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Sagot :
To solve the problem of balancing the combustion reaction for cyclohexane ([tex]\(C_6H_{12}\)[/tex]), we'll follow a step-by-step approach:
1. Identify the chemical equation for the combustion reaction:
[tex]\[ C_6H_{12} + O_2 \rightarrow CO_2 + H_2O \][/tex]
2. Determine the number of atoms of each element on both sides of the equation:
- Reactants:
- 1 molecule of [tex]\(C_6H_{12}\)[/tex] contains:
- Carbon (C): 6 atoms
- Hydrogen (H): 12 atoms
- [tex]\(O_2\)[/tex] molecules will contain oxygen. We need to balance coefficients later.
- Products:
- [tex]\(CO_2\)[/tex] contains:
- Carbon (C): 1 atom
- Oxygen (O): 2 atoms
- [tex]\(H_2O\)[/tex] contains:
- Hydrogen (H): 2 atoms
- Oxygen (O): 1 atom
3. Balance each element, starting with carbon:
- On the reactant side, we have 6 carbon atoms from [tex]\(C_6H_{12}\)[/tex].
- Therefore, we need 6 carbon atoms on the product side, which means we will have 6 [tex]\(CO_2\)[/tex] molecules.
[tex]\[ C_6H_{12} + O_2 \rightarrow 6 CO_2 + H_2O \][/tex]
4. Balance hydrogen atoms next:
- On the reactant side, we have 12 hydrogen atoms from [tex]\(C_6H_{12}\)[/tex].
- Therefore, we need 12 hydrogen atoms on the product side, which means we will have 6 [tex]\(H_2O\)[/tex] molecules (since [tex]\(H_2O\)[/tex] contains 2 hydrogen atoms each).
[tex]\[ C_6H_{12} + O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
5. Balance oxygen atoms last:
- On the product side, we have:
- From [tex]\(6 CO_2\)[/tex]: [tex]\(6 \times 2 = 12\)[/tex] oxygen atoms
- From [tex]\(6 H_2O\)[/tex]: [tex]\(6 \times 1 = 6\)[/tex] oxygen atoms
- Total oxygen atoms needed: [tex]\(12 + 6 = 18\)[/tex] oxygen atoms
- [tex]\(O_2\)[/tex] molecule contains 2 oxygen atoms. To get 18 oxygen atoms, we need 9 [tex]\(O_2\)[/tex] molecules.
[tex]\[ C_6H_{12} + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
6. Final balanced equation:
[tex]\[ C_6H_{12} + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
7. Conclusion:
For every molecule of cyclohexane ([tex]\(C_6H_{12}\)[/tex]) burned, 6 molecules of carbon dioxide ([tex]\(CO_2\)[/tex]) are produced. Thus, the correct answer is:
A. 6
1. Identify the chemical equation for the combustion reaction:
[tex]\[ C_6H_{12} + O_2 \rightarrow CO_2 + H_2O \][/tex]
2. Determine the number of atoms of each element on both sides of the equation:
- Reactants:
- 1 molecule of [tex]\(C_6H_{12}\)[/tex] contains:
- Carbon (C): 6 atoms
- Hydrogen (H): 12 atoms
- [tex]\(O_2\)[/tex] molecules will contain oxygen. We need to balance coefficients later.
- Products:
- [tex]\(CO_2\)[/tex] contains:
- Carbon (C): 1 atom
- Oxygen (O): 2 atoms
- [tex]\(H_2O\)[/tex] contains:
- Hydrogen (H): 2 atoms
- Oxygen (O): 1 atom
3. Balance each element, starting with carbon:
- On the reactant side, we have 6 carbon atoms from [tex]\(C_6H_{12}\)[/tex].
- Therefore, we need 6 carbon atoms on the product side, which means we will have 6 [tex]\(CO_2\)[/tex] molecules.
[tex]\[ C_6H_{12} + O_2 \rightarrow 6 CO_2 + H_2O \][/tex]
4. Balance hydrogen atoms next:
- On the reactant side, we have 12 hydrogen atoms from [tex]\(C_6H_{12}\)[/tex].
- Therefore, we need 12 hydrogen atoms on the product side, which means we will have 6 [tex]\(H_2O\)[/tex] molecules (since [tex]\(H_2O\)[/tex] contains 2 hydrogen atoms each).
[tex]\[ C_6H_{12} + O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
5. Balance oxygen atoms last:
- On the product side, we have:
- From [tex]\(6 CO_2\)[/tex]: [tex]\(6 \times 2 = 12\)[/tex] oxygen atoms
- From [tex]\(6 H_2O\)[/tex]: [tex]\(6 \times 1 = 6\)[/tex] oxygen atoms
- Total oxygen atoms needed: [tex]\(12 + 6 = 18\)[/tex] oxygen atoms
- [tex]\(O_2\)[/tex] molecule contains 2 oxygen atoms. To get 18 oxygen atoms, we need 9 [tex]\(O_2\)[/tex] molecules.
[tex]\[ C_6H_{12} + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
6. Final balanced equation:
[tex]\[ C_6H_{12} + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O \][/tex]
7. Conclusion:
For every molecule of cyclohexane ([tex]\(C_6H_{12}\)[/tex]) burned, 6 molecules of carbon dioxide ([tex]\(CO_2\)[/tex]) are produced. Thus, the correct answer is:
A. 6
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