To balance the chemical equation, we need to ensure that the number of atoms of each element on the reactant side is equal to the number of atoms of the same element on the product side. Here is the unbalanced equation:
[tex]\( Al (s) + 3 Zn(NO_3)_2(aq) \rightarrow Al(NO_3)_3(aq) + Zn (s) \)[/tex]
1. Balance the Aluminum (Al) atoms:
- There is 1 Al atom on the reactant side and 1 Al atom on the product side.
- No coefficient change is needed for Al at this step.
2. Balance the Zinc (Zn) atoms:
- There are 3 Zn atoms on the reactant side (3 [tex]\( Zn(NO_3)_2 \)[/tex]) and 1 Zn atom on the product side.
- Therefore, we need to place a coefficient of 3 in front of [tex]\( Zn \)[/tex] on the product side:
[tex]\[
Al (s) + 3 Zn(NO_3)_2(aq) \rightarrow Al(NO_3)_3(aq) + 3 Zn (s)
\][/tex]
3. Balance the Nitrate [tex]\( (NO_3) \)[/tex] groups:
- On the reactant side, there are 6 nitrate groups (3 [tex]\(\times\)[/tex] 2 from [tex]\( Zn(NO_3)_2 \)[/tex]).
- On the product side, there are 3 nitrate groups (from [tex]\( Al(NO_3)_3 \)[/tex]).
- To balance the oxygens and nitrogens, we notice that each [tex]\( Zn(NO_3)_2 \)[/tex] unit already contributes 2 nitrate groups, which is correctly balancing the oxygens and nitrogens when paired with the product terms.
After following these steps, the balanced equation is:
[tex]\[
Al (s) + 3 Zn(NO_3)_2(aq) \rightarrow Al(NO_3)_3(aq) + 3 Zn (s)
\][/tex]
We observe that the coefficient for [tex]\( Al (s) \)[/tex] is [tex]\( 1 \)[/tex].
Therefore, the correct answer is:
C. 1
