Let's analyze the balanced chemical reaction and answer each part of the question systematically.
The balanced equation is:
[tex]\[ 3 \text{Fe} + 4 \text{H}_2\text{O} \rightarrow \text{Fe}_3\text{O}_4 + 4 \text{H}_2 \][/tex]
### 2.1 How many moles of [tex]\(\text{Fe}_3\text{O}_4\)[/tex] will be formed from 12 moles of Fe?
From the balanced equation, the molar ratio of Fe to Fe[tex]\(_3\)[/tex]O[tex]\(_4\)[/tex] is 3:1. This means 3 moles of Fe produce 1 mole of Fe[tex]\(_3\)[/tex]O[tex]\(_4\)[/tex].
To find the moles of Fe[tex]\(_3\)[/tex]O[tex]\(_4\)[/tex] formed from 12 moles of Fe, we use the ratio:
[tex]\[ \text{Moles of Fe}_3\text{O}_4 = \frac{12 \text{ moles of Fe}}{3} = 4 \text{ moles} \][/tex]
Thus, 4 moles of [tex]\(\text{Fe}_3\text{O}_4\)[/tex] will be formed from 12 moles of Fe.
### 2.2 How many moles of Fe are needed to produce 16 moles of [tex]\(\text{H}_2\)[/tex]?
From the balanced equation, the molar ratio of Fe to H[tex]\(_2\)[/tex] is 3:4. This means 3 moles of Fe produce 4 moles of H[tex]\(_2\)[/tex].
To find the moles of Fe needed to produce 16 moles of H[tex]\(_2\)[/tex], we use the ratio:
[tex]\[ \text{Moles of Fe} = \frac{3}{4} \times 16 \text{ moles of H}_2 = 12 \text{ moles} \][/tex]
Thus, 12 moles of Fe are needed to produce 16 moles of [tex]\(\text{H}_2\)[/tex].
### 2.3 How many moles of [tex]\(\text{H}_2\)[/tex] will be formed if 40 moles of [tex]\(\text{Fe}_3\text{O}_4\)[/tex] are formed?
From the balanced equation, the molar ratio of Fe[tex]\(_3\)[/tex]O[tex]\(_4\)[/tex] to H[tex]\(_2\)[/tex] is 1:4. This means 1 mole of Fe[tex]\(_3\)[/tex]O[tex]\(_4\)[/tex] produces 4 moles of H[tex]\(_2\)[/tex].
To find the moles of H[tex]\(_2\)[/tex] formed from 40 moles of Fe[tex]\(_3\)[/tex]O[tex]\(_4\)[/tex], we use the ratio:
[tex]\[ \text{Moles of H}_2 = 4 \times 40 \text{ moles of Fe}_3\text{O}_4 = 160 \text{ moles} \][/tex]
Thus, 160 moles of [tex]\(\text{H}_2\)[/tex] will be formed if 40 moles of [tex]\(\text{Fe}_3\text{O}_4\)[/tex] are formed.
### 2.4 How many moles of [tex]\(\text{H}_2\text{O}\)[/tex] are needed to react with 14.5 moles of Fe?
From the balanced equation, the molar ratio of Fe to H[tex]\(_2\)[/tex]O is 3:4. This means 3 moles of Fe react with 4 moles of H[tex]\(_2\)[/tex]O.
To find the moles of H[tex]\(_2\)[/tex]O needed to react with 14.5 moles of Fe, we use the ratio:
[tex]\[ \text{Moles of H}_2\text{O} = \frac{4}{3} \times 14.5 \text{ moles of Fe} = \frac{4 \times 14.5}{3} = \frac{58}{3} \approx 19.33 \text{ moles} \][/tex]
Thus, approximately 19.33 moles of [tex]\(\text{H}_2\text{O}\)[/tex] are needed to react with 14.5 moles of Fe.
In summary:
2.1. 4 moles of [tex]\(\text{Fe}_3\text{O}_4\)[/tex] will be formed from 12 moles of Fe.
2.2. 12 moles of Fe are needed to produce 16 moles of [tex]\(\text{H}_2\)[/tex].
2.3. 160 moles of [tex]\(\text{H}_2\)[/tex] will be formed if 40 moles of [tex]\(\text{Fe}_3\text{O}_4\)[/tex] are formed.
2.4. Approximately 19.33 moles of [tex]\(\text{H}_2\text{O}\)[/tex] are needed to react with 14.5 moles of Fe.
