To determine which equation represents the conservation of atoms, we need to analyze each equation to ensure that the number of atoms of each element in the reactants equals the number of atoms in the products.
### Equation 1: [tex]\( TiO_2 + 2Al \rightarrow 2Al_2O_3 + Ti \)[/tex]
Reactants:
- Titanium (Ti): [tex]\(1\)[/tex] atom (from [tex]\( TiO_2 \)[/tex])
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\( TiO_2 \)[/tex])
- Aluminum (Al): [tex]\(2\)[/tex] atoms
Products:
- [tex]\(2\)[/tex] [tex]\( Al_2O_3 \)[/tex] contains:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
- Titanium (Ti): [tex]\(1\)[/tex] atom
Atom counts:
- Ti: Reactants - [tex]\(1\)[/tex], Products - [tex]\(1\)[/tex] (Balanced)
- O: Reactants - [tex]\(2\)[/tex], Products - [tex]\(6\)[/tex] (Not Balanced)
- Al: Reactants - [tex]\(2\)[/tex], Products - [tex]\(4\)[/tex] (Not Balanced)
### Equation 2: [tex]\( TiO_2 + 4Al \rightarrow 2Al_2O_3 + Ti \)[/tex]
Reactants:
- Titanium (Ti): [tex]\(1\)[/tex] atom (from [tex]\( TiO_2 \)[/tex])
- Oxygen (O): [tex]\(2\)[/tex] atoms (from [tex]\( TiO_2 \)[/tex])
- Aluminum (Al): [tex]\(4\)[/tex] atoms
Products:
- [tex]\(2\)[/tex] [tex]\( Al_2O_3 \)[/tex] contains:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
- Titanium (Ti): [tex]\(1\)[/tex] atom
Atom counts:
- Ti: Reactants - [tex]\(1\)[/tex], Products - [tex]\(1\)[/tex] (Balanced)
- O: Reactants - [tex]\(2\)[/tex], Products - [tex]\(6\)[/tex] (Not Balanced)
- Al: Reactants - [tex]\(4\)[/tex], Products - [tex]\(4\)[/tex] (Balanced)
### Equation 3: [tex]\( 3TiO_2 + 2Al \rightarrow 2Al_2O_3 + 3Ti \)[/tex]
Reactants:
- Titanium (Ti): [tex]\(3\)[/tex] atoms (from [tex]\( 3TiO_2 \)[/tex])
- Oxygen (O): [tex]\(3 \times 2 = 6\)[/tex] atoms (from [tex]\( 3TiO_2 \)[/tex])
- Aluminum (Al): [tex]\(2\)[/tex] atoms
Products:
- [tex]\(2\)[/tex] [tex]\( Al_2O_3 \)[/tex] contains:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
- Titanium (Ti): [tex]\(3\)[/tex] atoms
Atom counts:
- Ti: Reactants - [tex]\(3\)[/tex], Products - [tex]\(3\)[/tex] (Balanced)
- O: Reactants - [tex]\(6\)[/tex], Products - [tex]\(6\)[/tex] (Balanced)
- Al: Reactants - [tex]\(2\)[/tex], Products - [tex]\(4\)[/tex] (Not Balanced)
### Equation 4: [tex]\( 3TiO_2 + 4Al \rightarrow 2Al_2O_3 + 3Ti \)[/tex]
Reactants:
- Titanium (Ti): [tex]\(3\)[/tex] atoms (from [tex]\( 3TiO_2 \)[/tex])
- Oxygen (O): [tex]\(3 \times 2 = 6\)[/tex] atoms (from [tex]\( 3TiO_2 \)[/tex])
- Aluminum (Al): [tex]\(4\)[/tex] atoms
Products:
- [tex]\(2\)[/tex] [tex]\(Al_2O_3\)[/tex] contains:
- Aluminum (Al): [tex]\(2 \times 2 = 4\)[/tex] atoms
- Oxygen (O): [tex]\(2 \times 3 = 6\)[/tex] atoms
- Titanium (Ti): [tex]\(3\)[/tex] atoms
Atom counts:
- Ti: Reactants - [tex]\(3\)[/tex], Products - [tex]\(3\)[/tex] (Balanced)
- O: Reactants - [tex]\(6\)[/tex], Products - [tex]\(6\)[/tex] (Balanced)
- Al: Reactants - [tex]\(4\)[/tex], Products - [tex]\(4\)[/tex] (Balanced)
Therefore, the equation that represents the conservation of atoms is:
[tex]\[ (4) \quad 3TiO_2 + 4Al \rightarrow 2Al_2O_3 + 3Ti \][/tex]
