Q22 / 75 · JEE Main 2025 (24 Jan Shift 1) · Chemistry
Consider the following reaction occurring in the blast furnace:
$\mathrm{Fe}_3 \mathrm{O}_{4(\mathrm{~s})}+4 \mathrm{CO}_{(\mathrm{g})} \rightarrow 3 \mathrm{Fe}_{(\mathrm{l})}+4 \mathrm{CO}_{2(\mathrm{~g})}$
' $x$ ' kg of iron is produced when $2.32 \times 10^3 \mathrm{~kg} \mathrm{Fe}_3 \mathrm{O}_4$ and $2.8 \times 10^2 \mathrm{~kg} \mathrm{CO}$ are brought together in the furnace. The value of ' $x$ ' is _____. (nearest integer)
Given:
molar mass of $\mathrm{Fe}_3 \mathrm{O}_4=232 \mathrm{~g} \mathrm{~mol}^{-1}$
molar mass of $\mathrm{CO}=28 \mathrm{~g} \mathrm{~mol}^{-1}$
molar mass of $\left.\mathrm{Fe}=56 \mathrm{~g} \mathrm{~mol}^{-1}\right\}$
Correct answer: 420
Solution
$\begin{aligned}
& \text { moles of } \mathrm{Fe}_3 \mathrm{O}_4=\frac{2.32 \times 10^3 \times 10^3}{232}=10000 \mathrm{~mol} \\
& \text { moles of } \mathrm{CO}=\frac{2.8 \times 10^2 \times 10^3}{28}=10000 \mathrm{~mol} \\
& \mathrm{Fe}_3^3 \mathrm{O}_4+4 \mathrm{CO} \longrightarrow 3 \mathrm{Fe}+4 \mathrm{CO}_2 \\
& 10^4 \mathrm{~mol} \quad 10^4 \mathrm{~mol}
\end{aligned}$
CO is L.R.
mole of $\mathrm{Fe}=\frac{3}{4} \times 10^4$
mass of $\mathrm{Fe}=\frac{3}{4} \times \frac{10^4 \times 56}{1000} \mathrm{~kg}=420 \mathrm{~kg}$
Hence, the correct answer is 420.