One thing that is critical to remember is that all of the atoms on one side need to be on the other side in exactly the same quantities. For example, in number two, the left side has:
1 Fe
3 O
3 H
The right side has:
2 Fe
4 O
2 H
What you do now is pick one atom, for example Fe. Figure out what you need to multiply by what to get the numbers of Fe on both sides equal. In this case, you multiply the Fe(OH)3 by 2.
2 Fe(OH)3 ---> Fe2O3 + H2O
Now the left side has:
2 Fe
6 O
6 H
Now, you need to balance the O by increasing the number of O's on the right. The only way to do this without changing the number of Fe's again is to increase the number of H2O molecules; multiply it by 3.
2 Fe(OH)3 ---> Fe2O3 + 3 H2O
Now the right side has:
2 Fe
6 O
6 H
The numbers of each kind of atom are the same on both sides, so you're done. See how the process works?
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