CHE 140/170 Handout – Weighted Averages & Atomic Masses
Weighted Averages & Atomic Masses
There are three isotopes of hydrogen that have the following masses: 1 amu, 2 amu and 3 amu.
The value reported on the periodic table is about 1 amu. This is because atomic mass values on
the periodic table are weighted averages of all the naturally occurring isotopes! This makes
hydrogen’s atomic mass about 1 amu instead of the 2 amu that a straight average would
calculate. So, how do we calculate a weighted atomic mass?
Step 1: Multiple each mass by the decimal abundance (not percentage).
Step 2: Add up the results of Step 1.
Step 3: Make sure answer reasonable!
So, for hydrogen that would be…
Mass of isotope
(amu)
1.0078
2.0141
3.0161
Abundance
99.985%
0.015%
0%
1.0078 amu × .99985 = 1.00765 amu
2.0141 amu × .00015 = 0.000302 amu
+ 3.0161 amu × 0 =
0 amu
1.0080 amu
Now it’s your turn! Calculate the weighted atomic mass for the following elements.
1. lithium
Mass of isotope
(amu)
6.015122
7.016003
Abundance
7.5%
92.5%
6.015122 amu × 0.075 = 0.451 amu
+ 7.016003 amu × 0.925 = 6.490 amu
6.94 amu
2. sulfur
Mass of isotope
(amu)
31.9721
32.9715
33.9679
Abundance
95.0%
0.76%
4.22%
3. carbon
Mass of isotope
(amu)
12.00000
13.00336
Abundance
98.89%
1.11%
31.9721 amu × 0.950 = 30.37 amu
32.9715 amu × 0.0076 = 0.251 amu
+ 33.9679 amu × 0.0422 = 1.433 amu
32.1 amu
12.00000 amu × 0.9889 = 11.867 amu
+ 13.003363 amu × 0.0111 = 0.1443 amu
12.01 amu
4. oxygen
Mass of isotope
(amu)
15.9949
16.9991
17.9992
Abundance
15.9949 amu × 0.99759 = 15.9563 amu
99.759%
0.037%
0.204%
16.9991 amu × 0.00037 = 0.00629 amu
+ 17.9992 amu × 0.00204 = 0.03672 amu
15.999 amu
Weighted Averages key.doc
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