Question
Balance the following equations : $\ce{Fe_2O_3}+ H_2 \rightarrow Fe + \ce{H_2O}$

Answer

$\ce{Fe_2O_3}+ H_2 \rightarrow Fe + \ce{H_2O}$ There are $2$ atoms of $Fe$ on left.
$\ce{Fe_2O_2}+ H_2 \rightarrow \ce{2Fe} + \ce{H_2O}$
Now equate $O$ atoms and use $\ce{3H_2 O}$ on right.
$\ce{Fe_2O_2}+ H_2 \rightarrow 2 Fe +\ce{3 H _2 O}$
But $H$ atoms on right are $6$ make $\ce{3 H _2}$ on left.
$\therefore \ce{Fe_2 O_3}+\ce{3 H_2} \rightarrow 2 Fe +\ce{3H_2O} $ It is balanced.

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