To balance the given chemical reaction:
[tex]\[ Z_n + AgNO_3 \rightarrow Zn\left(NO_3\right)_2 + Ag \][/tex]
### Step-by-Step Balancing:
1. Write the unbalanced equation:
[tex]\[ Z_n + AgNO_3 \rightarrow Zn\left(NO_3\right)_2 + Ag \][/tex]
2. Identify the number of atoms of each element on both sides of the equation:
- Reactants:
- [tex]\( Zn \)[/tex]: 1
- [tex]\( Ag \)[/tex]: 1
- [tex]\( N \)[/tex]: 1
- [tex]\( O \)[/tex]: 3
- Products:
- [tex]\( Zn \)[/tex]: 1
- [tex]\( Ag \)[/tex]: 1
- [tex]\( N \)[/tex]: 2
- [tex]\( O \)[/tex]: 6
3. Balance the atoms one element at a time:
- Balance the nitrogen (N) and oxygen (O) atoms by adjusting the coefficient of [tex]\(AgNO_3\)[/tex] on the reactant side.
Since there are 2 nitrogen atoms (N) in the product [tex]\( Zn\left(NO_3\right)_2 \)[/tex], you will need 2 molecules of [tex]\( AgNO_3 \)[/tex]:
[tex]\[ Z_n + 2AgNO_3 \rightarrow Zn\left(NO_3\right)_2 + Ag \][/tex]
4. Update the atom count:
- Reactants:
- [tex]\( Zn \)[/tex]: 1
- [tex]\( Ag \)[/tex]: 2
- [tex]\( N \)[/tex]: 2
- [tex]\( O \)[/tex]: 6
- Products:
- [tex]\( Zn \)[/tex]: 1
- [tex]\( Ag \)[/tex]: 1
- [tex]\( N \)[/tex]: 2
- [tex]\( O \)[/tex]: 6
5. Balance the silver (Ag) atoms:
There are 2 silver (Ag) atoms on the reactant side (from [tex]\( 2AgNO_3\)[/tex]), so you need 2 silver atoms on the product side:
[tex]\[ Z_n + 2AgNO_3 \rightarrow Zn\left(NO_3\right)_2 + 2Ag \][/tex]
6. Update and verify the final atom count:
- Reactants:
- [tex]\( Zn \)[/tex]: 1
- [tex]\( Ag \)[/tex]: 2
- [tex]\( N \)[/tex]: 2
- [tex]\( O \)[/tex]: 6
- Products:
- [tex]\( Zn \)[/tex]: 1
- [tex]\( Ag \)[/tex]: 2
- [tex]\( N \)[/tex]: 2
- [tex]\( O \)[/tex]: 6
The equation is now balanced.
### Final Balanced Equation:
[tex]\[ Zn + 2AgNO_3 \rightarrow Zn\left(NO_3\right)_2 + 2Ag \][/tex]
This is the balanced chemical equation for the given reactants and products.
