To determine which chemical equation is balanced, we need to examine the number of atoms of each element on both the reactant (left-hand side, LHS) and product (right-hand side, RHS) sides of each equation. An equation is balanced if the number of atoms of each element is the same on both sides.
Let's go through each equation step-by-step to identify if it is balanced.
### 1. Equation:
[tex]\[ Mg_3N_2 + H_2O \rightarrow 3 MgO + 2 NH_3 \][/tex]
- LHS:
- [tex]\( Mg_3N_2 \)[/tex]:
- Mg: 3
- N: 2
- [tex]\( H_2O \)[/tex]:
- H: 2
- O: 1
Totals on LHS:
- Mg: 3
- N: 2
- H: 2
- O: 1
- RHS:
- [tex]\( 3 MgO \)[/tex]:
- Mg: 3
- O: 3
- [tex]\( 2 NH_3 \)[/tex]:
- N: 2
- H: 6
Totals on RHS:
- Mg: 3
- N: 2
- H: 6
- O: 3
The numbers of Hydrogen (H) and Oxygen (O) atoms are not balanced, so this equation is not balanced.
### 2. Equation:
[tex]\[ C_3H_8 + 5 O_2 \rightarrow H_2O + 3 CO_2 \][/tex]
- LHS:
- [tex]\( C_3H_8 \)[/tex]:
- C: 3
- H: 8
- [tex]\( 5 O_2 \)[/tex]:
- O: 10
Totals on LHS:
- C: 3
- H: 8
- O: 10
- RHS:
- [tex]\( H_2O \)[/tex]:
- H: 2
- O: 1
- [tex]\( 3 CO_2 \)[/tex]:
- C: 3
- O: 6
Totals on RHS:
- C: 3
- H: 2
- O: 7 (1 from water and 6 from CO2)
The numbers of Hydrogen (H) and Oxygen (O) atoms are not balanced, so this equation is not balanced.
### 3. Equation:
[tex]\[ Zn + 2 HCl \rightarrow ZnCl_2 + H_2 \][/tex]
- LHS:
- [tex]\( Zn \)[/tex]:
- Zn: 1
- [tex]\( 2 HCl \)[/tex]:
- H: 2
- Cl: 2
Totals on LHS:
- Zn: 1
- H: 2
- Cl: 2
- RHS:
- [tex]\( ZnCl_2 \)[/tex]:
- Zn: 1
- Cl: 2
- [tex]\( H_2 \)[/tex]:
- H: 2
Totals on RHS:
- Zn: 1
- H: 2
- Cl: 2
The numbers of Zinc (Zn), Hydrogen (H), and Chlorine (Cl) atoms are balanced, so this equation is balanced.
### 4. Equation:
[tex]\[ 3 H_2SO_4 + 2 Fe \rightarrow Fe_2(SO_4)_3 + H_2 \][/tex]
- LHS:
- [tex]\( 3 H_2SO_4 \)[/tex]:
- H: 6
- S: 3
- O: 12
- [tex]\( 2 Fe \)[/tex]:
- Fe: 2
Totals on LHS:
- H: 6
- S: 3
- O: 12
- Fe: 2
- RHS:
- [tex]\( Fe_2(SO_4)_3 \)[/tex]:
- Fe: 2
- S: 3
- O: 12
- [tex]\( H_2 \)[/tex]:
- H: 2
Totals on RHS:
- Fe: 2
- S: 3
- O: 12
- H: 2
The number of Hydrogen (H) atoms is not balanced, so this equation is not balanced.
### Conclusion:
The only equation that is balanced is the third one:
[tex]\[ Zn + 2 HCl \rightarrow ZnCl_2 + H_2 \][/tex]
