Let's analyze and verify the balanced chemical equation:
[tex]\[
2 \, \text{C}_4\text{H}_{10} + 13 \, \text{O}_2 \rightarrow 8 \, \text{CO}_2 + 10 \, \text{H}_2\text{O}
\][/tex]
### Step 1: Count the number of atoms of each element on the reactant side
1. Carbon (C):
[tex]\[
2 \times 4 = 8 \text{ atoms of C}
\][/tex]
2. Hydrogen (H):
[tex]\[
2 \times 10 = 20 \text{ atoms of H}
\][/tex]
3. Oxygen (O):
[tex]\[
13 \times 2 = 26 \text{ atoms of O}
\][/tex]
### Step 2: Count the number of atoms of each element on the product side
1. Carbon (C):
[tex]\[
8 \times 1 = 8 \text{ atoms of C}
\][/tex]
2. Hydrogen (H):
[tex]\[
10 \times 2 = 20 \text{ atoms of H}
\][/tex]
3. Oxygen (O):
[tex]\[
8 \times 2 + 10 \times 1 = 16 + 10 = 26 \text{ atoms of O}
\][/tex]
### Step 3: Compare the number of atoms on both sides
- Carbon (C): Both sides have [tex]\( 8 \text{ atoms of C} \)[/tex].
- Hydrogen (H): Both sides have [tex]\( 20 \text{ atoms of H} \)[/tex].
- Oxygen (O): Both sides have [tex]\( 26 \text{ atoms of O} \)[/tex].
Therefore, the balanced equation has 8 atoms of carbon, 26 atoms of oxygen, and 20 atoms of hydrogen on each side of the equation.
### Final Answer
[tex]\[
\text{This equation is balanced because there are } 8 \text{ atoms of carbon (C), } 26 \text{ atoms of oxygen (O), and } 20 \text{ atoms of hydrogen (H) on each side of the equation}.
\][/tex]
