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How many grams of Fe are produced from [tex][tex]$94.0 \, \text{g}$[/tex][/tex] of [tex][tex]$FeO$[/tex][/tex] given the following reaction:

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

Be sure to include significant figures and units in your answer.

Your Answer:
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Sagot :

GinnyAnswer
To determine how many grams of Fe are produced from 94.0 grams of FeO based on the provided reaction:
[tex]\[ 3 \text{FeO} + 2 \text{Al} \rightarrow 3 \text{Fe} + \text{Al}_2\text{O}_3 \][/tex]

### Step-by-Step Solution:

1. Determine the molar mass of FeO:
The molar mass of FeO is 71.844 grams per mole.

2. Convert the mass of FeO to moles:
Given that the mass of FeO is 94.0 grams, we can calculate the moles of FeO as follows:
[tex]\[ \text{moles of FeO} = \frac{\text{mass of FeO}}{\text{molar mass of FeO}} \][/tex]
[tex]\[ \text{moles of FeO} = \frac{94.0 \text{ g}}{71.844 \text{ g/mol}} = 1.308 \text{ mol (to three significant figures)} \][/tex]

3. Relate the moles of FeO to moles of Fe produced:
According to the balanced chemical reaction, the molar ratio of FeO to Fe is 1:1. Therefore, the moles of Fe produced will be the same as the moles of FeO.

[tex]\[ \text{moles of Fe} = \text{moles of FeO} = 1.308 \text{ mol} \][/tex]

4. Determine the molar mass of Fe:
The molar mass of Fe is 55.845 grams per mole.

5. Convert the moles of Fe to grams:
To find the mass of Fe produced, we multiply the moles of Fe by its molar mass:
[tex]\[ \text{mass of Fe} = \text{moles of Fe} \times \text{molar mass of Fe} \][/tex]
[tex]\[ \text{mass of Fe} = 1.308 \text{ mol} \times 55.845 \text{ g/mol} = 73.1 \text{ g (to three significant figures)} \][/tex]

### Final Answer:
The mass of Fe produced from 94.0 grams of FeO is:
[tex]\[ \boxed{73.1 \ \text{grams}} \][/tex]
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