Question

current attempt in progress

in a blast furnace, iron(iii) oxide reacts with coke (carbon) to produce molten iron and carbon monoxide:

fe₂o₃ + 3c → 2fe + 3co

how many kilograms of iron would be formed from 134 kg of fe₂o₃?

kg

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Explanation:

Step1: Calculate the molar mass of \(Fe_2O_3\)

The molar mass of \(Fe\) is \(55.85\space g/mol\), and the molar mass of \(O\) is \(16.00\space g/mol\).
For \(Fe_2O_3\), \(M = 2\times55.85+3\times16.00=111.7 + 48=159.7\space g/mol\)

Step2: Calculate the number of moles of \(Fe_2O_3\)

Given \(m = 134\space kg=134000\space g\)
\(n=\frac{m}{M}=\frac{134000}{159.7}\approx839.1\space mol\)

Step3: Use the stoichiometry of the reaction

From the reaction \(Fe_2O_3+3C
ightarrow2Fe + 3CO\), the mole ratio of \(Fe_2O_3\) to \(Fe\) is \(1:2\)
So the number of moles of \(Fe\) produced \(n_{Fe}=2\times n_{Fe_2O_3}=2\times839.1 = 1678.2\space mol\)

Step4: Calculate the mass of \(Fe\)

The molar mass of \(Fe\) is \(55.85\space g/mol\)
\(m_{Fe}=n_{Fe}\times M_{Fe}=1678.2\times55.85\approx93727\space g = 93.7\space kg\)

Answer:

\(93.7\space kg\)