[calejone]

Found this forum through Reddit. Sorry if this isn't the place to ask basic chemistry questions. Also I have searched for awhile on how to do this and cannot find an answer on specifically getting the mass of multiple isotopes.

Essentially I understand the question: What is the mass in grams of 15,000 atoms of Os?

I multiply (15,000 atoms Os) * (1 mole Os / 6.022e23 atoms Os) * (190.23g Os / 1 mole Os) and you get 4.7e-18 grams of Os. That makes sense to me and I understand that the "190.23g Os / 1 mole Os" part comes from the atomic weight of Os being 190.23.

However I don't understand how to answer the question: What is the approximate mass of 250 atoms of Cr-54?

In the first question I just had to use the atomic mass provided by the periodic table. But now, I think, since Cr-54 is an isotope of chromium that the atomic mass of it will be different now considering it has 24p and 30n. Should I be using "54g Cr / 1 mole Cr"? As in: (250 atoms Cr) * (1 mole Os / 6.022e23 atoms Cr) * (54g Cr / 1 mole Cr) so the answer is 2.2e-20?

Any help on this would be much appreciated. Again, sorry if that's not what this forum is about or if someone has already answered this question before.

[Borek]

However I don't understand how to answer the question: What is the approximate mass of 250 atoms of Cr-54?

Don't worry - it is actually a bit complicated.

That is - on some basic level it is obvious what a mass of a single atom of a given isotope is. Problems start when you are interested in an exact value - as it has to be found in isotope data tables, and our trusty periodic table is of no use.

Exact mass of a nucleus is lower than sum of masses of protons and neutrons, the difference is called binding energy or mass deficit. When the nucleus is created some of the energy is emitted away lowering mass of product (E=mc²) - that's why nuclei are in general quite stable, that's why we can produce energy in nuclear reactors. Calculating mass deficit is insanely difficult, so the best approach is to find the mass experimentally and put it in the tables.

That being said, googling mass of an isotope is - luckily - trivial.

[calejone]

I figured it out incase anyone needs the answer. Substitute the mass number of the isotope in for the weighted average you usually would use for the atom. So in the example I originally posted you would just use 54 from the Cr-54 as in: (250 atoms Cr) * (1 mole Os / 6.022e23 atoms Cr) * (54g Cr / 1 mole Cr) = 2.2e-20.

Also to be clear the question asked the approximate mass of Cr-54 with 250 atoms

[Borek]

Substitute the mass number of the isotope in for the weighted average

Something is wrong, you are not calculating the weighted average of anything here. Just a mass.

Also to be clear the question asked the approximate mass of Cr-54 with 250 atoms

A lot depends on "how approximate" In this case you are off by 0.1%, which is probably perfectly acceptable.