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Consider again the thermite reaction. If 0.0257 g Al reacts completely, what mass of Fe forms? Use the periodic table to find molar masses.



$Fe_2 O_3 + 2 Al \rightarrow Al_2 O_3 + 2 Fe$



The correct setup allows you to cancel terms to yield the mass of iron:

$0.0257 \text{ g Al} \times \frac{1 \text{ mol Al}}{26.98 \text{ g Al}} \times \frac{2 \text{ mol Fe}}{2 \text{ mol Al}} \times \frac{55.85 \text{ g Fe}}{1 \text{ mol Fe}} = ? \text{ g Fe}$



What mass of Fe forms? Make sure to give your answer with the correct number of significant figures.



A total of 0.0257 g Al forms [ ] g Fe.

Verified Answer :

  • Convert the mass of aluminum to moles using its molar mass (\(0.0257 \text{ g} / 26.98 \text{ g/mol} \approx 0.00095256 \text{ mol}\)).
  • Use the \(1:1\) stoichiometric ratio to find the moles of iron produced (0.00095256 mol).
  • Multiply the moles of iron by its molar mass (\(55.85 \text{ g/mol}\)) to find the mass of iron.
  • Round the final result to three significant figures, resulting in \(\boxed{0.0532 \text{ g}}\).

Explanation

  1. Problem Analysis

The chemical reaction provided is the thermite reaction: \(\text{Fe}_2\text{O}_3 + 2\text{Al} \rightarrow \text{Al}_2\text{O}_3 + 2\text{Fe}\). We are given a mass of \(0.0257 \text{ g}\) of aluminum (\(\text{Al}\)) and need to determine the resulting mass of iron (\(\text{Fe}\)) formed. The molar masses are \(\text{Al} \approx 26.98 \text{ g/mol}\) and \(\text{Fe} \approx 55.85 \text{ g/mol}\). The stoichiometric ratio from the balanced equation shows that 2 moles of \(\text{Al}\) react to produce 2 moles of \(\text{Fe}\), which means the molar ratio of \(\text{Al}\) to \(\text{Fe}\) is \(1:1\).

  1. Calculation and Conclusion

To find the mass of iron formed, we first convert the given mass of aluminum into moles:
\[\text{moles of Al} = \frac{\text{mass of Al}}{\text{molar mass of Al}} = \frac{0.0257 \text{ g}}{26.98 \text{ g/mol}} \approx 0.00095256 \text{ mol}.\]
Since the reaction stoichiometry is \(1:1\), the number of moles of iron produced is equal to the number of moles of aluminum reacted, which is approximately \(0.00095256 \text{ mol}\). Finally, we convert the moles of iron back to mass:
\[\text{mass of Fe} = \text{moles of Fe} \times \text{molar mass of Fe} = 0.00095256 \text{ mol} \times 55.85 \text{ g/mol} \approx 0.0532 \text{ g}.\]
The initial mass given, \(0.0257 \text{ g}\), has three significant figures, so the result is rounded to three significant figures.

Examples

The thermite reaction is an excellent real-life example of a redox reaction, often used in welding railway tracks. By understanding stoichiometry, engineers can precisely calculate how much iron is produced, ensuring enough material is generated to bond heavy steel components together safely and durably. This principle of chemical accounting is essential in industrial processes where resource management and material strength are critical for safety and efficiency.

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