Question

When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxide produced in grams is ----- (nearest integer).

Hint:

Use stoichiometry to calculate the mass of the product based on the limiting reagent in the reaction.

Answer 1

Correct Answer: 153

To find the mass of aluminium oxide (Al₂O₃) produced, we start with the balanced chemical equation for the reaction: 

4Al + 3O₂ → 2Al₂O₃

1. **Molar Mass Calculation:**
- Al (Aluminium) = 27 g/mol
- O₂ (Oxygen) = 32 g/mol
- Al₂O₃ (Aluminium oxide) = (2×27 + 3×16) g/mol = 102 g/mol

2. **Determine Limiting Reagent:**

The moles of Al from 81.0 g:

n(Al) = 81.0 g / 27 g/mol = 3.0 mol

The moles of O₂ from 128.0 g:

n(O₂) = 128.0 g / 32 g/mol = 4.0 mol

According to the equation, 4 moles of Al react with 3 moles of O₂. Calculate the required oxygen for 3.0 mol of Al:

Required O₂ = (3.0 mol Al) × (3/4) = 2.25 mol O₂

Since 2.25 mol of O₂ is less than the available 4.0 mol, Al is the limiting reagent.

3. **Calculate Mass of Al₂O₃ Produced:**

From 3.0 mol of Al (1.5 mol of Al₂O₃):

n(Al₂O₃) = 3.0 mol × (2/4) = 1.5 mol

Mass of Al₂O₃ = 1.5 mol × 102 g/mol = 153.0 g

The mass of aluminium oxide produced is 153 g.

This value falls within the expected range of 153 to 153 g.

Answer 2

The reaction between aluminium and oxygen is: \[ 4\text{Al} + 3\text{O}_2 \rightarrow 2\text{Al}_2\text{O}_3. \] - Moles of aluminium = \( \frac{81.0}{27.0} = 3 \text{ moles} \). - Moles of oxygen = \( \frac{128.0}{32.0} = 4 \text{ moles} \). From the stoichiometry of the reaction, 4 moles of aluminium reacts with 3 moles of oxygen to produce 2 moles of aluminium oxide. Thus, 3 moles of aluminium will produce: \[ \frac{2}{4} \times 3 = 1.5 \text{ moles of } \text{Al}_2\text{O}_3. \] The molar mass of aluminium oxide \( \text{Al}_2\text{O}_3 \) is: \[ \text{Molar mass of Al}_2\text{O}_3 = 2(27.0) + 3(16.0) = 102.0 \text{ g/mol}. \] Thus, the mass of aluminium oxide produced is: \[ 1.5 \times 102.0 = 153 \text{ g}. \] The mass of aluminium oxide produced is 153 g.