Answered

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.



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



Select the correct setup for this calculation.


A$0.0257 g Al \times \frac{1 mol Al}{26.98 g Al} \times \frac{2 mol Fe}{2 mol Al} \times \frac{55.85 g Fe}{1 mol Fe}$
B$0.0257 g Al \times \frac{26.98 g Al}{1 mol Al} \times \frac{2 mol Al}{2 mol Fe} \times \frac{55.85 g Fe}{1 mol Fe}$
C$0.0257 g Al \times \frac{1 mol Al}{26.98 g Al} \times \frac{2 mol Al}{2 mol Fe} \times \frac{1 mol Fe}{55.85 g Fe}$

Verified Answer :

  • Identify the balanced chemical reaction: \(\text{Fe}_2\text{O}_3 + 2\text{Al} \rightarrow \text{Al}_2\text{O}_3 + 2\text{Fe}\).
  • Convert the given mass of Aluminum to moles of Aluminum using its molar mass (\(26.98\text{ g/mol}\)).
  • Use the stoichiometric ratio from the balanced equation (\(2\text{ mol Fe} / 2\text{ mol Al}\)) to find the moles of Iron produced.
  • Multiply by the molar mass of Iron (\(55.85\text{ g/mol}\)) to determine the mass of Iron produced.
  • The correct setup is Option 1, which calculates to \(\boxed{0.0532\text{ g}}\).

Explanation

  1. Analysis of the Chemical Reaction and Stoichiometry

To determine the mass of iron (Fe) produced from a given mass of aluminum (Al) in the thermite reaction, we first look at the balanced chemical equation: \[\text{Fe}_2\text{O}_3 + 2\text{Al} \rightarrow \text{Al}_2\text{O}_3 + 2\text{Fe}\] This equation tells us that 2 moles of Al react to produce 2 moles of Fe. The molar masses required for the calculation are given: the molar mass of Al is \(26.98\text{ g/mol}\) and the molar mass of Fe is \(55.85\text{ g/mol}\).

  1. Selecting the Correct Calculation Setup

To calculate the mass of Fe, we follow a dimensional analysis approach to ensure the units cancel correctly:

  1. Start with the given mass of Al: \(0.0257\text{ g Al}\).
  2. Convert the mass of Al to moles of Al using the molar mass: \(\frac{1\text{ mol Al}}{26.98\text{ g Al}}\).
  3. Convert moles of Al to moles of Fe using the stoichiometric ratio from the balanced equation: \(\frac{2\text{ mol Fe}}{2\text{ mol Al}}\).
  4. Convert moles of Fe to mass of Fe using the molar mass of Fe: \(\frac{55.85\text{ g Fe}}{1\text{ mol Fe}}\).

Combining these, we get:
\[0.0257\text{ g Al} \times \frac{1\text{ mol Al}}{26.98\text{ g Al}} \times \frac{2\text{ mol Fe}}{2\text{ mol Al}} \times \frac{55.85\text{ g Fe}}{1\text{ mol Fe}}\]
Comparing this to the provided options, this matches option 1.

  1. Conclusion

The calculation setup in option 1 is the correct way to determine the mass of Fe produced. By multiplying these conversion factors, the units of grams of Al, moles of Al, and moles of Fe all cancel out correctly, leaving only the units of grams of Fe. The final result for the mass of Fe is \[\frac{0.0257 \times 1 \times 2 \times 55.85}{26.98 \times 2 \times 1} \text{ g} \approx \boxed{0.0532\text{ g Fe}}.\]

Examples

In chemical engineering and industrial chemistry, calculating product yield from reactant mass is essential for process efficiency. For instance, in the thermite welding process used for repairing railway tracks, engineers need to precisely calculate the amount of iron produced to ensure a structural weld of the correct size and strength. By using molar ratios and stoichiometry, they can accurately predict the mass of the resulting iron based on the amount of aluminum and iron oxide used, ensuring that the process remains both safe and economically viable.

Related Questions