How Do You Solve What Is The Mass Of 5.12 X 10^24 Atoms Au? And Have The Answer In Grams?

The standard mass of Au or gold is 196.9 = 197 grams per mole. Therefore,

197 grams of Au = 1 mole

1 mole = 6.023 x 10²³ atoms

197 grams of Au = 6.023 x 10²³ atoms

1 gram of Au = 6.023 x 10²³ atoms/197 = 0.0306 x 10²³ = 3.06 x 10²¹ atoms

Or 1 atom = 197/ 6.023 x 10²³ = 32.708 x 10^-23 grams

5.12 X 10²⁴ atoms = 5.12 x 10²⁴ x 32.708 x 10^-23 grams

5.12 X 10²⁴ atoms = 167.465 x 10 grams

5.12 X 10²⁴ atoms = 1674.65 grams

Another way to explain it is:

The number of atoms in one mole is 6.022*10^23 atoms (because 1 mole of anything is 6.022*10^23 of that thing, just like 1 dozen of anything is 12 of that thing.  6.022*10^23 is called Avogadro's number)

The weight of 1 mole of Au is 196.97 grams (molar mass - to get this, you take the atomic mass on the periodic table and change the AMUs to grams).  For the sake of comparison to the previous answer, I will round up to 197 grams - atomic mass varies anyway according to what periodic table you use.

If you use 1 mole = 6.022*10^23 as a way to convert 5.12*10^24 atoms of Au to moles, you would set up the equation like this:

5.12*10^24 atoms Au * 1 mol/6.022*10^23 atoms  = approximately 8.5 moles (the unit "atoms" cancel each other out in the equation)

Then if you use the molar mass of Au to convert the moles to grams, you would set up the equation like this:

8.5 moles * 197g/1 mole = 1,674.45 grams (the unit "moles" cancel each other out in the equation)

My answer is slightly different than the previous one but that's because I was taught a slightly different number for Avogadro's number.  Both answers are correct, I was just trying to show the equations in a different way.