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To determine which combustion reaction is balanced correctly, we need to ensure that the number of atoms for each element on the reactant side is equal to the number of atoms for the same element on the product side. Let's analyze each option in detail.
### Option A:
[tex]\[ C_4H_6 + 1.5 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(1.5 \times 2 = 3\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since the oxygen atoms are not balanced (3 on reactants and 11 on products), this reaction is not balanced.
### Option B:
[tex]\[ C_4H_6 + 4 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(4 \times 2 = 8\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since the oxygen atoms are not balanced (8 on reactants and 11 on products), this reaction is not balanced.
### Option C:
[tex]\[ C_4H_6 + 5.5 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(5.5 \times 2 = 11\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since all atoms are balanced (carbon, hydrogen, and oxygen), this reaction is balanced.
### Option D:
[tex]\[ C_4H_6 + 11 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(11 \times 2 = 22\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since the oxygen atoms are not balanced (22 on reactants and 11 on products), this reaction is not balanced.
### Conclusion:
The balanced combustion reaction is:
[tex]\[ \boxed{C} \, C_4H_6 + 5.5 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
### Option A:
[tex]\[ C_4H_6 + 1.5 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(1.5 \times 2 = 3\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since the oxygen atoms are not balanced (3 on reactants and 11 on products), this reaction is not balanced.
### Option B:
[tex]\[ C_4H_6 + 4 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(4 \times 2 = 8\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since the oxygen atoms are not balanced (8 on reactants and 11 on products), this reaction is not balanced.
### Option C:
[tex]\[ C_4H_6 + 5.5 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(5.5 \times 2 = 11\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since all atoms are balanced (carbon, hydrogen, and oxygen), this reaction is balanced.
### Option D:
[tex]\[ C_4H_6 + 11 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
- Carbon (C):
- Reactants: 4 (from [tex]\(C_4H_6\)[/tex])
- Products: 4 (from [tex]\(4 CO_2\)[/tex])
- Hydrogen (H):
- Reactants: 6 (from [tex]\(C_4H_6\)[/tex])
- Products: 6 (from [tex]\(3 H_2O\)[/tex])
- Oxygen (O):
- Reactants: [tex]\(11 \times 2 = 22\)[/tex]
- Products: [tex]\(4 \times 2 + 3 = 8 + 3 = 11\)[/tex]
Since the oxygen atoms are not balanced (22 on reactants and 11 on products), this reaction is not balanced.
### Conclusion:
The balanced combustion reaction is:
[tex]\[ \boxed{C} \, C_4H_6 + 5.5 O_2 \rightarrow 4 CO_2 + 3 H_2O \][/tex]
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