The problem asks to determine the mass of FeSO₄ · 7H₂O in a sample of 3.660 g based on the mass of Fe₂O₃ (0.472 g) obtained after a series of reactions.

Let's break down the solution step by step:

1. Chemical Reaction Involved

When FeSO₄ · 7H₂O is dissolved and treated, iron (Fe²⁺) is converted to Fe³⁺, which precipitates as Fe₂O₃ after heating. The key is to relate the amount of Fe₂O₃ produced to the original amount of FeSO₄ · 7H₂O.

• Molar mass of Fe₂O₃: $\text{Fe}_2\text{O}_3 = 2 \times 55.85 \, (\text{Fe}) + 3 \times 16 \, (\text{O}) = 159.7 \, \text{g/mol}$

• Moles of Fe₂O₃ produced: $\text{moles of Fe}_2\text{O}_3 = \frac{\text{mass of Fe}_2\text{O}_3}{\text{molar mass of Fe}_2\text{O}_3} = \frac{0.472 \, \text{g}}{159.7 \, \text{g/mol}} = 0.002955 \, \text{mol}$

2. Determine Moles of Iron (Fe³⁺)

Fe₂O₃ contains two moles of Fe atoms for every mole of Fe₂O₃.

• Moles of Fe in 0.472 g of Fe₂O₃: $\text{moles of Fe} = 2 \times 0.002955 \, \text{mol} = 0.00591 \, \text{mol}$

3. Relate to FeSO₄ · 7H₂O

Each mole of Fe in FeSO₄ · 7H₂O corresponds to one mole of FeSO₄ · 7H₂O.

• Moles of FeSO₄ · 7H₂O: $\text{moles of FeSO₄ · 7H₂O} = 0.00591 \, \text{mol}$

4. Calculate the Mass of FeSO₄ · 7H₂O

Now, using the molar mass of FeSO₄ · 7H₂O (278.01 g/mol):

• Mass of FeSO₄ · 7H₂O: $\text{mass of FeSO₄ · 7H₂O} = 0.00591 \, \text{mol} \times 278.01 \, \text{g/mol} = 1.643 \, \text{g}$

Thus, the mass of FeSO₄ · 7H₂O in the 3.660 g sample is 1.643 g.

Would you like further details on any part of the calculation? Here are some additional questions to explore this problem further:

1. How does the mass of FeSO₄ · 7H₂O compare to the total sample mass of 3.660 g?
2. What assumptions are made when calculating the moles of iron from Fe₂O₃?
3. How would the result change if the sample had been impure or contained other iron salts?
4. Can you describe the reaction steps converting Fe²⁺ to Fe₂O₃?
5. Why is NH₃ added to the reaction to precipitate Fe₂O₃?

Tip: Always double-check stoichiometric ratios when converting between compounds, especially in precipitation reactions!