A prospector collects 15.00 g of pure gold. Given that 2.561 mol of gold has a mass of 504.4 g, how many Au atoms are in the sample?

1. First recover the molar mass of gold from the given pair: 504.4 g / 2.561 mol = 196.95 grams per mole. 2. Convert the sample mass to moles: 15.00 g / 196.95 g/mol = 0.07616 mol of gold. 3. Convert moles to atoms with Avogadro's number: 0.07616 mol x 6.022 x 10^23 atoms per mole. 4. The product is 4.59 x 10^22 atoms of gold. 5. Units check: grams cancel in step 2 and moles cancel in step 3, leaving a pure count of atoms. 6. Sanity check: 15.00 g is under a tenth of a mole of gold, so the count should be a bit under a tenth of Avogadro's number. 7. The value 1.79 x 10^22 treats 504.4 g as if it were the molar mass of gold, skipping step 1. 8. The value 1.54 x 10^24 multiplies 2.561 mol by Avogadro's number, ignoring the 15.00 g sample entirely. 9. The value 4.59 x 10^21 is a one decade slip in the exponent. _Source: OpenStax Chemistry (CC BY 4.0), Ch 3 "Composition of Substances and Solutions", section 3.1 Formula Mass and the Mole Concept_