Question

Lars is balancing equations with his study group. He is unsure about one equation because each member of the study group came up with a different answer. Which is the proper way to balance the equation Ca(OH)2 + H3PO4 → Ca3(PO4)2 + H2O?

Ca(OH)2 + H3PO4 → Ca3(PO4)2 + 6H2O
3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O
3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 3H2O
Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O

Answer 1

To balance the equation \( \text{Ca(OH)}_2 + \text{H}_3\text{PO}_4 \rightarrow \text{Ca}_3(\text{PO}_4)_2 + \text{H}_2\text{O} \), we will look at the number of each type of atom on both sides of the equation.

1. **Reactants:**
- Calcium (Ca): 1 (in \( \text{Ca(OH)}_2 \))
- Oxygen (O): 2 (from \( \text{Ca(OH)}_2 \)) + 4 (from \( \text{H}_3\text{PO}_4 \)) = 6
- Hydrogen (H): 2 (from \( \text{Ca(OH)}_2 \)) + 3 (from \( \text{H}_3\text{PO}_4 \)) = 5
- Phosphorus (P): 1 (in \( \text{H}_3\text{PO}_4 \))

2. **Products:**
- Calcium: 3 (from \( \text{Ca}_3(\text{PO}_4)_2 \))
- Oxygen: 8 (from \( \text{Ca}_3(\text{PO}_4)_2 \)) + 1 (from \( \text{H}_2\text{O} \)) = 9
- Hydrogen: 2 (from \( \text{H}_2\text{O} \))
- Phosphorus: 2 (in \( \text{Ca}_3(\text{PO}_4)_2 \))

To balance this equation, we need to equalize the number of each atom on each side.

By inspection (and testing the different options provided), the option that seems to make the most sense is:

**3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O**

Let’s verify:

- **Reactants:**
- Ca: \( 3 \) (from \( 3 \times \text{Ca(OH)}_2 \))
- H: \( 6 \) (from \( 3 \times \text{Ca(OH)}_2 \)) + \( 6 \) (from \( 2 \times \text{H}_3\text{PO}_4 \)) = \( 12 \)
- O: \( 6 \) (from \( 3 \times \text{Ca(OH)}_2 \)) + \( 8 \) (from \( 2 \times \text{H}_3\text{PO}_4 \)) = \( 14 \)
- P: \( 2 \) (from \( 2 \times \text{H}_3\text{PO}_4 \))

- **Products:**
- Ca: \( 3 \) (from \( \text{Ca}_3(\text{PO}_4)_2 \))
- H: \( 6 \) (from \( 6 \times \text{H}_2\text{O} \))
- O: \( 8 \) (from \( \text{Ca}_3(\text{PO}_4)_2 \)) + \( 6 \) (from \( 6 \times \text{H}_2\text{O} \)) = \( 14 \)
- P: \( 2 \) (in \( \text{Ca}_3(\text{PO}_4)_2 \))

Now both sides balance perfectly with:

**3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O**

Thus, the proper way to balance the equation is:

**3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O**