To balance the chemical equation [tex]\(2P + 3Cl_2 \rightarrow PCl_3\)[/tex] and ensure the law of conservation of mass is properly represented, follow these steps:
1. Identify the number of atoms for each element on the left side of the equation:
- Phosphorus (P): 2 atoms
- Chlorine (Cl): [tex]\(3 \text{ molecules of } Cl_2 \times 2 \text{ Cl atoms per molecule} = 6 \text{ atoms}\)[/tex]
2. Identify the number of atoms for each element on the right side of the equation:
- Phosphorus (P): 1 atom per molecule of [tex]\(PCl_3\)[/tex]
- Chlorine (Cl): 3 atoms per molecule of [tex]\(PCl_3\)[/tex]
3. Determine the coefficient that balances the phosphorus atoms:
- The left side has 2 phosphorus atoms.
- Therefore, you need 2 phosphorus atoms on the right side.
- Since each [tex]\(PCl_3\)[/tex] molecule has 1 phosphorus atom, you need 2 molecules of [tex]\(PCl_3\)[/tex] to have 2 phosphorus atoms.
4. Determine the coefficient that balances the chlorine atoms:
- The left side has 6 chlorine atoms.
- To balance this with the right side, you need 6 chlorine atoms.
- Since each [tex]\(PCl_3\)[/tex] molecule has 3 chlorine atoms, you need 2 molecules of [tex]\(PCl_3\)[/tex] to get [tex]\(2 \text{ molecules} \times 3 \text{ chlorine atoms} = 6 \text{ chlorine atoms}\)[/tex].
By balancing both the phosphorus and the chlorine atoms, you determine that the coefficient for [tex]\(PCl_3\)[/tex] that correctly balances the chemical equation is:
[tex]\[ \boxed{2} \][/tex]
