Question

Use the balanced equation to solve the problem.2Al2O34AI + 30₂51.2g of aluminum oxide, Al2O3, decompose.What mass of aluminum, Al, is made?g

Answer 1

The mass of Al produced is 26.98 grams

Step-by-step 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

`\text{ 2Al}_2O_3\text{ }\rightarrow\text{ 4Al + 3O}_2`

Step 2; Find the number of moles of aluminum oxide

`\text{ mole = }\frac{\text{ mass}}{\text{ molar mass}}`

Recall, that the molar mass of Al2O3 is 101.96 g/mol

`\begin{gathered} \text{ mole = }\frac{\text{ 51.2}}{\text{ 101.96}} \\ \text{ mole = 0.502 mol} \end{gathered}`

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

`\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{ }*\text{ x mol Al = 4 moles Al }*\text{ 0.502 mol Al}_2O_3 \\ \text{ Isolate x mol Al} \\ \text{ x mol Al = }\frac{\text{ 4 moles Al }*0.502mol\cancel{Al_2}O_3}{2moles\cancel{Al_2}O_3} \\ \\ \text{ x mol Al = }\frac{4\text{ }*\text{ 0.502}}{2} \\ \text{ x mol Al = 2 }*\text{ 0.502} \\ \text{ x mol Al = 1.00 mol} \end{gathered}`

The number of mol of Al is 1.00 mol

Step 4; Find the mass of Al

`\begin{gathered} \text{ mole = }\frac{\text{ mass}}{\text{ molar mass}} \\ \text{ cross multiply} \\ \text{ mass = mole }*\text{ molar mass} \end{gathered}`

Recall, that the molar mass of Al is 26.98 g/mol

`\begin{gathered} \text{ mass = 1.00 }*\text{ 26.98} \\ \text{ mass = 26.98 grams} \end{gathered}`

The mass of Al produced is 26.98 grams