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Question

How would you balance the following equation: $$Fe + O_{2} \rightarrow Fe_{2}O_{3}$$?


Solution

Step 1: Tally the number of atoms based on subscript.
$$Fe + O_{2} \rightarrow Fe_{2}O_{3}$$ (unbalanced)
left side: $$Fe = 1; O = 2$$
right side: $$Fe = 2; O = 3$$

Step 2: Start balancing the simple molecules first, in this case the $$O_{2}$$
$$Fe + 3O_{2} \rightarrow Fe_{2}O_{3}$$
left side: $$Fe = 1; O = 2 \times 3 = 6$$
right side: $$Fe = 2; O = 3$$

Since there are now $$6\ O$$ atoms on the left, there must also be $$6\ O$$ atoms on the right. Notice that the right hand is one big molecule so whatever coefficient we would use to balance the $$O$$ atoms, we would also need to apply to the bonded $$Fe$$ atom.

$$Fe + 3O_{2} \rightarrow 2Fe_{2}O_{3}$$
left side: $$Fe = 1; O = 2 \times 3 = 6$$
right side: $$Fe = 2 \times 2 = 4; O = 3 \times 2 = 6$$

Step 3: Now balance the rest of the equation.
$$4Fe + 3O_{2} \rightarrow 2Fe_{2}O_{3}$$
left side: $$Fe = 1 \times 4 = 4; O = 2 \times 3 = 6$$
right side: $$Fe = 2 \times 2 = 4; O = 3 \times 2 = 6$$

The equation is now balanced.

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