To balance the chemical equation [tex]\( P_4(s) + Cl_2(g) \rightarrow PCl_3(l) \)[/tex], let's follow a step-by-step process to determine the appropriate coefficients.
1. Identify the elements involved and their quantities on both sides of the equation:
- Reactants: [tex]\( P_4 \)[/tex] and [tex]\( Cl_2 \)[/tex]
- Products: [tex]\( PCl_3 \)[/tex]
2. Count the number of atoms for each element on both sides:
- Phosphorus (P):
- Reactants: 4 (from [tex]\( P_4 \)[/tex])
- Products: Each [tex]\( PCl_3 \)[/tex] molecule contains 1 phosphorus atom.
- Chlorine (Cl):
- Reactants: Each [tex]\( Cl_2 \)[/tex] molecule contains 2 chlorine atoms.
- Products: Each [tex]\( PCl_3 \)[/tex] molecule contains 3 chlorine atoms.
3. Start balancing with the element that is present in the least number of molecular forms:
- Phosphorus (P): To balance the phosphorus atoms, we need 4 molecules of [tex]\( PCl_3 \)[/tex] because we have 4 atoms of phosphorus in [tex]\( P_4 \)[/tex]:
[tex]\[ P_4 + Cl_2 \rightarrow 4PCl_3 \][/tex]
4. Next, balance the chlorine (Cl) atoms:
- We now have 4 molecules of [tex]\( PCl_3 \)[/tex], which means we need: [tex]\( 4 \times 3 = 12 \)[/tex] chlorine atoms on the product side.
- Since each [tex]\( Cl_2 \)[/tex] molecule provides 2 chlorine atoms, we need [tex]\( \frac{12}{2} = 6 \)[/tex] molecules of [tex]\( Cl_2 \)[/tex]:
[tex]\[ P_4 + 6Cl_2 \rightarrow 4PCl_3 \][/tex]
5. Check the balanced equation:
- Reactant side: 4 phosphorus atoms (from [tex]\( P_4 \)[/tex]) and 12 chlorine atoms (from [tex]\( 6Cl_2 \)[/tex]).
- Product side: 4 phosphorus atoms (from [tex]\( 4PCl_3 \)[/tex]) and 12 chlorine atoms (from [tex]\( 4PCl_3 \)[/tex]).
The equation is now balanced:
[tex]\[ P_4(s) + 6Cl_2(g) \rightarrow 4PCl_3(l) \][/tex]
Therefore, the coefficient that should be placed in front of [tex]\( PCl_3 \)[/tex] to balance this equation is [tex]\( 4 \)[/tex].
