Average Atomic Mass Answer Key (CHEM 1405)

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The average atomic mass of elements can be determined from relative abundance of each isotope in a naturally occurring element sample. This relative abundance is obtained by running an elemental sample through a mass spectrometer. The “spectra” is shown on the readout as different “peaks” or lines at different masses. The machine very accurately records the experimental data and delivers it in the following form. The atomic masses in the periodic table are based on the weighted average of the masses of all isotopes of an element.

Calculate the average atomic mass for the following sets of isotopes.

1. Carbon sample

Isotope	Mass of isotope	Relative Abundance
C-12	12.0 amu	4945
C-13	13.003 amu	55

$LaTeX: 12.0amu\times4945=59300amu$ $12.0amu\times4945=59300amu$

$LaTeX: 13.003amu\times55=720amu$ $13.003amu\times55=720amu$

Total "weighted" mass = 59300 amu + 720 amu = 6.00 x 104 amu

Total abundance = 4945 + 55 = 5000.

Average Atomic Mass $LaTeX: =\frac{6.00\times10^4amu}{5000}=12.0amu$ $=\frac{6.00\times10^4amu}{5000}=12.0amu$

2. Iridium sample

Isotope	Mass of isotope	Relative Abundance
Ir-191	191.0 amu	37.58%
Ir-193	193.0 amu	62.42%

$LaTeX: 191.0amu\times37.58\%=7178amu\cdot\%$ $191.0amu\times37.58\%=7178amu\cdot\%$

$LaTeX: 193.0amu\times62.42\%=12050amu\cdot\%$ $193.0amu\times62.42\%=12050amu\cdot\%$

Total "weighted" mass = $LaTeX: 7178amu\cdot\%+12050amu\cdot\%=19230amu\cdot\%$ $7178amu\cdot\%+12050amu\cdot\%=19230amu\cdot\%$

Total abundance = 37.58% + 62.42% = 100.00%

Average Atomic Mass $LaTeX: =\frac{19230amu\cdot\%}{100.00\%}=192.3amu$ $=\frac{19230amu\cdot\%}{100.00\%}=192.3amu$

3. Chromium sample

Isotope	Mass of isotope	Relative Abundance
Cr-50	49.946 amu	4.35%
Cr-52	51.941 amu	83.80%
Cr-53	52.941 amu	9.50%
Cr-54	53.939 amu	2.35%

$LaTeX: 49.946amu\times4.35\%=217amu\cdot\%$ $49.946amu\times4.35\%=217amu\cdot\%$

$LaTeX: 51.941amu\times83.80\%=4353amu\cdot\%$ $51.941amu\times83.80\%=4353amu\cdot\%$

$LaTeX: 52.941amu\times9.50\%=503amu\cdot\%$ $52.941amu\times9.50\%=503amu\cdot\%$

$LaTeX: 53.939amu\times2.35\%=127amu\cdot\%$ $53.939amu\times2.35\%=127amu\cdot\%$

Total "weighted" mass = $LaTeX: 217amu\cdot\%+4353amu\cdot\%+503amu\cdot\%+127amu\cdot\%=5200.amu\cdot\%$ $217amu\cdot\%+4353amu\cdot\%+503amu\cdot\%+127amu\cdot\%=5200.amu\cdot\%$

Total abundance = 4.35% + 83.80% + 9.50% + 2.35% = 100.00%

Average Atomic Mass $LaTeX: =\frac{5200amu\cdot\%}{100.00\%}=52.00amu$ $=\frac{5200amu\cdot\%}{100.00\%}=52.00amu$

4. Chlorine sample

Isotope	Mass of isotope	Relative Abundance
Cl-35	34.9689 amu	75.771%
Cl-37	36.9659 amu	24.229%

$LaTeX: 34.9689amu\times75.771\%=2649.6amu\cdot\%$ $34.9689amu\times75.771\%=2649.6amu\cdot\%$

$LaTeX: 36.9659amu\times24.229\%=895.65amu\cdot\%$ $36.9659amu\times24.229\%=895.65amu\cdot\%$

Total "weighted" mass = $LaTeX: 2649.6amu\cdot\%+895.65amu\cdot\%=3545.3amu\cdot\%$ $2649.6amu\cdot\%+895.65amu\cdot\%=3545.3amu\cdot\%$

Total abundance = 75.771% + 24.229% = 100.000%

Average Atomic Mass $LaTeX: =\frac{3545.3amu\cdot\%}{100.000\%}=35.453amu$ $=\frac{3545.3amu\cdot\%}{100.000\%}=35.453amu$

5. Lithium sample

Isotope	Mass of isotope	Relative Abundance
Li-6	6.0151 amu	150
Li-7	7.0160 amu	1850

$LaTeX: 6.0151amu\times150=9.0\times10^2amu$ $6.0151amu\times150=9.0\times10^2amu$

$LaTeX: 7.0160amu\times1850=1.30\times10^4amu$ $7.0160amu\times1850=1.30\times10^4amu$

Total "weighted" mass = $LaTeX: 9.0\times10^2amu+1.30\times10^4amu=1.39\times10^4amu$ $9.0\times10^2amu+1.30\times10^4amu=1.39\times10^4amu$

Total abundance = 150 + 1850 = 2.00 x 10³

Average Atomic Mass $LaTeX: =\frac{1.39\times10^4amu}{2.00\times10^3}=6.95amu$ $=\frac{1.39\times10^4amu}{2.00\times10^3}=6.95amu$

