| MadSci Network: Chemistry |
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My teacher has given us the abundances of isotopes of a few elements and
shown us how to calculate the relative atomic mass (RAM) of the element as
a
weighted average. Why are the RAM's I calculate different to the RAM's on
my periodic table? How do I get the right values to calculate the correct
RAM of an element?
Your question is a very good one, and has to do with the fact that isotope mass numbers are not exact masses. Every nucleus has a different binding energy per nucleon -- a nucleon is a proton or a neutron -- and this energy shows up as a small amount of mass according to the famous equation E = mc². Atomic masses are always given relative to a standard mass. This standard mass is ¹²C = 12.000000... atomic mass units (for why, see this answer). This means that ¹²C is the only atom that has a mass expressible as an integer! Other atoms have non-integer exact masses, and these need to be taken into account when calculating your weighted averages. Even other isotopes of carbon have non-integer masses!
As an example, let's try to calculate the average atomic mass of tin. Tin has a number of stable isotopes:
The average atomic mass of tin is 118.711. Using nominal atomic masses, the weighted average mass of tin is 118.806, but using actual atomic masses the weighted average is 118.708. Of course this is still not quite right; the small remaining error can be put down to the fact that we are quoting too many significant figures for our answer! The percentages I quote above give us, at most, three sig figs but with "118.708" we are giving six. Even so, our answer is good to five sig figs. If we use all of the sig figs in the masses and percentages given by Web Elements, we obtain the correct average atomic mass.
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