The multistep smelting of ferric oxide to form elemental iron occurs at high temperatures in a blast furnace. In the first step, ferric oxide reacts with carbon monoxide to form Fe₃O.₄ This substance reacts with more carbon monoxide to formiron(II) oxide, which reacts with still more carbon monoxide to form molten iron. Carbon dioxide is also produced in each step.
(a) Write an overall balanced equation for the iron-smelting process.
(b) How many grams of carbon monoxide are required to form 45.0 metric tons of iron from ferric oxide?

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kobenhavn kobenhavn · Answer 1 · 2021-01-30T03:00:28+01:00

Answer: a) [tex]Fe_2O_3+3CO\rightarrow 2Fe+3CO_2[/tex]

b) 33749996 grams

Explanation:

a) The balanced chemical reactions will be :

[tex]3Fe_2O_3+CO\rightarrow CO_2+2Fe_3O_4[/tex]

[tex]2Fe_3O_4+2CO\rightarrow 6FeO+2CO_2[/tex]

[tex]6FeO+6CO\rightarrow 6Fe+6CO_2[/tex]

Overall equation : [tex]3Fe_2O_3+9CO\rightarrow 6Fe+9CO_2[/tex]

Overall balanced equation : [tex]Fe_2O_3+3CO\rightarrow 2Fe+3CO_2[/tex]

b) Amount of iron = 45 metric ton = 45000 kg = 45000000g

To calculate the moles :

[tex]\text{Moles of solute}=\frac{\text{given mass}}{\text{Molar Mass}}[/tex]

[tex]\text{Moles of} Fe=\frac{45000000g}{56g/mol}=803571moles[/tex]

[tex]Fe_2O_3+3CO\rightarrow 2Fe+3CO_2[/tex]

According to stoichiometry :

2 moles of [tex]Fe[/tex] are produced from= 3 moles of [tex]CO[/tex]

Thus 803571 moles of [tex]Fe[/tex] are produced from=[tex]\frac{3}{2}\times 803571=1205357moles[/tex] of [tex]CO[/tex]

Mass of [tex]CO=moles\times {\text {Molar mass}}=1205357moles\times 28g/mol=33749996g[/tex]

Thus 33749996 g of carbon monoxide are required to form 45.0 metric tons of iron from ferric oxide