To ensure that the chemical equation follows the Law of Conservation of Mass, we need to make sure that the number of atoms of each element is the same on both sides of the equation. The given chemical equation is:
[tex]\[ 2 P + 3 Cl_2 \rightarrow \text{PCl}_3 \][/tex]
Let's count the atoms for each element on both sides of the equation:
#### On the Left Side:
- For Phosphorus (P): There are 2 atoms.
- For Chlorine (Cl): There are 3 molecules of [tex]\(Cl_2\)[/tex], and since each [tex]\(Cl_2\)[/tex] molecule has 2 Cl atoms, we have [tex]\(3 \times 2 = 6\)[/tex] chlorine atoms.
#### On the Right Side:
- For Phosphorus (P): In one molecule of [tex]\( \text{PCl}_3 \)[/tex], there is 1 phosphorus atom.
- For Chlorine (Cl): In one molecule of [tex]\( \text{PCl}_3 \)[/tex], there are 3 chlorine atoms.
To balance the equation, we need to adjust the coefficient of [tex]\( \text{PCl}_3 \)[/tex] so that the number of phosphorus and chlorine atoms is the same on both sides.
Let's determine the coefficient for [tex]\( \text{PCl}_3 \)[/tex]:
1. Balancing Phosphorus Atoms:
- We have 2 phosphorus atoms on the left side.
- To match this on the right side, we need 2 molecules of [tex]\( \text{PCl}_3 \)[/tex]:
[tex]\[
2 \text{PCl}_3 \rightarrow 2 \text{(Phosphorus)}
\][/tex]
2. Balancing Chlorine Atoms:
- We have 6 chlorine atoms on the left side (from [tex]\( 3 Cl_2 \)[/tex]).
- Each [tex]\( \text{PCl}_3 \)[/tex] molecule contains 3 chlorine atoms.
- With a coefficient of 2 for [tex]\( \text{PCl}_3 \)[/tex], we get:
[tex]\[
2 \times 3 \text{(Chlorine)} = 6 \text{(Chlorine)}
\][/tex]
So the balanced equation would be:
[tex]\[
2 P + 3 Cl_2 \rightarrow 2 \text{PCl}_3
\][/tex]
Thus, the correct coefficient for [tex]\( \text{PCl}_3 \)[/tex] to represent the law of conservation of mass is:
[tex]\[
\boxed{2}
\][/tex]
