Blast Furnace

Can some1 show me how to workout this problem?

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is
Fe2O3 + 3CO  2Fe + 3CO2
Suppose that 1.64 x 103 kg of Fe are obtained from a 2.62 x 103 kg sample of Fe2O3. Assuming that the reaction goes to completion, what is the percent purity of Fe2O3 in the original sample?

My answer is 4.9 x 1o^-4%. I am not sure about the answer.

From the balanced equation:
1mol Fe2O3 will produce 2 mol Fe

You produced 1.64*10^3 kg Fe = 1.64*10^6g Fe
Molar mass Fe = 55.847g/mol
moles of Fe produced: 1.64*10^6 / 55.847 = 29,365.9 mol Fe

This must have come from 29,365.9/2 = 14,682.9 mol Fe2O3
Molar mass Fe2O3 = 159.6887 g/mol
Mass of 14,682.9 mol Fe2O3 = 159.6887*14,682.9 = 2,344,705 g Fe2O3
This is: 2.34*10^3kg Fe2O3

You had 2.62*10^3 kg Fe2O3 impure ore:
%purity = (2.34*10^3) / 2.62*10^3) *100 = 89.3% pure

The purity of the Fe2O3 is 89.3%

Can I give you a word of advice ( NOT CRITICISM - BUT ADVICE)
I say to my own students many time: when you have completed a science problem - have a look and ask yourself if the answer you have obtained is reasonable. If it does not appear so, then go back and try and find where you went wrong.
You have obtained an answer of 4.9*10^-4 % purity: That means that 1000kg of the impure Fe2O3 will contain 0.005 kg or 5 g of Fe2O3 . Now you must know that iron is a very cheap commodity and iron manufacturers cannot use a raw material where they get only 5g of usable raw material for every ton of product they buy. This may be true of gold, platinum or diamonds., but not iron. So you must conclude that your answer is not correct. Compare what I have done with your working and see if you can find your mistake.

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