To determine the appropriate coefficient for phosphorus trichloride ([tex]\(PCl_3\)[/tex]) that satisfies the law of conservation of mass, we need to ensure that the number of atoms for each element is the same on both sides of the chemical equation.
Given the equation:
[tex]\[2 P + 3 Cl_2 \rightarrow PCl_3\][/tex]
Let's analyze the elements on both sides:
1. On the reactant side (left side of the arrow):
- Phosphorus (P): There are 2 atoms of phosphorus.
- Chlorine (Cl): [tex]\(3 Cl_2\)[/tex] means [tex]\(3 \times 2 = 6\)[/tex] atoms of chlorine.
2. On the product side (right side of the arrow):
- [tex]\(PCl_3\)[/tex]: To balance the equation, the phosphorus and chlorine atoms should match those on the reactant side.
Therefore, we need enough [tex]\(PCl_3\)[/tex] to have:
- 2 atoms of phosphorus and
- 6 atoms of chlorine
Since [tex]\(PCl_3\)[/tex] contains 1 phosphorus atom and 3 chlorine atoms:
- To have 2 atoms of phosphorus in [tex]\(PCl_3\)[/tex], we need 2[tex]\(PCl_3\)[/tex]
- To have 6 atoms of chlorine in [tex]\(PCl_3\)[/tex], we also need [tex]\(2 \times 3 = 6\)[/tex] chlorine atoms.
So, the balanced equation should be:
[tex]\[2 P + 3 Cl_2 \rightarrow 2 PCl_3\][/tex]
Hence, the coefficient that shows the law of conservation of mass in this chemical equation is:
[tex]\[ \boxed{2} \][/tex]
