How to convert a compound from grams to atoms

Question

The question is: Convert the amount of chalk CaCO3 used from grams to number of atoms

The amount used is 0.20g and this figure needs to be converted to # of atoms.

I found two examples from different books:

Example #1. Convert 2.12 mol C3H8 to # of atoms. (it consider 11 atoms in a molecule)

2.12 mol C3H8 x 6.02 x 10^23 molecules C3H8 / 1 mol C3H8 x 11 atoms /1 molecules C3H8

ans: 1.40 x 10^23 atoms

(it says desired conversion is moles -->molecules-->atoms)

Example # 2 Convert 7.52g CH4 to # of atoms

Molar mass of CH4 is 16.040g CH4/mol

7.52g CH4 x 1mol CH4/ 16.040g CH4 x 6.02 x 10^23 atoms/ 1 mol CH4

ans: 2.82 x 10^23 atoms of CH4

This example convert grams ---> moles ---> atoms

So back to my original question: convert 0.20 grams of CaCO3 to # of atoms.

Should I follow example # 1: (molar mass is 100.09 g CaCO3)

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 molecules CaCO3

ans: 6.01x10^25 atoms of CaCO3

Or Example 2:

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

6.02 x 10^23 atoms CaCO3 / 1mol CaCO3

ans: 1.02 x 10^25 atoms of CaCO3

If I follow the two different approach from different books, I have different answers.

Which is correct? I just want to convert 0.20g of CaCO3 to number of atoms.

Thank you for your help

Answer 1

The problem you're running into is the distinction between atoms and molecules. One molecule of CaCO3 has 5 total atoms (1 Ca + 1 C + 3 O). In your answer in example 1, you've identified how many atoms there are in your sample of CaCO3 (how many atoms of of Ca, C, and O, there is no such thing as an atom of CaCO3).

In your solution in example 2, you've identified how many molecules of CaCO3 there are in your sample.

It all depends on if you're wanting to identify the number of atoms, or the number of CaCO3 molecules.