Answer :
Balancing a chemical equation involves ensuring that there are the same number of atoms of each element on the reactant side as on the product side. Let's go through the process of balancing the equation step-by-step.
The given unbalanced equation is:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
1. Identify the number of atoms of each element on both sides of the equation.
- Reactants side:
- Fe: 1 atom
- O: 2 atoms
- Products side:
- Fe: 2 atoms (in [tex]\( Fe_2O_3 \)[/tex])
- O: 3 atoms (in [tex]\( Fe_2O_3 \)[/tex])
2. Balance the iron (Fe) atoms.
- There are 2 Fe atoms in [tex]\( Fe_2O_3 \)[/tex] on the product side. So, we need 2 Fe atoms on the reactant side as well. Put a coefficient of 2 in front of Fe:
[tex]\[ 2 Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
3. Balance the oxygen (O) atoms.
- There are 2 O atoms in [tex]\( O_2 \)[/tex] and 3 O atoms in [tex]\( Fe_2O_3 \)[/tex].
- To balance the O atoms, the number of O atoms on the reactant side must be a multiple of 3. Since we have an even number of O atoms on the reactant side from [tex]\( O_2 \)[/tex] (2 atoms in each [tex]\( O_2 \)[/tex] molecule), we should aim for the smallest common multiple of 2 and 3, which is 6.
Therefore, we need to balance 6 O atoms on both sides:
- Let’s put a coefficient of 3 in front of [tex]\( O_2 \)[/tex] to get 6 O atoms:
[tex]\[ 2 Fe + 3 O_2 \rightarrow Fe_2O_3 \][/tex]
- On the product side, we need 2 molecules of [tex]\( Fe_2O_3 \)[/tex] to get 6 O atoms:
[tex]\[ 2 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
4. Re-balance the iron (Fe) atoms again since adjusting the oxygen atoms affected them.
- The right-side now has 2 molecules of [tex]\( Fe_2O_3 \)[/tex], which means it contains 4 Fe atoms (2 Fe atoms per molecule of [tex]\( Fe_2O_3 \)[/tex]).
- Therefore, we need 4 Fe atoms on the reactant side:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
Now the equation is balanced:
- Reactants: 4 Fe and 6 O atoms (from [tex]\( 3 O_2 \)[/tex])
- Products: 4 Fe atoms (2 molecules of [tex]\( Fe_2O_3 \)[/tex] each containing 2 Fe atoms) and 6 O atoms (2 molecules of [tex]\( Fe_2O_3 \)[/tex] each containing 3 O atoms)
Thus, the correct balanced equation is:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
So, the correct answer is option A:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
The given unbalanced equation is:
[tex]\[ Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
1. Identify the number of atoms of each element on both sides of the equation.
- Reactants side:
- Fe: 1 atom
- O: 2 atoms
- Products side:
- Fe: 2 atoms (in [tex]\( Fe_2O_3 \)[/tex])
- O: 3 atoms (in [tex]\( Fe_2O_3 \)[/tex])
2. Balance the iron (Fe) atoms.
- There are 2 Fe atoms in [tex]\( Fe_2O_3 \)[/tex] on the product side. So, we need 2 Fe atoms on the reactant side as well. Put a coefficient of 2 in front of Fe:
[tex]\[ 2 Fe + O_2 \rightarrow Fe_2O_3 \][/tex]
3. Balance the oxygen (O) atoms.
- There are 2 O atoms in [tex]\( O_2 \)[/tex] and 3 O atoms in [tex]\( Fe_2O_3 \)[/tex].
- To balance the O atoms, the number of O atoms on the reactant side must be a multiple of 3. Since we have an even number of O atoms on the reactant side from [tex]\( O_2 \)[/tex] (2 atoms in each [tex]\( O_2 \)[/tex] molecule), we should aim for the smallest common multiple of 2 and 3, which is 6.
Therefore, we need to balance 6 O atoms on both sides:
- Let’s put a coefficient of 3 in front of [tex]\( O_2 \)[/tex] to get 6 O atoms:
[tex]\[ 2 Fe + 3 O_2 \rightarrow Fe_2O_3 \][/tex]
- On the product side, we need 2 molecules of [tex]\( Fe_2O_3 \)[/tex] to get 6 O atoms:
[tex]\[ 2 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
4. Re-balance the iron (Fe) atoms again since adjusting the oxygen atoms affected them.
- The right-side now has 2 molecules of [tex]\( Fe_2O_3 \)[/tex], which means it contains 4 Fe atoms (2 Fe atoms per molecule of [tex]\( Fe_2O_3 \)[/tex]).
- Therefore, we need 4 Fe atoms on the reactant side:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
Now the equation is balanced:
- Reactants: 4 Fe and 6 O atoms (from [tex]\( 3 O_2 \)[/tex])
- Products: 4 Fe atoms (2 molecules of [tex]\( Fe_2O_3 \)[/tex] each containing 2 Fe atoms) and 6 O atoms (2 molecules of [tex]\( Fe_2O_3 \)[/tex] each containing 3 O atoms)
Thus, the correct balanced equation is:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
So, the correct answer is option A:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2O_3 \][/tex]
