To balance the equation \(2 \text{NH}_4\text{NO}_3 → ____ \text{N}_2 + __ \text{H}_2\text{O} + ___ \text{O}_2\), we need to determine the correct coefficients for each product.
-
Start with the reactant:
- 2 moles of \( \text{NH}_4\text{NO}_3 \) contain:
- Nitrogen (N): \( 2 \times 2 = 4 \) N
- Hydrogen (H): \( 2 \times 4 = 8 \) H
- Oxygen (O): \( 2 \times 3 = 6 \) O
- 2 moles of \( \text{NH}_4\text{NO}_3 \) contain:
-
Analyzing products to balance Nitrogen (N):
- To produce 4 N: \( 2 \text{N}_2 \) (because each \( \text{N}_2 \) has 2 N).
-
Balancing Hydrogen (H):
- Producing 8 H from the water requires \( 4 \text{H}_2\text{O} \) (because each \( \text{H}_2\text{O} \) has 2 H).
-
Balancing Oxygen (O):
- The total O from the products needs to equal 6.
- From \( 4 \text{H}_2\text{O} \): \( 4 \) O
- From \( 2 \text{N}_2 \): \( 0 \) O (does not contribute)
- From \( \frac{1}{2} \text{O}_2 \): \( 2 \) O
- Total O: \( 4 + 2 = 6 \)
Putting that all together, we get: \[ 2 \text{NH}_4\text{NO}_3 → 2 \text{N}_2 + 4 \text{H}_2\text{O} + 1 \text{O}_2 \]
So the balanced coefficients are 2, 4, and 1.
Therefore, the correct response is:
2, 4, 1.