Respuesta :
ANSWER
The mass of Al produced is 26.98 grams
EXPLANATION
Given that;
The mass of aluminum oxide metal is 51.2 g
Follow the steps below to find the mass of Al atom
Step 1; Write the balanced equation of the reaction
[tex]\text{ 2Al}_2O_3\text{ }\rightarrow\text{ 4Al + 3O}_2[/tex]Step 2; Find the number of moles of aluminum oxide
[tex]\text{ mole = }\frac{\text{ mass}}{\text{ molar mass}}[/tex]Recall, that the molar mass of Al2O3 is 101.96 g/mol
[tex]\begin{gathered} \text{ mole = }\frac{\text{ 51.2}}{\text{ 101.96}} \\ \text{ mole = 0.502 mol} \end{gathered}[/tex]The number of moles of Al2O3 is 0.502 mol
Step 3; Find the number of moles of Al using stoichiometry ratio
In the given equation, 2 moles Al2O3 give 4 moles Al
Let the number of moles of Al be x
[tex]\begin{gathered} \text{ 2 moles Al}_2O_3\text{ }\rightarrow\text{ 4 moles Al} \\ \text{ 0.502 mol Al}_2O_3\text{ }\rightarrow\text{ x mol Al} \\ \text{ cross multiply} \\ \text{ 2 moles Al}_2O_3\text{ }\times\text{ x mol Al = 4 moles Al }\times\text{ 0.502 mol Al}_2O_3 \\ \text{ Isolate x mol Al} \\ \text{ x mol Al = }\frac{\text{ 4 moles Al }\times0.502mol\cancel{Al_2}O_3}{2moles\cancel{Al_2}O_3} \\ \\ \text{ x mol Al = }\frac{4\text{ }\times\text{ 0.502}}{2} \\ \text{ x mol Al = 2 }\times\text{ 0.502} \\ \text{ x mol Al = 1.00 mol} \end{gathered}[/tex]The number of mol of Al is 1.00 mol
Step 4; Find the mass of Al
[tex]\begin{gathered} \text{ mole = }\frac{\text{ mass}}{\text{ molar mass}} \\ \text{ cross multiply} \\ \text{ mass = mole }\times\text{ molar mass} \end{gathered}[/tex]Recall, that the molar mass of Al is 26.98 g/mol
[tex]\begin{gathered} \text{ mass = 1.00 }\times\text{ 26.98} \\ \text{ mass = 26.98 grams} \end{gathered}[/tex]The mass of Al produced is 26.98 grams
