Sure! Let's balance the given chemical equation step by step and determine the number of carbon dioxide ([tex]\(\text{CO}_2\)[/tex]) and water ([tex]\(\text{H}_2\text{O}\)[/tex]) molecules produced for each molecule of butene ([tex]\(\text{C}_4\text{H}_8\)[/tex]) that reacts.
The given unbalanced equation for the oxidation of butene is:
[tex]\[
\text{C}_4\text{H}_8 + 6 \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O}
\][/tex]
### Step 1: Balance Carbon Atoms
First, we balance the carbon atoms. There are 4 carbon atoms in [tex]\(\text{C}_4\text{H}_8\)[/tex], so we need 4 molecules of [tex]\(\text{CO}_2\)[/tex] to balance the carbons.
[tex]\[
\text{C}_4\text{H}_8 + 6 \text{O}_2 \rightarrow 4 \text{CO}_2 + \text{H}_2\text{O}
\][/tex]
### Step 2: Balance Hydrogen Atoms
Next, we balance the hydrogen atoms. There are 8 hydrogen atoms in [tex]\(\text{C}_4\text{H}_8\)[/tex], so we need 4 molecules of [tex]\(\text{H}_2\text{O}\)[/tex] (since each [tex]\(\text{H}_2\text{O}\)[/tex] has 2 hydrogen atoms) to balance the hydrogens.
[tex]\[
\text{C}_4\text{H}_8 + 6 \text{O}_2 \rightarrow 4 \text{CO}_2 + 4 \text{H}_2\text{O}
\][/tex]
### Step 3: Check the Balance of Oxygen Atoms
Now, we check if the oxygen atoms are balanced. On the reactant side, we have 6 molecules of [tex]\(\text{O}_2\)[/tex], which gives us [tex]\(6 \times 2 = 12\)[/tex] oxygen atoms.
On the product side, we have:
- [tex]\(4 \times \text{CO}_2 = 4 \times 2 = 8\)[/tex] oxygen atoms from [tex]\(\text{CO}_2\)[/tex]
- [tex]\(4 \times \text{H}_2\text{O} = 4 \times 1 = 4\)[/tex] oxygen atoms from [tex]\(\text{H}_2\text{O}\)[/tex]
So, the total number of oxygen atoms on the product side is [tex]\(8 + 4 = 12\)[/tex], which matches the number of oxygen atoms on the reactant side.
The final balanced equation is:
[tex]\[
\text{C}_4\text{H}_8 + 6 \text{O}_2 \rightarrow 4 \text{CO}_2 + 4 \text{H}_2\text{O}
\][/tex]
### Conclusion
For each molecule of [tex]\(\text{C}_4\text{H}_8\)[/tex] that reacts, 4 molecules of [tex]\(\text{CO}_2\)[/tex] and 4 molecules of [tex]\(\text{H}_2\text{O}\)[/tex] are produced. Therefore, the correct answer is:
Four carbon dioxide molecules and four water molecules.
