Question

considering the following chemical reaction: 4 al(s) + 3 o₂(g) → 2 al₂o₃. which of the following statements are false?
○ the reaction of 1 mole of al will produce 1/4 mole of al₂o₃.
○ in order to produce 101.96 grams of aluminum oxide, you must begin with 1.5 moles of o₂.
○ the reaction of one mole of aluminum requires 3/4 mole of oxygen gas to completely react with it.
○ the reaction of 26.98 g of aluminum will produce 0.5 mole of al₂o₃.

Explanation:

Step1: Analyze the first statement

From the reaction \(4\text{Al}(s) + 3\text{O}_2(g)
ightarrow2\text{Al}_2\text{O}_3\), the mole ratio of \(\text{Al}\) to \(\text{Al}_2\text{O}_3\) is \(4:2 = 2:1\). So 1 mole of \(\text{Al}\) should produce \(\frac{1}{2}\) mole of \(\text{Al}_2\text{O}_3\), not \(\frac{1}{4}\) mole. So this statement is false.

Step2: Analyze the second statement

Molar mass of \(\text{Al}_2\text{O}_3\) is \(2\times27 + 3\times16= 54 + 48 = 102\space g/mol\). 101.96 g is approximately 1 mole of \(\text{Al}_2\text{O}_3\). From the reaction, mole ratio of \(\text{O}_2\) to \(\text{Al}_2\text{O}_3\) is \(3:2\). So moles of \(\text{O}_2\) needed for 1 mole of \(\text{Al}_2\text{O}_3\) is \(\frac{3}{2}=1.5\) moles. This statement is true.

Step3: Analyze the third statement

Mole ratio of \(\text{Al}\) to \(\text{O}_2\) is \(4:3\). So 1 mole of \(\text{Al}\) requires \(\frac{3}{4}\) mole of \(\text{O}_2\). This statement is true.

Step4: Analyze the fourth statement

Molar mass of \(\text{Al}\) is 26.98 g/mol. So 26.98 g of \(\text{Al}\) is 1 mole. From the reaction, 4 moles of \(\text{Al}\) produce 2 moles of \(\text{Al}_2\text{O}_3\), so 1 mole of \(\text{Al}\) produces 0.5 moles of \(\text{Al}_2\text{O}_3\). This statement is true.

Answer:

The reaction of 1 mole of Al will produce 1/4 mole of \( \text{Al}_2\text{O}_3 \) (the first statement) is false.