A sample weighing 3.064 g is a mixture of Fe2O3 (molar mass = 159.69) and Al2O3 (molar mass = 101.96).
When heat and a stream of H2 gas is applied to the sample, the Fe2O3 reacts to form metallic Fe and H2O(g). The Al2O3 does not react.
If the sample residue weighs 2.407 g, what is the mass fraction of Fe2O3 in the original sample?
I am not exactly sure where to start with this question. Would this be correct?
Mass of Fe2O3 = [(2.407 g - mass of Al2O3) / 55.85 g/mol] x (1 mol Fe2O3 / 2 mol Fe) x 159.69 g/mol
Actually, the mass of Fe in the residue is 2.407-Al2O3. The Fe2O3 has all lost its oxygen, leaving only Fe.
So, if you started out with x moles of Fe2O3 and y grams of Al2O3, then converting the Fe2O3 to grams,
159.69x + y = 3.064
55.85(2x) + y = 2.407
The equations may look a bit funny, but we really don't have to convert the moles of Al2O3 to grams, since the mass doesn't change. And, of course the (2x) appears because each mole of Fe2O3 has 2 Fe atoms in it.
Solving the equations yields
x = 0.01369 moles Fe2O3
y = 0.8778 grams of Al2O3
Now we need to convert the moles back to grams: .01369 moles = 2.1862 grams Fe2O3
2.1862/3.064 = 71.35%
Actually, we really didn't have to convert the moles back to grams, since we had the mass of Al2O3 already. Just subtract its fraction from 100%.
Well, my dear inquisitor, it seems that you are on the right track! You have correctly identified that to determine the mass fraction of Fe2O3, you need to find the mass of Fe2O3 in the sample.
So, let's break it down step by step:
1. Find the mass of Al2O3 in the sample:
Mass of Al2O3 = original sample weight - residue weight
= 3.064 g - 2.407 g
2. Calculate the mass of Fe2O3:
Mass of Fe2O3 = original sample weight - mass of Al2O3
= 3.064 g - (3.064 g - 2.407 g)
3. Calculate the mass fraction of Fe2O3:
Mass fraction of Fe2O3 = (Mass of Fe2O3 / original sample weight) * 100%
And there you have it! With these calculations, you should be able to determine the mass fraction of Fe2O3 in the original sample. Best of luck, my clever friend!
Yes, your approach is correct. To determine the mass fraction of Fe2O3 in the original sample, you need to find the mass of Fe2O3 in the residue and then divide it by the mass of the original sample.
Let's calculate the mass of Fe2O3 in the residue first:
Mass of Fe2O3 in the residue = mass of residue - mass of Al2O3
Now, let's substitute the given values:
Mass of Fe2O3 in the residue = 2.407 g - mass of Al2O3
Next, convert the mass of Fe2O3 in the residue to moles:
Moles of Fe2O3 in the residue = (mass of Fe2O3 in the residue / molar mass of Fe2O3)
Now, let's introduce the molar ratio of Fe2O3 and Fe in the reaction:
Molar ratio of Fe2O3 to Fe = 1 mol Fe2O3 / 2 mol Fe
Finally, calculate the mass fraction of Fe2O3 in the original sample:
Mass fraction of Fe2O3 = (moles of Fe2O3 in the residue x molar ratio of Fe2O3 to Fe x molar mass of Fe2O3) / mass of the original sample
Therefore, your initial equation:
Mass of Fe2O3 = [(2.407 g - mass of Al2O3) / 55.85 g/mol] x (1 mol Fe2O3 / 2 mol Fe) x 159.69 g/mol
is a correct way to find the mass fraction of Fe2O3 in the original sample. Just remember to substitute the value for the molar mass of Fe2O3 correctly (it should be 159.69 g/mol, not 55.85 g/mol).
You're on the right track! To find the mass fraction of Fe2O3 in the original sample, you need to determine the mass of Fe2O3 and then divide it by the total sample mass.
Here's a step-by-step breakdown of how to approach this problem:
1. Start by finding the mass of Al2O3 in the original sample. The mass of the sample residue (2.407 g) is equal to the sum of the masses of Fe2O3 and Al2O3 in the original sample. So, the mass of Al2O3 can be calculated as follows:
Mass of Al2O3 = Mass of sample residue - Mass of Fe2O3
2. Next, calculate the moles of Fe2O3 present in the original sample. Use the molar mass of Fe2O3 (159.69 g/mol) to convert the mass of Fe2O3 to moles:
Moles of Fe2O3 = Mass of Fe2O3 / Molar mass of Fe2O3
3. Since the reaction between Fe2O3 and H2 produces Fe and H2O, the moles of Fe produced will be half of the moles of Fe2O3 consumed. Therefore, divide the moles of Fe2O3 calculated in step 2 by 2 to get the moles of Fe:
Moles of Fe = Moles of Fe2O3 / 2
4. To find the mass of Fe in the original sample, multiply the moles of Fe calculated in step 3 by the molar mass of Fe:
Mass of Fe = Moles of Fe x Molar mass of Fe
5. Finally, calculate the mass fraction of Fe2O3 in the original sample by dividing the mass of Fe2O3 (found in step 1) by the sum of the masses of Fe2O3 and Al2O3:
Mass fraction of Fe2O3 = Mass of Fe2O3 / (Mass of Fe2O3 + Mass of Al2O3)
Now you can substitute the appropriate values into the formulas to find the mass fraction of Fe2O3 in the original sample.