Let's break down the combustion reaction of butane step-by-step to determine the number of each type of atom on both sides of the equation:
The given balanced equation is:
[tex]\[ 2 C_4H_{10} + 13 O_2 \rightarrow 8 CO_2 + 10 H_2O \][/tex]
First, we need to identify the number of each type of atom on the reactant side and the product side:
### Reactant Side:
1. Carbon (C):
- In [tex]\(2 C_4H_{10}\)[/tex]:
- Each [tex]\(C_4H_{10}\)[/tex] molecule contains 4 carbon atoms.
- Therefore, [tex]\(2 C_4H_{10}\)[/tex] contains [tex]\(2 \times 4 = 8\)[/tex] carbon atoms.
2. Oxygen (O):
- In [tex]\(13 O_2\)[/tex]:
- Each [tex]\(O_2\)[/tex] molecule contains 2 oxygen atoms.
- Therefore, [tex]\(13 O_2\)[/tex] contains [tex]\(13 \times 2 = 26\)[/tex] oxygen atoms.
3. Hydrogen (H):
- In [tex]\(2 C_4H_{10}\)[/tex]:
- Each [tex]\(C_4H_{10}\)[/tex] molecule contains 10 hydrogen atoms.
- Therefore, [tex]\(2 C_4H_{10}\)[/tex] contains [tex]\(2 \times 10 = 20\)[/tex] hydrogen atoms.
### Product Side:
1. Carbon (C):
- In [tex]\(8 CO_2\)[/tex]:
- Each [tex]\(CO_2\)[/tex] molecule contains 1 carbon atom.
- Therefore, [tex]\(8 CO_2\)[/tex] contains [tex]\(8 \times 1 = 8\)[/tex] carbon atoms.
2. Oxygen (O):
- In [tex]\(8 CO_2\)[/tex]:
- Each [tex]\(CO_2\)[/tex] molecule contains 2 oxygen atoms.
- Therefore, [tex]\(8 CO_2\)[/tex] contains [tex]\(8 \times 2 = 16\)[/tex] oxygen atoms.
- In [tex]\(10 H_2O\)[/tex]:
- Each [tex]\(H_2O\)[/tex] molecule contains 1 oxygen atom.
- Therefore, [tex]\(10 H_2O\)[/tex] contains [tex]\(10 \times 1 = 10\)[/tex] oxygen atoms.
- Adding oxygen atoms from both products:
- Total oxygen atoms = [tex]\(16 + 10 = 26\)[/tex] oxygen atoms.
3. Hydrogen (H):
- In [tex]\(10 H_2O\)[/tex]:
- Each [tex]\(H_2O\)[/tex] molecule contains 2 hydrogen atoms.
- Therefore, [tex]\(10 H_2O\)[/tex] contains [tex]\(10 \times 2 = 20\)[/tex] hydrogen atoms.
So, the equation is balanced because it has:
- [tex]\(\boxed{8}\)[/tex] atoms of carbon (C) on each side,
- [tex]\(\boxed{26}\)[/tex] atoms of oxygen (O) on each side, and
- [tex]\(\boxed{20}\)[/tex] atoms of hydrogen (H) on each side.
