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Well, firstly you need to know if it is pure gold. Assuming that it is, convert the grams to moles

19.7g Au x 1molAu/197.0gAu = 0.1moles Au

And then, to get the number of atoms in 0.1 moles of gold, multiply it by Avogadro's number, 6.22x10^23 atoms per mole

0.1mol Au x 6.22x10^23atoms/mole = 6.22x10^22

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Q: How many atoms are in a gold ring that has a mass of 19.7 grams?
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