Question
Iron can be obtained by reduction of iron oxide $$\left( {F{e_3}{O_4}} \right)$$ with $$CO$$ according to the reaction : $$F{e_3}{O_4} + 4CO \to 3Fe + 4C{O_2}$$
How many kilograms of $$F{e_3}{O_4}$$ should be heated with $$CO$$ to get $$3\,kg$$ of iron ?
A.
8.12$$\,kg$$
B.
4.14$$\,kg$$
C.
6.94$$\,kg$$
D.
16.8$$\,kg$$
Answer :
4.14$$\,kg$$
Solution :
\[\underset{232\,g}{\mathop{F{{e}_{3}}{{O}_{4}}}}\,+4CO\to \underset{\begin{smallmatrix}
56\times 3 \\
=168\,g
\end{smallmatrix}}{\mathop{3Fe}}\,+4C{{O}_{2}}\]
$$3\,moles$$ of $$Fe$$ is produced from $$1\,mole$$ of $$F{e_3}{O_4}$$
$$168\,g$$ of $$Fe$$ is produced from $$232\,g$$ of $$F{e_3}{O_4}$$
$$3\,kg$$ of $$Fe$$ will be produced from $$\frac{{232}}{{168}} \times 3000\,g$$ $$ = 4142.8\,g$$ or $$4.14\,kg$$ of $$F{e_3}{O_4}$$