An ore contains Fe3O4 and no other iron. The iron in a 38.9-gram sample of the ore is all converted by a series of chemical reactions to Fe2O3. The mass of Fe2O3 is measured to be 12.5 g. What was the mass of Fe3O4 in the sample of ore?
Please show all work, not just the answer, thanks for your help :)
12.5 g Fe2O3 x (2*molar mass Fe3O4/3*molar mass Fe2O3) = ? g Fe3O4
Why is the molar mass of Fe3O4 being multiplied by 2? and why is the molar mass for Fe2O3 being multiplied by 3? Thanks
The factor (2*molar mass Fe3O4/3*molar mass Fe2O3) is called the chemical factor. It isn't taught in schools anymore (a mistake I think) because it can be arrived at through another procedure. The entire process is this.
4Fe3O4 + 2O2 ==> 6Fe2O3 + O2
12.5g Fe2O3 x (4 mols Fe3O4/6 mols Fe2O3) or 12.5 g Fe2O3 x (2 mol Fe3O4/3 mol Fe2O3). Now we convert the mols to grams. mm = molar mass
12.5 Fe2O3 x (2 mol Fe3O4/3 mol Fe2O3) x (mm Fe3O4 in g/1 mol Fe3O4) x (1 mol Fe2O3/mm Fe2O3 in g) = now put in the numbers.
12.5 g Fe2O3 x (2/3) x (231.5/159.7) = ?
Note that mol Fe3O4 in the numerator cancels with mol Fe3O4 in the denominator AND mols Fe2O3 in the denominator cancels with mol Fe2O3 in the numerator to leave you with
12.5g Fe2O3 x (2*molar mass Fe3O4/3*molar mass Fe2O3) =
12.5g Fe2O3 x (2*231.5/3*159.7) = ?
The bottom line is that one need not go through that exercise to arrive at the chemical factor if you keep the atoms of Fe equal. So if we want to convert ANYTHING to ANYTHING (in this case we want to convert what we have (12.5g Fe2O3) in to grams Fe3O4 so
12.5 g Fe2O3 = 2*(molar mass Fe3O4/3*molar mass Fe2O3 = ?
Suppose we have 10 g Mg2P2O7 and we want to convert that to grams P2O5 we would do this.
10g Mg2P2O7 x (molar mass P2O5/molar mass Mg2P2O7) = ? (We just kept the P atoms equal)
(For whatever it's worth, Mg2P2O7 is magnesium pyrophosphate.)
So when you wrote the balanced equation, how did you know that you had to add O2 in the equation?
Thanks, sorry for the trouble
So the bottom line is, that the chemical factor is used to make the amount of atoms equal?
Actually I didn't need to add the O2 at all but I thought it would confuse you if I just wrote
2Fe3O4 ==> 3Fe2O3. I thought if I did that you would respond that the equation wasn't balanced (it isn't) but since this is for converting Fe2O3 into Fe3O4 we're only worried about the Fe atoms balancing.
As for the last note, I'm not sure I agree with you. The chemical factor is used to convert grams of one thing into grams of something else. In order to make it work you must keep the "atom of interest" equal which is what I did with the 2 and 3 above.
Oh! That makes much more sense, so the chemical factor is used to keep the atom of interest equal, which in this case was the Fe, and when we look at the atom of interest we don't need to worry about the rest of the formula being balanced, meaning in the example, as long as the Fe atoms=6, it didn't matter that the oxygen's were unbalanced, is that correct?
You have. :-).
To convert grams Mg3N2 to grams Mg the method is
g Mg3N2 x (factor) and (factor) = (3*atomic mass Mg/molar mass Mg3N2). If we wanted to know grams N2 it would be
molar mass N2/molar mass Mg3N2. etc.
The chemical factor is just a short cut for converting grams of one thing to mols of something else and then to grams of the something else. I think it's a great shortcut.
To solve this problem, we need to use stoichiometry and the law of conservation of mass. Here are the steps to find the mass of Fe3O4 in the sample of ore:
Step 1: Obtain the molar masses
The molar masses of Fe3O4 and Fe2O3 are needed to calculate the number of moles. The atomic masses are:
Fe = 55.85 g/mol
O = 16.00 g/mol
The molar mass of Fe3O4:
Fe (3 atoms) = 3 * 55.85 g/mol = 167.55 g/mol
O (4 atoms) = 4 * 16.00 g/mol = 64.00 g/mol
Total molar mass of Fe3O4 = 167.55 g/mol + 64.00 g/mol = 231.55 g/mol
The molar mass of Fe2O3:
Fe (2 atoms) = 2 * 55.85 g/mol = 111.70 g/mol
O (3 atoms) = 3 * 16.00 g/mol = 48.00 g/mol
Total molar mass of Fe2O3 = 111.70 g/mol + 48.00 g/mol = 159.70 g/mol
Step 2: Calculate the number of moles of Fe2O3
The number of moles of Fe2O3 can be found using its molar mass:
moles of Fe2O3 = mass of Fe2O3 (in grams) / molar mass of Fe2O3
moles of Fe2O3 = 12.5 g / 159.70 g/mol
moles of Fe2O3 ≈ 0.0782 mol
Step 3: Determine the mole ratio between Fe2O3 and Fe3O4
From the balanced chemical equation, we know that one mole of Fe3O4 reacts with one mole of Fe2O3. Therefore, the number of moles of Fe3O4 is also 0.0782 mol.
Step 4: Calculate the mass of Fe3O4
The mass of Fe3O4 can be calculated using the moles of Fe3O4 and its molar mass:
mass of Fe3O4 = moles of Fe3O4 * molar mass of Fe3O4
mass of Fe3O4 = 0.0782 mol * 231.55 g/mol
mass of Fe3O4 ≈ 18.1 g
Therefore, the mass of Fe3O4 in the sample of ore is approximately 18.1 grams.