Converting moles to number of atoms

Question

I asked several people and each time I got different answers.

I'm suppose to find out how much atoms of chalk CaCO3 I used after I wrote something.

I used 0.20 grams of CaCO3. Now I need to find the total number of atoms I used.

I read my book, it says the desired conversion is: moles is to molecules to atoms.

0.20 g CaCO3 x 1 mol CaCO3 / 100.09 g CaCO3 x

6.02 x 10 ^23 molecules CaCO3 / 1 mol CaCO3 x

5 atoms / 1 molecule CaCO3

So total 6.017 x 10^21 atoms.

Some others told me:

0.2 g CaCO3 x 1 mol CaCO3 / 100.09 g CaCO3 x

6.02 x 10 ^23 atoms CaCO3 / 1 mol CaCO3

I'm not sure which is correct. Esp. CaCO3 is molecule, not a single element. Not sure if there is a different approach if I convert single element vs. molecule from grams to atoms?

I need an "expert" help, thank you very much!

Answer 1

Hi Liz,

When converting from one SI unit to another you must make sure that you convert to the intermediate that is the common unit between the value in which you are given, and the units you must find this value in. So, when you have 0.20 g of CaCO₃ and you need to find atoms of CaCO₃ you start by taking 0.20 g of the compound and converting to moles. You do this by taking the mass you are given which is 0.20 g, and dividing by the molar mass of the compound which is 100.09 g contained in 1 mole. The molar mass is found by taking each element's mass number and multiplying it by the amount you have in the formula; so

Ca (1 molecule of Ca) = 40.078 amu x 1 molecule of Ca = 40.078 g of Ca

C (1 molecule of C) = 12.011 amu x 1 molecule of C = 12.011 g of C

O (3 molecules of O) = 15.99 amu x 3 molecules of O = 47.97 g of O

Then you take the numbers you calculated and add them all up to give you the final molar mass = 100.059 g in 1 mole

Once you have done this, the next step is to take the number you found in moles and then multiplying by 6.022 x 10²³ atoms contained in 1 mole. By doing this step-wise manner you can cross out the units that you have converted and then you will be left with the units desired; which in this case you started with grams and ended with atoms.

In short, the way your book solved the problem is the correct way of doing it! You have to go from grams to moles to molecules.