1. What coefficients would balance the following equation? Al \( +\ldots \mathrm{O}_{2} \rightarrow \) Al2 \( \mathrm{O}_{3} \) \( 2 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 1 \mathrm{Al}_{2} \mathrm{O}_{3} \) \( 2 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3} \) \( 3 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3} \) \( 4 \mathrm{Al}+3 \mathrm{O}_{2} \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3} \)

To balance the chemical equation: \[ \text{Al} + \mathrm{O}_2 \rightarrow \mathrm{Al}_2\mathrm{O}_3 \] Let's determine the correct coefficients step-by-step. 1. **Write the unbalanced equation with coefficients:** \[ a\,\text{Al} + b\,\mathrm{O}_2 \rightarrow c\,\mathrm{Al}_2\mathrm{O}_3 \] 2. **Balance the aluminum (Al) atoms:** - On the left: \( a \) Al atoms - On the right: \( 2c \) Al atoms \[ a = 2c \] 3. **Balance the oxygen (O) atoms:** - On the left: \( 2b \) O atoms - On the right: \( 3c \) O atoms \[ 2b = 3c \] 4. **Find integer solutions for \( a \), \( b \), and \( c \):** - From \( 2b = 3c \), choose \( c = 2 \) (smallest integer making \( b \) an integer) - Then, \( b = 3 \) - From \( a = 2c \), \( a = 4 \) 5. **Write the balanced equation:** \[ 4\,\text{Al} + 3\,\mathrm{O}_2 \rightarrow 2\,\mathrm{Al}_2\mathrm{O}_3 \] **Therefore, the correct balanced equation corresponds to option 4:** \[ 4\,\text{Al} + 3\,\mathrm{O}_2 \rightarrow 2\,\mathrm{Al}_2\mathrm{O}_3 \] **Answer:** \( 4\,\mathrm{Al} + 3\,\mathrm{O}_{2} \rightarrow 2\,\mathrm{Al}_{2}\mathrm{O}_{3} \)