how many atoms are in 500.0 grams of iron

Converting between units in Chemistry is as follows:

$$Grams\Leftrightarrow Mols\Leftrightarrow Atoms$$

 

 

So, firstly, you need to convert from grams to mols of Fe (gFe is grams of Fe -- Note that they cancel):

Fe = 55.845g per mol

$$\left({\mathtt{500}}{\mathtt{\,\times\,}}{\mathtt{gFe}}\right){\mathtt{\,\times\,}}\left({\frac{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{molFe}}\right)}{\left({\mathtt{55.845}}{\mathtt{\,\times\,}}{\mathtt{gFe}}\right)}}\right) = {\mathtt{8.953}}{\mathtt{\,\times\,}}{\mathtt{molFe}}$$ 

 

Lastly you'll need to convert from mols to atoms (molFe is mols of Fe -- Again note that they cancel):

The number of atoms per mol is represented by Avogadro's Constant = 6.022 x 10^23.

$$\left({\mathtt{8.953}}{\mathtt{\,\times\,}}{\mathtt{molFe}}\right){\mathtt{\,\times\,}}\left({\frac{\left({\mathtt{6.022}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{23}}}{\mathtt{\,\times\,}}{\mathtt{atomsFe}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{molFe}}\right)}}\right) = {\mathtt{5.39}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{24}}}{\mathtt{\,\times\,}}{\mathtt{atomsFe}}$$

 

5.39 x 10^24 atoms of Fe in 500g of Fe.