Michael S. answered • 13d
B.S. in Chemistry, Indiana University; Organic Chem Teaching Intern
3.01 × 1021 formula units
You already did the hard part. Once you have moles, getting to particles is a single multiplication — by Avogadro's number.
The step you are missing
formula units = moles × 6.022 × 1023 units/mol
= (0.00500 mol)(6.022 × 1023) = 3.01 × 1021 formula units
(Carrying your unrounded moles, 0.500 / 100.09 = 0.004996 mol, gives 3.008 × 1021 — same answer to three significant figures. Rounding mid-problem is a habit worth breaking, though; here it happens not to matter.)
The idea behind it
A mole is just a counting word, like "dozen." A dozen eggs is 12 eggs; a mole of anything is 6.022 × 1023 of that thing. So the question "how many formula units are in 0.005 mol?" is the same shape as "how many eggs are in 0.5 dozen?" — multiply the count-per-unit by how many units you have.
The two conversions in this problem run in opposite directions, which is why the step feels different:
grams → moles: divide by molar mass (100.09 g/mol)
moles → particles: multiply by 6.022 × 1023
If you ever forget which way, check the size of the answer. There must be a huge number of particles in half a gram of anything, so if your result comes out small, you divided when you should have multiplied.
Why "formula units" and not "molecules"
This is worth getting right because your instructor chose the word deliberately. CaCO3 is ionic — a lattice of Ca2+ and CO32− ions, with no discrete CaCO3 particle anywhere in it. "CaCO3" states the ratio of ions, so we count formula units rather than molecules.
Reserve "molecules" for covalent compounds such as H2O or CO2, where genuinely separate molecules exist. The arithmetic is identical either way; only the name changes.
If a follow-up asks for ions or atoms: each formula unit contains 1 Ca2+ and 1 CO32− (so 6.02 × 1021 ions total), and 5 atoms counting the carbonate's C and 3 O (so 1.50 × 1022 atoms). Read carefully which one is being asked for.
