Consider the unbalanced equation for the oxidation of butene.

[tex]\[ C_4H_8 + 6O_2 \rightarrow CO_2 + H_2O \][/tex]

For each molecule of [tex]\( C_4H_8 \)[/tex] that reacts, how many molecules of carbon dioxide and water are produced?

A. Two carbon dioxide molecules and two water molecules
B. Four carbon dioxide molecules and four water molecules
C. Two carbon dioxide molecules and four water molecules
D. Four carbon dioxide molecules and two water molecules



Answer :

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.