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Sagot :
To determine the correct balanced chemical equation for the reaction of iron [tex]\( Fe \)[/tex] with oxygen [tex]\( O_2 \)[/tex] to form iron(III) oxide [tex]\( Fe_2O_3 \)[/tex], we need to ensure both the number of iron atoms and the number of oxygen atoms are the same on both sides of the equation.
Let’s analyze each option by balancing the number of iron and oxygen atoms.
### Option A:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 4 \)[/tex] Fe and [tex]\( 3 \times 2 = 6 \)[/tex] O
- Right side: [tex]\( 2 \times 2 = 4 \)[/tex] Fe and [tex]\( 2 \times 3 = 6 \)[/tex] O
The number of iron atoms and oxygen atoms are balanced. This is a possible balanced equation.
### Option B:
[tex]\[ 3 Fe + 4 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 3 \)[/tex] Fe and [tex]\( 4 \times 2 = 8 \)[/tex] O
- Right side: [tex]\( 2 \times 2 = 4 \)[/tex] Fe and [tex]\( 2 \times 3 = 6 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
### Option C:
[tex]\[ 2 Fe + 4 O_2 \rightarrow 3 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 2 \)[/tex] Fe and [tex]\( 4 \times 2 = 8 \)[/tex] O
- Right side: [tex]\( 3 \times 2 = 6 \)[/tex] Fe and [tex]\( 3 \times 3 = 9 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
### Option D:
[tex]\[ 3 Fe + 3 O_2 \rightarrow 4 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 3 \)[/tex] Fe and [tex]\( 3 \times 2 = 6 \)[/tex] O
- Right side: [tex]\( 4 \times 2 = 8 \)[/tex] Fe and [tex]\( 4 \times 3 = 12 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
### Option E:
[tex]\[ 4 Fe + 4 O_2 \rightarrow 3 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 4 \)[/tex] Fe and [tex]\( 4 \times 2 = 8 \)[/tex] O
- Right side: [tex]\( 3 \times 2 = 6 \)[/tex] Fe and [tex]\( 3 \times 3 = 9 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
After examining all options, Option A:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
is the correct balanced equation for the reaction of iron with oxygen to form iron(III) oxide. Thus, the correct answer is:
A. [tex]\( 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \)[/tex]
Let’s analyze each option by balancing the number of iron and oxygen atoms.
### Option A:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 4 \)[/tex] Fe and [tex]\( 3 \times 2 = 6 \)[/tex] O
- Right side: [tex]\( 2 \times 2 = 4 \)[/tex] Fe and [tex]\( 2 \times 3 = 6 \)[/tex] O
The number of iron atoms and oxygen atoms are balanced. This is a possible balanced equation.
### Option B:
[tex]\[ 3 Fe + 4 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 3 \)[/tex] Fe and [tex]\( 4 \times 2 = 8 \)[/tex] O
- Right side: [tex]\( 2 \times 2 = 4 \)[/tex] Fe and [tex]\( 2 \times 3 = 6 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
### Option C:
[tex]\[ 2 Fe + 4 O_2 \rightarrow 3 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 2 \)[/tex] Fe and [tex]\( 4 \times 2 = 8 \)[/tex] O
- Right side: [tex]\( 3 \times 2 = 6 \)[/tex] Fe and [tex]\( 3 \times 3 = 9 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
### Option D:
[tex]\[ 3 Fe + 3 O_2 \rightarrow 4 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 3 \)[/tex] Fe and [tex]\( 3 \times 2 = 6 \)[/tex] O
- Right side: [tex]\( 4 \times 2 = 8 \)[/tex] Fe and [tex]\( 4 \times 3 = 12 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
### Option E:
[tex]\[ 4 Fe + 4 O_2 \rightarrow 3 Fe_2 O_3 \][/tex]
Counting the atoms:
- Left side: [tex]\( 4 \)[/tex] Fe and [tex]\( 4 \times 2 = 8 \)[/tex] O
- Right side: [tex]\( 3 \times 2 = 6 \)[/tex] Fe and [tex]\( 3 \times 3 = 9 \)[/tex] O
The number of iron atoms and oxygen atoms are not balanced. This equation is not balanced correctly.
After examining all options, Option A:
[tex]\[ 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \][/tex]
is the correct balanced equation for the reaction of iron with oxygen to form iron(III) oxide. Thus, the correct answer is:
A. [tex]\( 4 Fe + 3 O_2 \rightarrow 2 Fe_2 O_3 \)[/tex]
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