Answer :
To balance the chemical equation for the combustion of sugar, let's go through the steps meticulously.
The given chemical equation is:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(l) \][/tex]
### Step-by-Step Balancing:
1. Identify the number of each type of atom in the reactants and products:
- Reactants:
- Carbon (C): 6 (from C₆H₁₂O₆)
- Hydrogen (H): 12 (from C₆H₁₂O₆)
- Oxygen (O): 6 (from C₆H₁₂O₆) and part from O₂ (unknown amount)
- Products:
- Carbon (C): 1 (from [tex]\(\text{CO}_2\)[/tex])
- Hydrogen (H): 2 (from [tex]\(\text{H}_2\text{O}\)[/tex])
- Oxygen (O): 2 (from [tex]\(\text{CO}_2\)[/tex]) and 1 (from [tex]\(\text{H}_2\text{O}\)[/tex])
2. Balancing carbon atoms:
- We have 6 carbons on the left side from C₆H₁₂O₆
- Each [tex]\(\text{CO}_2\)[/tex] molecule contains 1 carbon atom
- Therefore, we need 6 [tex]\(\text{CO}_2\)[/tex] molecules to balance the carbon atoms.
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{O}_2 \rightarrow 6\text{CO}_2 + \text{H}_2\text{O} \][/tex]
3. Balancing hydrogen atoms:
- We have 12 hydrogens on the left side from C₆H₁₂O₆
- Each [tex]\(\text{H}_2\text{O}\)[/tex] molecule contains 2 hydrogen atoms
- Therefore, we need 6 [tex]\(\text{H}_2\text{O}\)[/tex] molecules to balance the hydrogen atoms.
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} \][/tex]
4. Balancing oxygen atoms:
- On the right side:
- We get 12 oxygens from 6 [tex]\(\text{CO}_2\)[/tex] (since each [tex]\(\text{CO}_2\)[/tex] has 2 oxygens)
- We get 6 oxygens from 6 [tex]\(\text{H}_2\text{O}\)[/tex] (since each [tex]\(\text{H}_2\text{O}\)[/tex] has 1 oxygen)
- Total oxygens in products = 12 (from [tex]\(\text{CO}_2\)[/tex]) + 6 (from [tex]\(\text{H}_2\text{O}\)[/tex]) = 18 oxygens
- On the left side, we already have 6 oxygens from C₆H₁₂O₆. Therefore, we need an additional 12 oxygens from [tex]\(\text{O}_2\)[/tex].
- Each [tex]\(\text{O}_2\)[/tex] molecule has 2 oxygens. Therefore, we need 12/2 = 6 [tex]\(\text{O}_2\)[/tex] molecules.
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} \][/tex]
Therefore, the correct sequence of coefficients to balance the equation is:
[tex]\[ 1, 6, 6, 6 \][/tex]
The answer is:
[tex]\[ \boxed{1, 6, 6, 6} \][/tex]
The given chemical equation is:
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) + \text{H}_2\text{O}(l) \][/tex]
### Step-by-Step Balancing:
1. Identify the number of each type of atom in the reactants and products:
- Reactants:
- Carbon (C): 6 (from C₆H₁₂O₆)
- Hydrogen (H): 12 (from C₆H₁₂O₆)
- Oxygen (O): 6 (from C₆H₁₂O₆) and part from O₂ (unknown amount)
- Products:
- Carbon (C): 1 (from [tex]\(\text{CO}_2\)[/tex])
- Hydrogen (H): 2 (from [tex]\(\text{H}_2\text{O}\)[/tex])
- Oxygen (O): 2 (from [tex]\(\text{CO}_2\)[/tex]) and 1 (from [tex]\(\text{H}_2\text{O}\)[/tex])
2. Balancing carbon atoms:
- We have 6 carbons on the left side from C₆H₁₂O₆
- Each [tex]\(\text{CO}_2\)[/tex] molecule contains 1 carbon atom
- Therefore, we need 6 [tex]\(\text{CO}_2\)[/tex] molecules to balance the carbon atoms.
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{O}_2 \rightarrow 6\text{CO}_2 + \text{H}_2\text{O} \][/tex]
3. Balancing hydrogen atoms:
- We have 12 hydrogens on the left side from C₆H₁₂O₆
- Each [tex]\(\text{H}_2\text{O}\)[/tex] molecule contains 2 hydrogen atoms
- Therefore, we need 6 [tex]\(\text{H}_2\text{O}\)[/tex] molecules to balance the hydrogen atoms.
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6 + \text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} \][/tex]
4. Balancing oxygen atoms:
- On the right side:
- We get 12 oxygens from 6 [tex]\(\text{CO}_2\)[/tex] (since each [tex]\(\text{CO}_2\)[/tex] has 2 oxygens)
- We get 6 oxygens from 6 [tex]\(\text{H}_2\text{O}\)[/tex] (since each [tex]\(\text{H}_2\text{O}\)[/tex] has 1 oxygen)
- Total oxygens in products = 12 (from [tex]\(\text{CO}_2\)[/tex]) + 6 (from [tex]\(\text{H}_2\text{O}\)[/tex]) = 18 oxygens
- On the left side, we already have 6 oxygens from C₆H₁₂O₆. Therefore, we need an additional 12 oxygens from [tex]\(\text{O}_2\)[/tex].
- Each [tex]\(\text{O}_2\)[/tex] molecule has 2 oxygens. Therefore, we need 12/2 = 6 [tex]\(\text{O}_2\)[/tex] molecules.
[tex]\[ \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O} \][/tex]
Therefore, the correct sequence of coefficients to balance the equation is:
[tex]\[ 1, 6, 6, 6 \][/tex]
The answer is:
[tex]\[ \boxed{1, 6, 6, 6} \][/tex]
