To determine which chemical equation correctly models the law of conservation of mass, we need to ensure that the number of each type of atom on the left-hand side (reactants) is equal to the number of each type of atom on the right-hand side (products). Let's analyze each option.
Option A: [tex]\( 3 KOH + H_3PO_4 \rightarrow K_3PO_4 + 3 H_2O \)[/tex]
- Left Side:
- Potassium (K): [tex]\(3 \times 1 = 3\)[/tex]
- Oxygen (O): [tex]\(3 \times 1 + 4 = 7\)[/tex]
- Hydrogen (H): [tex]\(3 \times 1 + 3 = 6\)[/tex]
- Phosphorus (P): 1
- Right Side:
- Potassium (K): 3
- Oxygen (O): 4 + [tex]\(3 \times 1 = 7\)[/tex]
- Hydrogen (H): [tex]\(3 \times 2 = 6\)[/tex]
- Phosphorus (P): 1
The counts are balanced: [tex]\(3 K\)[/tex], [tex]\(7 O\)[/tex], [tex]\(6 H\)[/tex], [tex]\(1 P\)[/tex].
Option B: [tex]\( KOH + H_3PO_4 \rightarrow K_3PO_4 + H_2O \)[/tex]
- Left Side:
- Potassium (K): 1
- Oxygen (O): 1 + 4 = 5
- Hydrogen (H): 1 + 3 = 4
- Phosphorus (P): 1
- Right Side:
- Potassium (K): 3
- Oxygen (O): 4 + 1 = 5
- Hydrogen (H): 2
- Phosphorus (P): 1
The counts are unbalanced: Potassium and Hydrogen are not equal.
Option C: [tex]\( 3 KOH + 2 H_3PO_4 \rightarrow 2 K_3PO_4 + 3 H_2O \)[/tex]
- Left Side:
- Potassium (K): [tex]\(3 \times 1 = 3\)[/tex]
- Oxygen (O): [tex]\(3 \times 1 + 2 \times 4 = 11\)[/tex]
- Hydrogen (H): [tex]\(3 \times 1 + 2 \times 3 = 9\)[/tex]
- Phosphorus (P): 2
- Right Side:
- Potassium (K): [tex]\(2 \times 3 = 6\)[/tex]
- Oxygen (O): [tex]\(4 \times 2 + 3 = 11\)[/tex]
- Hydrogen (H): [tex]\(3 \times 2 = 6\)[/tex]
- Phosphorus (P): 2
The counts are unbalanced: Potassium and Hydrogen are not equal.
Option D: [tex]\( 2 KOH + H_3PO_4 \rightarrow K_3PO_4 + 2 H_2O \)[/tex]
- Left Side:
- Potassium (K): [tex]\(2 \times 1 = 2\)[/tex]
- Oxygen (O): [tex]\(2 \times 1 + 4 = 6\)[/tex]
- Hydrogen (H): [tex]\(2 \times 1 + 3 = 5\)[/tex]
- Phosphorus (P): 1
- Right Side:
- Potassium (K): 3
- Oxygen (O): 4 + [tex]\(2 \times 1 = 6\)[/tex]
- Hydrogen (H): [tex]\(2 \times 2 = 4\)[/tex]
- Phosphorus (P): 1
The counts are unbalanced: Potassium and Hydrogen are not equal.
Thus, the chemical equation that models the law of conservation of mass is:
Option A: [tex]\( 3 KOH + H_3PO_4 \rightarrow K_3PO_4 + 3 H_2O \)[/tex]
