To determine why the chemical equation [tex]\( \mathrm{O_2 + 2 PCl_3 \rightarrow 2 POCl_3} \)[/tex] is said to be balanced, we need to count the number of atoms of each element on both the reactant and product sides of the equation. The equation is balanced if and only if the number of atoms for each element is the same on both sides.
Let’s examine each element in detail:
1. Oxygen (O)
- Reactant side: There is one molecule of [tex]\( \mathrm{O_2} \)[/tex], which contains [tex]\( 2 \)[/tex] oxygen atoms.
- Product side: There are [tex]\( 2 \)[/tex] molecules of [tex]\( \mathrm{POCl_3} \)[/tex]. Since each [tex]\( \mathrm{POCl_3} \)[/tex] molecule contains [tex]\( 1 \)[/tex] oxygen atom, [tex]\( 2 \times 1 = 2 \)[/tex] oxygen atoms.
2. Phosphorus (P)
- Reactant side: There are [tex]\( 2 \)[/tex] molecules of [tex]\( \mathrm{PCl_3} \)[/tex]. Each [tex]\( \mathrm{PCl_3} \)[/tex] molecule contains [tex]\( 1 \)[/tex] phosphorus atom, so there are [tex]\( 2 \times 1 = 2 \)[/tex] phosphorus atoms.
- Product side: There are [tex]\( 2 \)[/tex] molecules of [tex]\( \mathrm{POCl_3} \)[/tex]. Each [tex]\( \mathrm{POCl_3} \)[/tex] molecule contains [tex]\( 1 \)[/tex] phosphorus atom, so there are [tex]\( 2 \times 1 = 2 \)[/tex] phosphorus atoms.
3. Chlorine (Cl)
- Reactant side: There are [tex]\( 2 \)[/tex] molecules of [tex]\( \mathrm{PCl_3} \)[/tex]. Each [tex]\( \mathrm{PCl_3} \)[/tex] molecule contains [tex]\( 3 \)[/tex] chlorine atoms, so there are [tex]\( 2 \times 3 = 6 \)[/tex] chlorine atoms.
- Product side: There are [tex]\( 2 \)[/tex] molecules of [tex]\( \mathrm{POCl_3} \)[/tex]. Each [tex]\( \mathrm{POCl_3} \)[/tex] molecule contains [tex]\( 3 \)[/tex] chlorine atoms, so there are [tex]\( 2 \times 3 = 6 \)[/tex] chlorine atoms.
By summarizing the counts of each atom:
- Reactant side:
- Oxygen: [tex]\( 2 \)[/tex] atoms
- Phosphorus: [tex]\( 2 \)[/tex] atoms
- Chlorine: [tex]\( 6 \)[/tex] atoms
- Product side:
- Oxygen: [tex]\( 2 \)[/tex] atoms
- Phosphorus: [tex]\( 2 \)[/tex] atoms
- Chlorine: [tex]\( 6 \)[/tex] atoms
Since the number of atoms of each element is the same on both the reactant and product sides of the equation, the chemical equation is balanced.
Thus, the correct answer is:
C. The atoms are the same on both sides of the equation.
