To determine the correct coefficient for [tex]\( \text{PCl}_3 \)[/tex] that satisfies the law of conservation of mass, follow these steps:
1. Understand the chemical equation:
[tex]\[
2P + 3Cl_2 \rightarrow PCl_3
\][/tex]
2. Identify the number of atoms on both sides:
- On the reactant side:
- Phosphorus (P): There are 2 atoms of P (from the 2P).
- Chlorine (Cl): Each molecule of [tex]\( \text{Cl}_2 \)[/tex] contains 2 Cl atoms, and with 3 [tex]\( \text{Cl}_2 \)[/tex] molecules, there are [tex]\( 3 \times 2 = 6 \)[/tex] Cl atoms.
- On the product side:
- Each molecule of [tex]\( \text{PCl}_3 \)[/tex] contains 1 P atom and 3 Cl atoms.
3. Balance the atoms:
To ensure the conservation of mass, the number of each type of atom on the reactant side must equal the number on the product side.
- Phosphorus: The reactants have 2 P atoms, so the products must also have 2 P atoms.
- Since each [tex]\( \text{PCl}_3 \)[/tex] molecule contains 1 P atom, we need 2 [tex]\( \text{PCl}_3 \)[/tex] molecules to have 2 P atoms.
- Chlorine: The reactants have 6 Cl atoms, so the products must also have 6 Cl atoms.
- Since each [tex]\( \text{PCl}_3 \)[/tex] molecule contains 3 Cl atoms, having 2 [tex]\( \text{PCl}_3 \)[/tex] molecules provides [tex]\( 2 \times 3 = 6 \)[/tex] Cl atoms.
4. Determine the coefficient:
The coefficient that satisfies the balancing of both P and Cl atoms in the product [tex]\( \text{PCl}_3 \)[/tex] is 2.
Therefore, the coefficient for [tex]\( \text{PCl}_3 \)[/tex] that represents the law of conservation of mass in the chemical equation is:
[tex]\[
\boxed{2}
\][/tex]
