To determine how many carbon dioxide ([tex]\(CO_2\)[/tex]) molecules are produced for every cyclohexane ([tex]\(C_6H_{12}\)[/tex]) molecule burned, we need to balance the given combustion reaction. The unbalanced equation is:
[tex]\[ C_6H_{12} + O_2 \rightarrow CO_2 + H_2O + \text{heat} \][/tex]
Let's proceed with balancing the equation step-by-step.
1. Balance Carbon Atoms:
There are 6 carbon atoms in one molecule of cyclohexane ([tex]\(C_6H_{12}\)[/tex]). Therefore, we need 6 [tex]\(CO_2\)[/tex] molecules to balance the carbon atoms:
[tex]\[ C_6H_{12} + O_2 \rightarrow 6 CO_2 + H_2O + \text{heat} \][/tex]
2. Balance Hydrogen Atoms:
There are 12 hydrogen atoms in one molecule of cyclohexane ([tex]\(C_6H_{12}\)[/tex]). Therefore, we need 6 [tex]\(H_2O\)[/tex] molecules to balance the hydrogen atoms (since each [tex]\(H_2O\)[/tex] contains 2 hydrogen atoms):
[tex]\[ C_6H_{12} + O_2 \rightarrow 6 CO_2 + 6 H_2O + \text{heat} \][/tex]
3. Balance Oxygen Atoms:
Now, let's balance the oxygen atoms. On the product side, we have:
[tex]\[ 6 \times CO_2 \rightarrow 6 \times 2 = 12 \text{ oxygen atoms from } CO_2 \][/tex]
[tex]\[ 6 \times H_2O \rightarrow 6 \times 1 = 6 \text{ oxygen atoms from } H_2O \][/tex]
So, we have a total of [tex]\(12 + 6 = 18\)[/tex] oxygen atoms on the product side.
On the reactant side, we have [tex]\(O_2\)[/tex] molecules. To get 18 oxygen atoms, we need:
[tex]\[ \frac{18}{2} = 9 \text{ } O_2 \text{ molecules} \][/tex]
So the balanced equation is:
[tex]\[ C_6H_{12} + 9 O_2 \rightarrow 6 CO_2 + 6 H_2O + \text{heat} \][/tex]
Therefore, for every molecule of cyclohexane ([tex]\(C_6H_{12}\)[/tex]) burned, 6 molecules of carbon dioxide ([tex]\(CO_2\)[/tex]) are produced. Hence, the correct answer is:
C. 6