6. Hydrogen sample

Isotope	Mass of isotope	Relative Abundance
H-1	1.0078 amu	99.985%
H-2	2.0140 amu	0.015%

$LaTeX: 1.0078amu\times99.985\%=100.76amu\cdot\%$ $1.0078amu\times99.985\%=100.76amu\cdot\%$

$LaTeX: 2.0140amu\times0.015\%=0.030amu\cdot\%$ $2.0140amu\times0.015\%=0.030amu\cdot\%$

Total "weighted" mass = $LaTeX: 100.76amu\cdot\%+0.030amu\cdot\%=100.79amu\cdot\%$ $100.76amu\cdot\%+0.030amu\cdot\%=100.79amu\cdot\%$

Total abundance = 99.985% + 0.015% = 100.000%

Average Atomic Mass $LaTeX: =\frac{100.79amu\cdot\%}{100.000\%}=1.0079amu$ $=\frac{100.79amu\cdot\%}{100.000\%}=1.0079amu$

7. Oxygen sample

Isotope	Mass of isotope	Relative Abundance
O-16	15.995 amu	99.762%
O-17	16.999 amu	0.038%
O-18	17.999 amu	0.200%

$LaTeX: 15.995amu\times99.762\%=1595.7amu\cdot\%$ $15.995amu\times99.762\%=1595.7amu\cdot\%$

$LaTeX: 16.999amu\times0.038\%=0.65amu\cdot\%$ $16.999amu\times0.038\%=0.65amu\cdot\%$

$LaTeX: 17.999amu\times0.200\%=3.60amu\cdot\%$ $17.999amu\times0.200\%=3.60amu\cdot\%$

Total "weighted" mass = $LaTeX: 1595.7amu\cdot\%+0.65amu\cdot\%+3.60amu\cdot\%=1600.0amu\cdot\%$ $1595.7amu\cdot\%+0.65amu\cdot\%+3.60amu\cdot\%=1600.0amu\cdot\%$

Total abundance = 99.762% + 0.038% + 0.200% = 100.000%

Average Atomic Mass $LaTeX: =\frac{1600.0amu\cdot\%}{100.000\%}=16.000amu$ $=\frac{1600.0amu\cdot\%}{100.000\%}=16.000amu$

8. Copper sample

Isotope	Mass of isotope	Relative Abundance
Cu-63	62.940 amu	69.17%
Cu-65	64.928 amu	30.83%

$LaTeX: 62.940amu\times69.17\%=4354amu\cdot\%$ $62.940amu\times69.17\%=4354amu\cdot\%$

$LaTeX: 64.928amu\times30.83\%=2002amu\cdot\%$ $64.928amu\times30.83\%=2002amu\cdot\%$

Total "weighted" mass = $LaTeX: 4354amu\cdot\%+2002amu\cdot\%=6356amu\cdot\%$ $4354amu\cdot\%+2002amu\cdot\%=6356amu\cdot\%$

Total abundance = 69.17% + 30.83% = 100.000%

Average Atomic Mass $LaTeX: =\frac{6356amu\cdot\%}{100.00\%}=63.56amu$ $=\frac{6356amu\cdot\%}{100.00\%}=63.56amu$

9. Uranium sample

Isotope	Mass of isotope	Relative Abundance
U-235	235.044 amu	0.720%
U-238	238.051 amu	99.280%

$LaTeX: 235.044amu\times0.720\%=169amu\cdot\%$ $235.044amu\times0.720\%=169amu\cdot\%$

$LaTeX: 238.051amu\times99.280\%=23633amu\cdot\%$ $238.051amu\times99.280\%=23633amu\cdot\%$

Total "weighted" mass = $LaTeX: 169amu\cdot\%+23633amu\cdot\%=23803amu\cdot\%$ $169amu\cdot\%+23633amu\cdot\%=23803amu\cdot\%$

Total abundance = 0.720% + 99.280% = 100.000%

Average Atomic Mass $LaTeX: =\frac{23803amu\cdot\%}{100.00\%}=238.03amu$ $=\frac{23803amu\cdot\%}{100.00\%}=238.03amu$

10. Magnesium sample

Isotope	Mass of isotope	Relative Abundance
Mg-24	23.985 amu	78.70%
Mg-25	24.986 amu	10.13%
Mg-26	25.983 amu	11.17%

$LaTeX: 23.985amu\times78.70\%=1888amu\cdot\%$ $23.985amu\times78.70\%=1888amu\cdot\%$

$LaTeX: 24.986amu\times10.13\%=253.1amu\cdot\%$ $24.986amu\times10.13\%=253.1amu\cdot\%$

$LaTeX: 25.983amu\times11.17\%=290.2amu\cdot\%$ $25.983amu\times11.17\%=290.2amu\cdot\%$

Total "weighted" mass = $LaTeX: 1888amu\cdot\%+253.1amu\cdot\%+290.2amu\cdot\%=2431amu\cdot\%$ $1888amu\cdot\%+253.1amu\cdot\%+290.2amu\cdot\%=2431amu\cdot\%$

Total abundance = 78.70% + 10.13% + 11.17% = 100.00%

Average Atomic Mass $LaTeX: =\frac{2431amu\cdot\%}{100.00\%}=24.31amu$ $=\frac{2431amu\cdot\%}{100.00\%}=24.31amu$