Let's determine which of the provided chemical equations is balanced by analyzing each one:
1. Equation 1: \( \text{Mg}_3\text{N}_2 + \text{H}_2\text{O} \rightarrow 3 \text{MgO} + 2 \text{NH}_3 \)
On the left side, we have:
- 3 Mg atoms
- 2 N atoms
- 1 O atom
- 2 H atoms
On the right side, we have:
- 3 Mg atoms
- 2 N atoms
- 3 O atoms
- 6 H atoms
The numbers of oxygen and hydrogen atoms don't match, indicating this equation is not balanced.
2. Equation 2: \( \text{C}_3\text{H}_8 + 5 \text{O}_2 \rightarrow \text{H}_2\text{O} + 3 \text{CO}_2 \)
On the left side, we have:
- 3 C atoms
- 8 H atoms
- 10 O atoms (from 5 \( \text{O}_2 \))
On the right side, we have:
- 3 C atoms
- 2 H atoms (from 1 \( \text{H}_2\text{O} \))
- 7 O atoms (from 3 \( \text{CO}_2 \) and 1 \( \text{H}_2\text{O} \))
The numbers of hydrogen and oxygen atoms don't match, indicating this equation is not balanced.
3. Equation 3: \( \text{Zn} + 2 \text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \)
On the left side, we have:
- 1 Zn atom
- 2 H atoms
- 2 Cl atoms
On the right side, we have:
- 1 Zn atom
- 2 H atoms
- 2 Cl atoms
The number of each type of atom on both sides matches, indicating this equation is balanced.
4. Equation 4: \( 3 \text{H}_2\text{SO}_4 + 2 \text{Fe} \rightarrow \text{Fe}_2(\text{SO}_4)_3 + 3 \text{H}_2 \)
On the left side, we have:
- 3 H\(_2\)SO\(_4\)
- 6 H atoms
- 3 S atoms
- 12 O atoms
- 2 Fe atoms
On the right side, we have:
- 3 \(\text{H}_2\)
- 6 H atoms
- \(\text{Fe}_2(\text{SO}_4)_3\)
- 2 Fe atoms
- 3 S atoms
- 12 O atoms
The numbers of each type of atom on both sides match, indicating this equation is balanced.
Therefore, the equation that is balanced is:
[tex]\[ \boxed{3} \][/tex]
