Certainly! To determine the correct coefficient of [tex]\( \text{PCl}_3 \)[/tex] in the balanced chemical equation that ensures the law of conservation of mass is represented, let's carefully analyze the given equation:
The balanced chemical equation is:
[tex]\[ 2P + 3Cl_2 \rightarrow 2PCl_3 \][/tex]
This equation indicates the reactive proportions of the elements involved:
1. Atoms on Reactants Side:
- Phosphorus ([tex]\( P \)[/tex]): There are 2 atoms of phosphorus.
- Chlorine ([tex]\( Cl \)[/tex]): There are 3 molecules of chlorine gas ([tex]\( Cl_2 \)[/tex]), each molecule containing 2 chlorine atoms, thus making it [tex]\( 3 \times 2 = 6 \)[/tex] chlorine atoms.
2. Atoms on Products Side:
- [tex]\( PCl_3 \)[/tex]: There are 2 molecules of phosphorus trichloride, with each having 1 phosphorus atom and 3 chlorine atoms. So, in total:
- Phosphorus: [tex]\( 2 \times 1 = 2 \)[/tex] phosphorus atoms.
- Chlorine: [tex]\( 2 \times 3 = 6 \)[/tex] chlorine atoms.
Comparing these results, we observe:
- Both sides have 2 phosphorus atoms.
- Both sides have 6 chlorine atoms.
Since the number of atoms for each element is the same on both the reactant and product sides, the chemical equation respects the law of conservation of mass. Therefore, the coefficient for [tex]\( \text{PCl}_3 \)[/tex] that allows the equation to be balanced is 2.
Thus, the correct answer is:
[tex]\[ \boxed{2} \][/tex]
