Converting mass (g) into number of atoms

Question

I have a question to find the "total number of atoms" of a chalk CaCO3 used?

The total weight of the chalk I used is 0.20 g. The molar mass of CaCO3 is 100.09 g

So basically I'm converting 0.20 g into "total number of atoms".

I need to show my conversion factors, not sure which of the two of the followings is correct

0.20 g CaCO3 / 1 mol CaCO3 / 100.09 g CaCO3 = 1.998 x 10 ^-3 mol CaCO3

Should I just multiply 1.998 x 10^-3 mol CaCO3 to 6.02X10^23 atoms CaCO3 / 1 mol CaCO3?

OR

I need to convert the 1.998 x 10^-3 mol CaCO3 into molecules first, then to atom?

So 1.998 x 10 ^-3 mol CaCO3 x 6.02x10^23 molecules CaCO3 / 1 mol CaCO3 x

5 atoms / 1 molecules CaCO3

I'm confuses as there are examples in the book I need to count the number of atom in a molecules and another example is just says 1 mole = 6.02 x 10 ^23 atoms.

Please help, thank you!

Answer 1

Hi Liz! The problem actually isn't that bad once you have everything set up correctly and are able to see what you need to cancel out. I totally understand how frustrating and confusing this can be! The problem set up would look like this:

(0.20g) x (1 mol / 100.09g) x (6.02 x 10²³ atoms / 1 mol) = 1.20 x 10²¹ atoms

I think the part that might have messed you up is how you set up the problem, and the fact that 6.02 x 10²³ atoms is the standard conversion for all elements, so that's where it gets a little tricky. But, regardless the answer is 1.20 x 10²¹ atoms. Hope this helps! Feel free to reach out with any additional questions or help needed. :)