To balance the chemical equation \( \text{Na}_2\text{HPO}_4 \rightarrow \text{Na}_4\text{P}_2\text{O}_7 + \text{H}_2\text{O} \), we first need to determine the coefficients that will ensure the number of atoms of each element is the same on both sides.
Let's analyze the compounds:
On the left side:
- Sodium (Na): 2
- Hydrogen (H): 1
- Phosphorus (P): 1
- Oxygen (O): 4
On the right side:
- Sodium (Na): 4 (in Na4P2O7)
- Phosphorus (P): 2 (in Na4P2O7)
- Oxygen (O): 7 (in Na4P2O7) + 1 (in H2O) = 8
- Hydrogen (H): 2 (in H2O)
Now, we want to balance the equation. A breakdown would look as follows:
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To balance Sodium (Na), we put a coefficient of 2 in front of \( \text{Na}_2\text{HPO}_4 \):
- Left side: 4 Na, 1 H, 1 P, 4 O
- So far: \( 2\text{Na}_2\text{HPO}_4 \rightarrow \text{Na}_4\text{P}_2\text{O}_7 + \text{H}_2\text{O} \)
-
Update the right side to balance Phosphorus (P) by using a coefficient of 1 in front of \( \text{Na}_4\text{P}_2\text{O}_7 \):
- Let's check:
- Left side: 4 Na, 2 H, 2 P, 8 O
- Right side: 4 Na, 2 H, 2 P, 8 O
The final balanced equation is: \[ 2 \text{Na}_2\text{HPO}_4 \rightarrow 1 \text{Na}_4\text{P}_2\text{O}_7 + 2 \text{H}_2\text{O} \]
So the coefficients are:
- \( 2 \) for \( \text{Na}_2\text{HPO}_4 \)
- \( 1 \) for \( \text{Na}_4\text{P}_2\text{O}_7 \)
- \( 2 \) for \( \text{H}_2\text{O} \)
The balanced equation is: \[ 2 \text{Na}_2\text{HPO}_4 \rightarrow 1 \text{Na}_4\text{P}_2\text{O}_7 + 2 \text{H}_2\text{O} \]