Gold `(Au)` is a precious metal used mainly in jewelry. What is the mass in grams of one `AU` atoms ?
Strategy : We expect that the mass of a single `Au` atoms in grams would be very small number. The atomic mass of `Au` is `197.97 u`. Thus, its molar mass is `196.97g. Because each mode of a substance contains Avogadro's number of units of that substance contains. Avogadro's number of units of that substance dividing the mass of the substance in one mole (molar mas) by Avogadro's constant gives the mass of that unit of substnace.

Explanation

Mass of one `AU` atom `= ("Molar mass of Au")/("Avagadro's constant")`
`= (196.97 g mol^(-1))/(6.022xx10^(23) "atoms mol"^(-1))`
`= 32.71xx10^(-23) "g atom"^(-1)`
`= 3.271xx10^(-22) "g atoms"^(-1)`
We can also use units factors to get the desired result.
Mass of one `Au` atom
`= 1 "Au atom" xx ("1 mol Au atoms")/(6.022xx10^(23) "Au atoms") xx (196.97g)/("1 mol Au atom")`
`= 3.271xx10^(-22) g`