Answer : The number of moles of [tex]Fe_2O_3[/tex] produced will be, 0.241 moles.
Solution : Given,
Mass of Fe = 27.0 g
Molar mass of [tex]Fe[/tex] = 56 g/mole
First we have to calculate the moles of [tex]Fe[/tex].
[tex]\text{ Moles of }Fe=\frac{\text{ Mass of }Fe}{\text{ Molar mass of }Fe}=\frac{27.0g}{56g/mole}=0.482moles[/tex]
Now we have to calculate the moles of [tex]Fe_2O_3[/tex]
The balanced chemical reaction is,
[tex]4Fe+3O_2\rightarrow 2Fe_2O_3[/tex]
From the reaction, we conclude that
As, 4 mole of [tex]Fe[/tex] react to give 2 mole of [tex]Fe_2O_3[/tex]
So, 0.482 moles of [tex]Fe[/tex] react to give [tex]\frac{0.482}{4}\times 2=0.241[/tex] moles of [tex]Fe_2O_3[/tex]
Thus, the number of moles of [tex]Fe_2O_3[/tex] produced will be, 0.241 moles.