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]
