What is the mass, in grams, of 5.56 1023 molecules of aspirin, C9H8O4?

Answer 1

Hello, Lauren,

The definition of a mole makes this calculation possible. One mole is 6.02x10²³ particles of anything. In science, it typically describes the number of molecules or atoms. A key feature of the Periodic Table is that we can use the atomic masses of the elements to do two things: 1) they describe the mass of one atom of the element, in amu (atomic mass units), or 2) we can use the same number and use the label "grams/mole." Sounds magical, but it's true. For example, the atomic mass of carbon, C, is 12.01 amu. But we can also say that the "molar mass" of carbon is 12.01 g/mole. If we have 12.01 grams of carbon, we will have one mole of carbon atoms, or 6.02x10²³ carbon atoms.

We are told we have 5.56x10²³ molecules of aspirin, C₉H₈O₄. That's a lot to count, so I'll trust the number is correct. Since we know 1 mole is 6.02x10²³ , we can find what fraction of a mole we have of aspirin.

(5.56x10²³ molecules)/(6.02x10²³ molecules/mole) = 0.924 mole

Now we need the molar mass of C₉H₈O₄. Add the atomic masses of each atom (9 carbonsx12, 8 hydrogens x 1, and 4 oxygens x 16) to find the number of grams it takes to make a mole of C₉H₈O₄. I did it quickly, so check the number, but I get 180.2 grams/mole.

Now it's easy to convert molecules to grams - just watch the units:

0.924 mole x (180.2 g/mole) = 166 grams C₉H₈O₄ (3 sig figs)

Bob