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When 125 grams of FeO react with 25.0 grams of Al, how many grams of Fe can be produced?

[tex]\[ 3 \, \text{FeO} + 2 \, \text{Al} \rightarrow 3 \, \text{Fe} + \text{Al}_2\text{O}_3 \][/tex]

A. 25.9 g Fe
B. 38.7 g Fe
C. 50.9 g Fe
D. 77.6 g Fe



Answer :

To determine how many grams of iron (Fe) can be produced when 125 grams of iron(II) oxide (FeO) react with 25.0 grams of aluminum (Al), we need to follow these steps:

### Step 1: Write the balanced chemical equation.
The balanced chemical equation is:
[tex]\[ 3 \text{FeO} + 2 \text{Al} \rightarrow 3 \text{Fe} + \text{Al}_2\text{O}_3 \][/tex]

### Step 2: Calculate the molar masses of the reactants and products.
- Molar mass of FeO:
[tex]\[ \text{FeO} = 55.845\text{ g/mol (Fe)} + 15.999\text{ g/mol (O)} = 71.844\text{ g/mol} \][/tex]

- Molar mass of Al:
[tex]\[ \text{Al} = 26.981\text{ g/mol} \][/tex]

- Molar mass of Fe:
[tex]\[ \text{Fe} = 55.845\text{ g/mol} \][/tex]

### Step 3: Convert masses of the reactants to moles.
- Moles of FeO:
[tex]\[ \text{Mass of FeO} = 125\text{ g} \][/tex]
[tex]\[ \text{Moles of FeO} = \frac{125\text{ g}}{71.844\text{ g/mol}} \approx 1.7399\text{ moles} \][/tex]

- Moles of Al:
[tex]\[ \text{Mass of Al} = 25.0\text{ g} \][/tex]
[tex]\[ \text{Moles of Al} = \frac{25.0\text{ g}}{26.981\text{ g/mol}} \approx 0.9265\text{ moles} \][/tex]

### Step 4: Determine the limiting reactant.
The stoichiometric coefficients from the balanced equation are:
[tex]\[ 3 \text{FeO} : 2 \text{Al} \][/tex]

- Calculate the reactant ratio for FeO:
[tex]\[ \text{Reactant ratio for FeO} = \frac{1.7399\text{ moles}}{3} \approx 0.5799 \][/tex]

- Calculate the reactant ratio for Al:
[tex]\[ \text{Reactant ratio for Al} = \frac{0.9265\text{ moles}}{2} \approx 0.4633 \][/tex]

The limiting reactant is the one with the smaller reactant ratio. Here, it is aluminum (Al), with a reactant ratio of approximately 0.4633.

### Step 5: Calculate the moles of Fe produced.
Using the limiting reactant ratio (0.4633):
[tex]\[ \text{Moles of Fe produced} = 0.4633 \times 3 \approx 1.3899 \][/tex]

### Step 6: Convert the moles of Fe to grams.
[tex]\[ \text{Mass of Fe} = 1.3899\text{ moles} \times 55.845\text{ g/mol} \approx 77.6171\text{ g} \][/tex]

Therefore, the amount of iron (Fe) that can be produced is approximately:
[tex]\[ 77.6171 \text{ grams} \][/tex]

Among the given options, the closest answer is:
[tex]\[ \boxed{77.6 \text{ g Fe}} \][/tex]