To determine the number of moles of gold (Au) in a given quantity of atoms, you can use Avogadro's number, which is the conversion factor between the number of atoms and the number of moles. Avogadro's number is equal to 6.022 x 10^23 atoms per mole.

Given that you have 2.88 x 10^23 atoms of Au, you can calculate the number of moles as follows:

Number of moles of Au = Number of atoms / Avogadro's number

Number of moles of Au = (2.88 x 10^23 atoms) / (6.022 x 10^23 atoms/mole)

Number of moles of Au ≈ 0.478 moles

Therefore, 2.88 x 10^23 atoms of Au are equivalent to approximately 0.478 moles of Au.