Answer: 1.77 kg of manganese (IV) oxide reacts to produce 1.12kg of manganese metal.
Explanation:
The balanced chemical equation is:
[tex]4Al+3MnO_2\rightarrow 2Al_2O_3+3Mn[/tex]
To calculate the moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text {Molar mass}}[/tex]
moles of manganese = [tex]\frac{1.12\times 1000g}{55g/mol}=20.4mol[/tex]
According to stoichiometry :
3 moles of [tex]Mn[/tex] is produced by = 3 moles of [tex]MnO_2[/tex]
Thus 20.4 moles of [tex]Mn[/tex] is produced by =[tex]\frac{3}{3}\times 20.4=20.4moles[/tex] of [tex]MnO_2[/tex]
Mass of [tex]MnO_2=moles\times {\text {Molar mass}}=20.4moles\times 86.9g/mol=1773g=1.773kg[/tex] (1kg=1000g)
Thus 1.77 kg of manganese (IV) oxide reacts to produce 1.12kg of manganese metal.
