Answer to Question #154202 in General Chemistry for Sage Topaz

Question

It is desired to produce 2,000 kg of Fe in the reduction of its ore Fe₂O₃ using C as the reducing agent. What is the amount of C needed? How many Kg of the ore must be refined or reduced?

The equation: 2Fe₂O_3   +  3C = ----> 4Fe ₊ 3CO₂ 

Answer 1

Equation for the reaction;

2Fe₂O₃ + 3C + $\implies$ 4Fe + 3CO₂

Moles of Fe desired (in 2000Kg)

$Moles = \dfrac{mass(g)}{RAM(g/mol)} = \dfrac{2000 x1000g}{55.85g/mol}$

= 35810.2059 mol

Moles of carbon that is required

Mole ratio of Fe:C = 4:3

$Moles of C = \dfrac{3}{4}x35810.2059mol$

= 26 857 . 654 mol

Mass of C therefore = Moles x RAM

= 26 857 . 654 mol x 12g/mol

= 322 291 . 8532 g

= 322.292Kg

Moles of Fe₂O3 required;

Mole ratio of Fe : Fe₂O₃ = 4 : 2

Moles of Fe2O₃ = $\dfrac{2}{4} x 35810.2059 mol$

= 17 905 . 1030 mol

Mass of Fe₂O₃ = Moles x RFM

= 17 905 . 1030 mol x 159.7 g/mol

= 2 859 444 . 949g

= 2 859 . 445 Kg