Answer : The percent purity of
in the original sample is 87.94 %
Explanation :
The given balanced chemical reaction is:
![Fe_2O3+3CO\rightarrow 2Fe+3CO_2](https://tex.z-dn.net/?f=Fe_2O3%2B3CO%5Crightarrow%202Fe%2B3CO_2)
First we have to calculate the mass of Fe.
![\text{Moles of }Fe=\frac{\text{Mass of }Fe}{\text{Molar mass of }Fe}](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DFe%3D%5Cfrac%7B%5Ctext%7BMass%20of%20%7DFe%7D%7B%5Ctext%7BMolar%20mass%20of%20%7DFe%7D)
Molar mass of Fe = 55.8 g/mole
![\text{Moles of }Fe=\frac{1.79\times 10^3kg}{55.8g/mole}=\frac{1.79\times 10^3\times 1000g}{55.8g/mole}=3.15\times 10^4mole](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DFe%3D%5Cfrac%7B1.79%5Ctimes%2010%5E3kg%7D%7B55.8g%2Fmole%7D%3D%5Cfrac%7B1.79%5Ctimes%2010%5E3%5Ctimes%201000g%7D%7B55.8g%2Fmole%7D%3D3.15%5Ctimes%2010%5E4mole)
Now we have to calculate the moles of ![Fe_2O_3](https://tex.z-dn.net/?f=Fe_2O_3)
From the balanced chemical reaction we conclude that,
As, 2 moles of Fe produced from 1 mole of ![Fe_2O_3](https://tex.z-dn.net/?f=Fe_2O_3)
So,
of Fe produced from
mole of ![Fe_2O_3](https://tex.z-dn.net/?f=Fe_2O_3)
Now we have to calculate the mass of ![Fe_2O_3](https://tex.z-dn.net/?f=Fe_2O_3)
![\text{ Mass of }Fe_2O_3=\text{ Moles of }Fe_2O_3\times \text{ Molar mass of }Fe_2O_3](https://tex.z-dn.net/?f=%5Ctext%7B%20Mass%20of%20%7DFe_2O_3%3D%5Ctext%7B%20Moles%20of%20%7DFe_2O_3%5Ctimes%20%5Ctext%7B%20Molar%20mass%20of%20%7DFe_2O_3)
Molar mass of
= 159.69 g/mole
![\text{ Mass of }Fe_2O_3=(15750moles)\times (159.69g/mole)=2.515\times 10^6g=2.515\times 10^3kg](https://tex.z-dn.net/?f=%5Ctext%7B%20Mass%20of%20%7DFe_2O_3%3D%2815750moles%29%5Ctimes%20%28159.69g%2Fmole%29%3D2.515%5Ctimes%2010%5E6g%3D2.515%5Ctimes%2010%5E3kg)
Now we have to calculate the percent purity of
in the original sample.
Mass of original sample = ![2.86\times 10^3kg](https://tex.z-dn.net/?f=2.86%5Ctimes%2010%5E3kg)
![\text{Percent purity}=\frac{\text{Mass of }Fe_2O_3}{\text{Mass of sample}}\times 100](https://tex.z-dn.net/?f=%5Ctext%7BPercent%20purity%7D%3D%5Cfrac%7B%5Ctext%7BMass%20of%20%7DFe_2O_3%7D%7B%5Ctext%7BMass%20of%20sample%7D%7D%5Ctimes%20100)
![\text{Percent purity}=\frac{2.515\times 10^3kg}{2.86\times 10^3kg}\times 100=87.94\%](https://tex.z-dn.net/?f=%5Ctext%7BPercent%20purity%7D%3D%5Cfrac%7B2.515%5Ctimes%2010%5E3kg%7D%7B2.86%5Ctimes%2010%5E3kg%7D%5Ctimes%20100%3D87.94%5C%25)
Therefore, the percent purity of
in the original sample is 87.94 %