-13 (13.0034 amu). What is the average atomic mass? Does it match the Periodic Table? 20. Neon has three different isotopes. 90.51% of neon atoms have a mass of 19.992 amu. 0.27% of neon atoms have a mass of 20.944 amu. 9.22% of neon atoms have a mass of 21.991 amu. What is the relative atomic mass of neon? 21. Of all chlorine atoms, 75.771% are chlorine-35 (34.96885 amu). All other chlorine atoms are chlorine-37 (36.96590 amu). Determine the relative atomic mass of chlorine.