The reduction of iron(III) oxide (Fe203) to pure iron during the first step of steelmaking,

2Fe2O3(s) ---> 4 Fe(s) + 302(g)

is driven by the high-temperature combustion of coke, a purified form of coal:

C(s)+ O2(g) --> CO2(g)

Suppose at the temperature of a blast furnace the Gibbs free energies of formation ΔGr of CO2 and Fe2O3 are-439. kJ/mol and-830. kJ/mol, respectively. Calculate the minimum mass of coke needed to produce 850. t of pure iron. (One metric ton, symbol t, equals 1000 kg.)

The minimum mass of coke needed to produce 850 t is equal to 172223.4 kg

Explanation:

The balanced reaction for the formation of the is as follows:

2Fe + 3/2O2 = Fe2O3, ΔG = -830 kJ/mol

Fe2O3 = 2Fe + 3/2O2, ΔG = +830 kJ/mol

2Fe2O3 = 4Fe + 3O2, ΔG = (+830*2) = +1660 kJ/mol

the mass of iron = 850 ton = 850000 kg

the necessary energy will be equal to:

Energy = (1660*850000)/(4*56x10^-3) = 6.299x10^9 kJ

the energy released by 1 mole of CO2 is equal to 439 kJ/mol

mol of CO2 = 6.299x10^9/439 = 1.434x10^7 mol

now we will calculate the kilograms of coke that are required:

mass of coke = 1.434x10^7 mol * (12.01 g/mol) * (1 kg/1000 g) = 172223.4 kg

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