What weight of sample containing 8.00 % Fe3O4 must be taken to obtain a precipitate of Fe(OH)3 that, when ignited to Fe2O3, weighs 150 mg?
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To determine the weight of the sample containing 8.00% Fe3O4 that needs to be taken, we can follow these steps:
Step 1: Find the molar mass of Fe3O4.
- The molar mass of Fe3O4 can be calculated by adding up the atomic masses of its elements.
- From the periodic table, the atomic mass of Fe is 55.85 g/mol, and the atomic mass of O is 16.00 g/mol.
- Since Fe3O4 contains 3 Fe atoms and 4 O atoms, the molar mass of Fe3O4 is (3 * 55.85) + (4 * 16.00) = 231.40 g/mol.
Step 2: Convert the percentage of Fe3O4 to grams.
- If we assume the sample has a total weight of 100 grams, then the mass of Fe3O4 in the sample can be calculated as:
mass of Fe3O4 = (8.00 / 100) * 100 g = 8.00 g
Step 3: Convert the mass of Fe3O4 to moles.
- Using the molar mass of Fe3O4, we can convert the mass of Fe3O4 to moles:
moles of Fe3O4 = mass of Fe3O4 / molar mass of Fe3O4
moles of Fe3O4 = 8.00 g / 231.40 g/mol
Step 4: Calculate the moles of Fe(OH)3 formed.
- The balanced chemical equation for the reaction is:
Fe3O4 + 6OH- -> 2Fe(OH)3
- From the equation, we can see that 1 mole of Fe3O4 yields 2 moles of Fe(OH)3.
- Therefore, the moles of Fe(OH)3 formed can be calculated as:
moles of Fe(OH)3 = (moles of Fe3O4) * (2 moles of Fe(OH)3 / 1 mole of Fe3O4)
Step 5: Convert the moles of Fe(OH)3 to grams.
- We know the mass of Fe(OH)3 formed when ignited is 150 mg (or 0.150 g).
- Using the molar mass of Fe(OH)3, we can convert the moles of Fe(OH)3 to grams:
mass of Fe(OH)3 = moles of Fe(OH)3 * molar mass of Fe(OH)3
Step 6: Calculate the weight of the sample.
- Since we assumed the total weight of the sample is 100 grams, and we found the mass of Fe3O4 in the sample is 8 grams, we can calculate the weight of the sample as:
weight of the sample = (mass of Fe(OH)3 / mass of Fe3O4) * weight of Fe3O4
By substituting the values into the equation, you can calculate the weight of the sample.