Consider the following reaction:
`Mg_3N_2 + "p"H_2O to 3Mg(OH)_2 + "q"NH_3`
When the equation is balanced the sum of p and q is

Explanation

To solve the problem, we need to balance the chemical equation given and find the values of \( p \) and \( q \) in the reaction:

\[ \text{Mg}_3\text{N}_2 + p \text{H}_2\text{O} \rightarrow 3 \text{Mg(OH)}_2 + q \text{NH}_3 \]

### Step 1: Write down the unbalanced equation
The unbalanced equation is:
\[ \text{Mg}_3\text{N}_2 + p \text{H}_2\text{O} \rightarrow 3 \text{Mg(OH)}_2 + q \text{NH}_3 \]

### Step 2: Identify the number of atoms of each element on both sides
- **Reactants:**
- Magnesium (Mg): 3
- Nitrogen (N): 2
- Hydrogen (H): \( 2p \) (from \( p \text{H}_2\text{O} \))
- Oxygen (O): \( p \) (from \( p \text{H}_2\text{O} \))

- **Products:**
- Magnesium (Mg): 3 (from \( 3 \text{Mg(OH)}_2 \))
- Nitrogen (N): \( q \) (from \( q \text{NH}_3 \))
- Hydrogen (H): \( 6 + 3q \) (6 from \( 3 \text{Mg(OH)}_2 \) and \( 3q \) from \( q \text{NH}_3 \))
- Oxygen (O): 6 (from \( 3 \text{Mg(OH)}_2 \))

### Step 3: Balance the equation
1. **Balance Magnesium (Mg):**
- Reactants: 3 Mg
- Products: 3 Mg
- Already balanced.

2. **Balance Nitrogen (N):**
- Reactants: 2 N
- Products: \( q \)
- Set \( q = 2 \) to balance nitrogen.

3. **Balance Hydrogen (H):**
- Reactants: \( 2p \)
- Products: \( 6 + 3q = 6 + 3(2) = 12 \)
- Set \( 2p = 12 \) which gives \( p = 6 \).

4. **Balance Oxygen (O):**
- Reactants: \( p = 6 \)
- Products: 6 (from \( 3 \text{Mg(OH)}_2 \))
- Already balanced.

### Step 4: Write the balanced equation
The balanced equation is:
\[ \text{Mg}_3\text{N}_2 + 6 \text{H}_2\text{O} \rightarrow 3 \text{Mg(OH)}_2 + 2 \text{NH}_3 \]

### Step 5: Find the sum of \( p \) and \( q \)
Now that we have \( p = 6 \) and \( q = 2 \):
\[ p + q = 6 + 2 = 8 \]

### Final Answer
The sum of \( p \) and \( q \) is \( 8 \).

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