Get comprehensive answers to your questions with the help of IDNLearn.com's community. Discover the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
To balance the chemical equation for the combustion of propane ([tex]\( \text{CH}_3\text{CH}_2\text{CH}_3 \)[/tex]), we need to ensure that the number of each type of atom on the reactants side equals the number of each type on the products side. The unbalanced equation is:
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(g) \][/tex]
We need to balance the carbon, hydrogen, and oxygen atoms. Let's go step-by-step:
1. Balance Carbon (C) atoms:
[tex]\(\text{CH}_3\text{CH}_2\text{CH}_3\)[/tex] contains 3 carbon atoms. Therefore, we need 3 [tex]\(\text{CO}_2\)[/tex] molecules to balance the carbon on both sides.
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + \text{O}_2(g) \rightarrow 3\text{CO}_2(g) + \text{H}_2\text{O}(g) \][/tex]
2. Balance Hydrogen (H) atoms:
[tex]\(\text{CH}_3\text{CH}_2\text{CH}_3\)[/tex] contains 8 hydrogen atoms. Therefore, we need 4 [tex]\(\text{H}_2\text{O}\)[/tex] molecules to balance the hydrogen on both sides (since each [tex]\(\text{H}_2\text{O}\)[/tex] molecule contains 2 hydrogen atoms).
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + \text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \][/tex]
3. Balance Oxygen (O) atoms:
On the products side, we have:
- 3 [tex]\(\text{CO}_2\)[/tex] molecules contributing [tex]\(3 \times 2 = 6\)[/tex] oxygen atoms.
- 4 [tex]\(\text{H}_2\text{O}\)[/tex] molecules contributing [tex]\(4 \times 1 = 4\)[/tex] oxygen atoms.
This gives a total of [tex]\(6 + 4 = 10\)[/tex] oxygen atoms on the products side. Since [tex]\(\text{O}_2\)[/tex] is a diatomic molecule, each [tex]\(\text{O}_2\)[/tex] molecule provides 2 oxygen atoms. Therefore, we need [tex]\( \frac{10}{2} = 5 \)[/tex] [tex]\(\text{O}_2\)[/tex] molecules to balance the oxygen atoms.
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \][/tex]
So, the balanced chemical equation is:
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \][/tex]
Double-checking:
- Carbon: [tex]\(1 \text{ molecule of } \text{CH}_3\text{CH}_2\text{CH}_3 \)[/tex] = 3 atoms of C [tex]\(\rightarrow\)[/tex] [tex]\(3 \text{ molecules of } \text{CO}_2 \)[/tex] = 3 atoms of C.
- Hydrogen: [tex]\(1 \text{ molecule of } \text{CH}_3\text{CH}_2\text{CH}_3 \)[/tex] = 8 atoms of H [tex]\(\rightarrow\)[/tex] [tex]\(4 \text{ molecules of } \text{H}_2\text{O} \)[/tex] = 8 atoms of H.
- Oxygen: [tex]\(5 \text{ molecules of } \text{O}_2 \)[/tex]= 10 atoms of O [tex]\(\rightarrow\)[/tex] [tex]\(3 \text{ molecules of } \text{CO}_2 = 6\)[/tex] atoms of O and [tex]\(4 \text{ molecules of } \text{H}_2\text{O} = 4\)[/tex] atoms of O (6 + 4 = 10 atoms of O).
The balancing is correct.
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(g) \][/tex]
We need to balance the carbon, hydrogen, and oxygen atoms. Let's go step-by-step:
1. Balance Carbon (C) atoms:
[tex]\(\text{CH}_3\text{CH}_2\text{CH}_3\)[/tex] contains 3 carbon atoms. Therefore, we need 3 [tex]\(\text{CO}_2\)[/tex] molecules to balance the carbon on both sides.
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + \text{O}_2(g) \rightarrow 3\text{CO}_2(g) + \text{H}_2\text{O}(g) \][/tex]
2. Balance Hydrogen (H) atoms:
[tex]\(\text{CH}_3\text{CH}_2\text{CH}_3\)[/tex] contains 8 hydrogen atoms. Therefore, we need 4 [tex]\(\text{H}_2\text{O}\)[/tex] molecules to balance the hydrogen on both sides (since each [tex]\(\text{H}_2\text{O}\)[/tex] molecule contains 2 hydrogen atoms).
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + \text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \][/tex]
3. Balance Oxygen (O) atoms:
On the products side, we have:
- 3 [tex]\(\text{CO}_2\)[/tex] molecules contributing [tex]\(3 \times 2 = 6\)[/tex] oxygen atoms.
- 4 [tex]\(\text{H}_2\text{O}\)[/tex] molecules contributing [tex]\(4 \times 1 = 4\)[/tex] oxygen atoms.
This gives a total of [tex]\(6 + 4 = 10\)[/tex] oxygen atoms on the products side. Since [tex]\(\text{O}_2\)[/tex] is a diatomic molecule, each [tex]\(\text{O}_2\)[/tex] molecule provides 2 oxygen atoms. Therefore, we need [tex]\( \frac{10}{2} = 5 \)[/tex] [tex]\(\text{O}_2\)[/tex] molecules to balance the oxygen atoms.
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \][/tex]
So, the balanced chemical equation is:
[tex]\[ \text{CH}_3\text{CH}_2\text{CH}_3(g) + 5\text{O}_2(g) \rightarrow 3\text{CO}_2(g) + 4\text{H}_2\text{O}(g) \][/tex]
Double-checking:
- Carbon: [tex]\(1 \text{ molecule of } \text{CH}_3\text{CH}_2\text{CH}_3 \)[/tex] = 3 atoms of C [tex]\(\rightarrow\)[/tex] [tex]\(3 \text{ molecules of } \text{CO}_2 \)[/tex] = 3 atoms of C.
- Hydrogen: [tex]\(1 \text{ molecule of } \text{CH}_3\text{CH}_2\text{CH}_3 \)[/tex] = 8 atoms of H [tex]\(\rightarrow\)[/tex] [tex]\(4 \text{ molecules of } \text{H}_2\text{O} \)[/tex] = 8 atoms of H.
- Oxygen: [tex]\(5 \text{ molecules of } \text{O}_2 \)[/tex]= 10 atoms of O [tex]\(\rightarrow\)[/tex] [tex]\(3 \text{ molecules of } \text{CO}_2 = 6\)[/tex] atoms of O and [tex]\(4 \text{ molecules of } \text{H}_2\text{O} = 4\)[/tex] atoms of O (6 + 4 = 10 atoms of O).
The balancing is correct.
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.
