For the reaction : 4Fe+3O2-->2Fe2O3, if 100 g of Fe are used how much Fe2O3 are produced?

Question

I'm having such a hard time with this..It's my physics HW and I don't know how to solve this.

Answer 1

Ian's answer is correct. I just want to expand on why he did what he did.

 

 

 

We'd first like to figure out how many moles of Fe 100 grams is.

 

You can figure that out by looking at Fe's atomic mass on the Periodic Table: 55.85. That tells you that 1 mole of Fe weighs 55.85 grams. There are 55.85 g/mol of Fe, or 1 mol of Fe/55.85 g. Use the latter to convert 100 g into mol, since that way the units will work out:

 

100 g × 1 mol / 55.85 g = 100 g×mol / 55.85 g = 100 mol / 55.85 = 1.79 mol

 

 

 

Now, let's figure out how many moles of Fe₂O₃ there are, since there are 1.79 moles of Fe. The reaction equation tells you that 4 moles of Fe and 3 moles of O₂ will produce 2 moles of Fe₂O₃. The relevant part of that for us is that 4 moles of Fe will produce 2 moles of Fe₂O₃. In other words, there are 4 mol Fe/2 mol Fe₂O₃, or 2 mol Fe₂O₃/4 mol Fe. Use the latter to convert to moles of Fe₂O₃, since that way the units will work out:

 

1.79 mol Fe × 2 mol Fe₂O₃ / 4 mol Fe = (1.79(2) mol Fe × mol Fe₂O₃) / 4 mol Fe = 3.58 mol Fe₂O₃ / 4 = 0.895 mol Fe₂O₃

 

 

 

Finally, let's figure out how many grams of Fe₂O₃ there are if we have 0.895 moles. First, we'll need to use the atomic masses of Fe and O to find out how many moles there are per gram. We've got 2 Fe molecules and 3 O molecules, so we'll just find the atomic mass of Fe and multiply it by 2, then add that to the atomic mass of O multiplied by 3:

 

2(55.85 g/mol of Fe) + 3(16.00 g/mol of O) = 111.7 + 48.00 g/mol of Fe2O3 = 159.7 g/mol of Fe₂O₃

 

So, there are 159.7 g/mol of Fe₂O₃, or 1 mol of Fe₂O₃/159.7 g. Use the former to convert 0.895 mol of Fe₂O₃ into g, since that way the units will work out:

 

0.895 mol × 159.7 g / mol = 0.895(159.7) mol×g / mol = 142.9315 g

 

 

 

Thus, 142.93 grams of Fe₂O₃ are produced.

 

 

 

So, just to review, the steps were:

 

1. Figure out how many moles of Fe there are, given 100 grams of Fe

2. Figure out how many moles of Fe₂O₃ there are, given 1.79 moles of Fe

3. Figure out how many grams of Fe₂O₃ there are, given 0.895 moles of Fe₂O₃

 

 

 

That's exactly what Ian did; he just did it all in one step (and I think he made a slight error in multiplication, which is why his answer is a couple grams off):

 

100 g Fe x (1 mol Fe / 55.85 g Fe) x (2 mol Fe₂O₃ / 4 mol Fe) x (159.69 g Fe₂O₃ / mol Fe₂O₃)

 

100 g Fe x (conversion to mol Fe) x (conversion to mol Fe₂O₃) x (conversion to g Fe₂O₃)