Determining Average Atomic Mass

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Chemistry

F:\2014-2015\330_ModChem\330_sections\330_03_Atoms_Hx\03.03.03c_Average_Atomic_Mass.docx (9/26/2014)

Date: ___________________________ Name: ______________________________

Lab Table: Lab Partner(s):

§03.03c

_{Determining Average Atomic Mass}

Background

Determining the average mass of an element uses the same method as determining the weighted average of your grade. For example:

Category Percentage of Total Score Contribution to Total Grade (%/100) Contribution Relative

Tests 75 0.50 37.5

Labs 88 0.25 22.0

Quizzes 90 0.20 18.0

Homework 100 0.05 5.0

TOTAL SCORE: 82.5

Notice that although the percentage of each category is an integer, the total score has a decimal. Definition: The mass of an individual atom is measured in atomic mass units (amu). By

definition, 1 u is one-twelfth the mass of an unbound neutral atom of a carbon-12 atom. On the periodic table, the atomic mass for each element is the average atomic mass for all of the

isotopes of that element.

Task

Although the mass of any individual atom is an integer, the atomic masses on a periodic table have decimals. For example, the atomic mass of a chlorine atom is 35.45 u. Your task is to simulate how one calculates the average atomic mass, and to determine the average atomic mass of elements, and the relative abundance or mass of an individual isotope.

Model

Determining Average Atomic Mass for Copper. Isotope

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Atomic Mass (amu) (B) Relative Abundance (C) Relative Contribution (B*C=D) Copper-63 62.929 0.6917 43.528 Copper-65 64.927 0.3083 20.017

Average Atomic Mass (sum of relative contributions): 63.545 Check: The average atomic mass on the class periodic table is 63.55.

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Procedure

1. Determination of Average Atomic Mass

A. Count of the number of each atom of each isotope. (E.g., for a 0.5 of ‘A’, count out 50 ‘A’ and measure the average mass for all 50 atoms.

Isotope Atomic Mass (amu) (for one ‘atom’)

(A) Relative Abundance (B) Relative Contribution (amu) (C = A * B) A 11.985 0.50 5.993 B 12.950 0.35 4.533 C 14.001 0.15 2.100

Average Atomic Mass: 12.625

Calculate the average atomic masses for the following elements. Check your answer with a periodic table.

B. Magnesium (symbol _Mg___)

Isotope Atomic Mass (amu) Relative Abundance Relative Contribution (amu)

Mg-24 23.985042 0.7899 18.9458

Mg-25 24.985837 0.1000 2.4986

Mg-26 25.982593 0.1101 2.8607

Average Atomic Mass: 24.3051 (Check: Periodic Table: 24.31 amu)

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Chemistry Determining Average Atomic Mass p. 3

C. Molybdenum (symbol _Mo__)

Isotope Atomic Mass (amu) Relative Abundance Relative Contribution (amu)

Mo-92 91.906808 0.1484 13.6390 Mo-94 93.905085 0.0925 8.6862 Mo-95 94.905840 0.1592 15.1090 Mo-96 95.904678 0.1668 15.9969 Mo-97 96.906020 0.0955 9.2545 Mo-98 97.905406 0.2413 23.6246 Mo-100 99.907477 0.0963 9.6211

(Check: Periodic Table. 95.94 amu) D. Tin (symbol _Sn_)

Mass Number Atomic Mass (amu) Relative Abundance Relative Contribution (amu)

112 111.904826 0.0097 1.0855 114 113.902784 0.0065 0.7404 115 114.903348 0.0036 0.4136 116 115.901747 0.1453 16.8405 117 116.902956 0.0768 8.9781 118 117.901609 0.2422 28.5558 119 118.903310 0.0858 10.2019 120 119.902200 0.3259 39.0761 122 121.903440 0.0463 5.644 124 123.905274 0.0579 7.1741

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F:\2014-2015\330_ModChem\330_sections\330_03_Atoms_Hx\03.03.03c_Average_Atomic_Mass.docx (9/26/2014)

2. Determining Relative Abundances and Atomic Mass Units of Individual Isotopes. A. Calculate the atomic mass for gallium-71.

Isotope Atomic Mass (amu) Abundance Relative Relative Contribution (amu)

Gallium-69 68.918 0.600108 41.35824

Gallium-71 (c) 28.3648 / 0.39989 _{= 70.9315} (a) 1 - 0.600108 _{= 0.39989} (b) 69.723 – 41.35824 _{= 28.3648} Total Average Atomic Mass: 69.723

Show all work.

(a) Calculate relative abundance by subtracting the known relative abundance from 1 (total relative abundance)

(b) Ga-71 contribution = total (69.723) – Ga-69 (41.35824) (c) Calculate Ga-71 atomic mass.

B. The two of the three isotopes of silicon have atomic masses and percent abundances of 27.9769 amu (92.2297%) and 28.9765 amu (4.6832%) What is the percentage abundance and atomic mass for silicon-30? (Show all work.)

Isotope Atomic Mass

(amu) Abundance (%) Abundance Relative Relative Contribution (amu)

Silicon-28 27.9769 92.229 0.92229 25.80282

Silicon-29 28.9765 4.6832 0.046832 1.357027

Silicon-30 30.12363 0.030878 0.930157

From Periodic Table, Average atomic mass: 28.09

(a) Relative Abundance is given, so in order to find Atomic Mass, need to know the Average Atomic Mass. Look it up on a periodic table (28.09 g/mol).

(b) The sum of the Relative Contributions = 28.09; so solve for Si-30 Relative Contribution.

(c) Determine Atomic Mass for Si-30:

(Atomic Mass) * (Relative Abundance) = Relative Contribution.

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Chemistry Determining Average Atomic Mass p. 5

3. Extension

Antimony has two naturally occurring isotopes. The mass of antimony-121 is 120.904 amu and the mass of antimony-123 is 122.904 amu. Using the average atomic mass from the periodic table, find the abundance of each isotope. Show all work.