Suppose that 1.78 x 10^3 kg of Fe are obtained from a 5.80 x 10^3 kg sample of Fe2O3. Assuming that the reaction goes to completion, what is the percent purity of Fe2O3 in the original sample?

Convert kg Fe2O3 to kg Fe. The easy way to do that is

5.80E3 kg x (2*molar mass Fe/molar mass Fe2O3) = ?
Then %purity = (1.78E3/?)*100 = ?

To find the percent purity of Fe2O3 in the original sample, we need to compare the mass of Fe2O3 obtained with the total mass of the original sample.

First, let's calculate the amount of Fe2O3 that was present in the original sample. We can assume that the reaction goes to completion, meaning all the Fe2O3 reacts to form Fe.

Given:
Mass of Fe obtained (mFe) = 1.78 x 10^3 kg
Mass of the original sample (mOriginal) = 5.80 x 10^3 kg

Now, we need to determine the molar ratios between Fe2O3 and Fe. The balanced equation for the reaction is:
Fe2O3 + 3CO -> 2Fe + 3CO2

From the balanced equation, we can see that the molar ratio of Fe2O3 to Fe is 1:2. This means that for every 1 mole of Fe2O3, we should obtain 2 moles of Fe.

Next, we need to convert the masses given into moles using the molar mass of Fe2O3. The molar mass of Fe2O3 is calculated by adding the atomic masses of iron (Fe) and oxygen (O) atoms in its chemical formula:
Molar mass of Fe2O3 = (2 x atomic mass of Fe) + (3 x atomic mass of O)

Using the atomic masses from the periodic table:
Molar mass of Fe2O3 = (2 x 55.85 g/mol) + (3 x 16.00 g/mol)

Now, we can calculate the number of moles of Fe2O3 in the original sample:
Moles of Fe2O3 = (Mass of Fe2O3) / (Molar mass of Fe2O3)

Finally, we can calculate the percent purity of Fe2O3 in the original sample:
Percent purity = (Moles of Fe2O3 / Total moles) × 100

Please note that in this calculation, we assume that there is only Fe2O3 in the original sample and no impurities.

By following these steps and substituting the given values, you should be able to calculate the percent purity of Fe2O3 in the original sample.