In the reduction zone of a blast furnace, hematite (\text{Fe}_2\text{O}_3) reacts with gas… — JAMB UTME

In the reduction zone of a blast furnace, hematite (

\text{Fe}_2\text{O}_3

) reacts with gaseous carbon(II) oxide (

\text{CO}

) according to the balanced equation:

\text{Fe}_2\text{O}_3(s) + 3\text{CO}(g) \rightarrow 2\text{Fe}(l) + 3\text{CO}_2(g)

If a furnace charge containing $160.0\text{ kg}$ of pure $\text{Fe}_2\text{O}_3$ is reacted with $40.32\text{ m}^3$ of $\text{CO}$ gas measured at STP, which of the following correctly identifies the limiting reactant and the maximum mass of iron produced?
[ $\text{Fe} = 56$ , $\text{O} = 16$ , $\text{C} = 12$ ; Molar volume of gas at STP $= 22.4\text{ dm}^3\text{mol}^{-1}$ ]

$\text{CO}$ is the limiting reactant, yielding $67.2\text{ kg}$ of iron.Answer
B
$\text{Fe}_2\text{O}_3$ is the limiting reactant, yielding $112.0\text{ kg}$ of iron.
C
Carbon ( $\text{C}$ ) acts as the direct reducing agent in this zone, yielding $112.0\text{ kg}$ of iron.
D
$\text{CO}$ is the limiting reactant, yielding $100.8\text{ kg}$ of iron.

Answer

Carbon(II) oxide (

\text{CO}

) is the limiting reactant, yielding

67.2\text{ kg}

of iron.

Carbon(II) oxide (

\text{CO}

) is the limiting reactant because

1800\text{ mol}

\text{CO}

can only reduce

600\text{ mol}

\text{Fe}_2\text{O}_3

out of the available

1000\text{ mol}

. Based on the stoichiometric ratio of

3\text{ mol CO} : 2\text{ mol Fe}

1800\text{ mol}

\text{CO}

yields

1200\text{ mol}

of iron metal, which corresponds to

67.2\text{ kg}

Step-by-Step Solution

Calculate the moles of reactants provided

Moles of

\text{Fe}_2\text{O}_3 = \frac{160,000\text{ g}}{160\text{ g/mol}} = 1000\text{ mol}

. Moles of

\text{CO} = \frac{40,320\text{ dm}^3}{22.4\text{ dm}^3/\text{mol}} = 1800\text{ mol}

Converting quantities to moles allows stoichiometric comparison.

Determine the limiting reactant using the balanced equation stoichiometry

According to

\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2

1000\text{ mol}

\text{Fe}_2\text{O}_3

requires

3000\text{ mol}

\text{CO}

. Since only

1800\text{ mol}

\text{CO}

is available,

\text{CO}

is the limiting reactant.

The reactant that produces the lesser amount of product limits the reaction.

Calculate the theoretical yield of iron in kilograms

Moles of

\text{Fe}

produced

= 1800\text{ mol CO} \times \frac{2\text{ mol Fe}}{3\text{ mol CO}} = 1200\text{ mol Fe}

. Mass of

\text{Fe} = 1200\text{ mol} \times 56\text{ g/mol} = 67,200\text{ g} = 67.2\text{ kg}

Multiply moles of limiting reactant by the mole ratio and molar mass of iron.

Key Concept

Stoichiometric limiting reactant analysis in the blast furnace reduction of iron ore

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