To determine which equations are correctly balanced, we need to ensure that the number of atoms of each element on the reactants side is equal to the number of atoms of the same element on the products side for each equation:
1. Equation 1: [tex]\( CaCO_3 \rightarrow CaO + CO_2 \)[/tex]
- Reactants: [tex]\( CaCO_3 \)[/tex]
- Ca: 1
- C: 1
- O: 3
- Products: [tex]\( CaO + CO_2 \)[/tex]
- Ca: 1 (from [tex]\( CaO \)[/tex])
- C: 1 (from [tex]\( CO_2 \)[/tex])
- O: 1 (from [tex]\( CaO \)[/tex]) + 2 (from [tex]\( CO_2 \)[/tex]) = 3
Observing that the number of each type of atom on the reactants side matches the number on the products side, this equation is balanced.
2. Equation 2: [tex]\( Fe_2O_3 + 3H_2 \rightarrow 2Fe + 3H_2O \)[/tex]
- Reactants: [tex]\( Fe_2O_3 + 3H_2 \)[/tex]
- Fe: 2 (from [tex]\( Fe_2O_3 \)[/tex])
- O: 3 (from [tex]\( Fe_2O_3 \)[/tex])
- H: 2 [tex]\(\times\)[/tex] 3 = 6 (from [tex]\( 3H_2 \)[/tex])
- Products: [tex]\( 2Fe + 3H_2O \)[/tex]
- Fe: 2 (from [tex]\( 2Fe \)[/tex])
- H: 2 [tex]\(\times\)[/tex] 3 = 6 (from [tex]\( 3H_2O \)[/tex])
- O: 1 [tex]\(\times\)[/tex] 3 = 3 (from [tex]\( 3H_2O \)[/tex])
Observing that the number of each type of atom on the reactants side matches the number on the products side, this equation is balanced.
3. Equation 3: [tex]\( Al + 3Br_2 \rightarrow AlBr_3 \)[/tex]
- Reactants: [tex]\( Al + 3Br_2 \)[/tex]
- Al: 1 (from [tex]\( Al \)[/tex])
- Br: 2 [tex]\(\times\)[/tex] 3 = 6 (from [tex]\( 3Br_2 \)[/tex])
- Products: [tex]\( AlBr_3 \)[/tex]
- Al: 1 (from [tex]\( AlBr_3 \)[/tex])
- Br: 3 (from [tex]\( AlBr_3 \)[/tex])
Observing that the number of each type of atom on the reactants side does not match the number on the products side (Br atoms are not balanced), this equation is not balanced.
4. Equation 4: [tex]\( H_2O + 2O_2 \rightarrow H_2O_2 \)[/tex]
- Reactants: [tex]\( H_2O + 2O_2 \)[/tex]
- H: 2 (from [tex]\( H_2O \)[/tex])
- O: 1 (from [tex]\( H_2O \)[/tex]) + 2 [tex]\(\times\)[/tex] 2 = 5 (from [tex]\( 2O_2 \)[/tex])
- Products: [tex]\( H_2O_2 \)[/tex]
- H: 2 (from [tex]\( H_2O_2 \)[/tex])
- O: 2 (from [tex]\( H_2O_2 \)[/tex])
Observing that the number of each type of atom on the reactants side does not match the number on the products side (O atoms are not balanced), this equation is not balanced.
From this detailed analysis, the correctly balanced equations are:
1. [tex]\( CaCO_3 \rightarrow CaO + CO_2 \)[/tex]
2. [tex]\( Fe_2O_3 + 3H_2 \rightarrow 2Fe + 3H_2O \)[/tex]
Therefore, the correctly balanced equations are:
[tex]\[ [1, 2] \][/tex]
