Sure, let's balance the chemical equation step by step:
The given chemical equation is:
[tex]\[ \mathrm{C_6H_{12}O_6} + \mathrm{O_2} \rightarrow \mathrm{CO_2} + \mathrm{H_2O} \][/tex]
To balance this equation, we need to ensure that the number of each type of atom on the reactant side (left) is equal to the number on the product side (right). Let's go through this systematically:
### Step-by-step balancing:
1. Carbon (C):
- On the reactant side, there are 6 carbon atoms in [tex]\(\mathrm{C_6H_{12}O_6}\)[/tex].
- On the product side, carbon is present in [tex]\(\mathrm{CO_2}\)[/tex]. To balance the carbons, we need 6 [tex]\(\mathrm{CO_2}\)[/tex] molecules: [tex]\[\mathrm{C_6H_{12}O_6} + \mathrm{O_2} \rightarrow 6\mathrm{CO_2} + \mathrm{H_2O}\][/tex]
2. Hydrogen (H):
- On the reactant side, there are 12 hydrogen atoms in [tex]\(\mathrm{C_6H_{12}O_6}\)[/tex].
- On the product side, hydrogen is present in [tex]\(\mathrm{H_2O}\)[/tex]. To balance the hydrogens, we need 6 [tex]\(\mathrm{H_2O}\)[/tex] molecules: [tex]\[\mathrm{C_6H_{12}O_6} + \mathrm{O_2} \rightarrow 6\mathrm{CO_2} + 6\mathrm{H_2O}\][/tex]
3. Oxygen (O):
- On the reactant side, oxygen atoms are in [tex]\(\mathrm{C_6H_{12}O_6}\)[/tex] and [tex]\(\mathrm{O_2}\)[/tex]. There are 6 oxygens from [tex]\(\mathrm{C_6H_{12}O_6}\)[/tex] plus an unknown number from [tex]\(\mathrm{O_2}\)[/tex].
- On the product side, we have oxygen in both [tex]\(\mathrm{CO_2}\)[/tex] and [tex]\(\mathrm{H_2O}\)[/tex]. From 6 [tex]\(\mathrm{CO_2}\)[/tex], we have [tex]\(6 \times 2 = 12\)[/tex] oxygen atoms. From 6 [tex]\(\mathrm{H_2O}\)[/tex], we have [tex]\(6 \times 1 = 6\)[/tex] oxygen atoms. So, the total oxygen count on the product side is [tex]\(12 + 6 = 18\)[/tex] oxygen atoms.
- On the reactant side, to balance these 18 oxygen atoms, we already have 6 from [tex]\(\mathrm{C_6H_{12}O_6}\)[/tex], so we need [tex]\(18 - 6 = 12\)[/tex] more oxygen atoms. Since [tex]\(\mathrm{O_2}\)[/tex] provides 2 oxygen atoms per molecule, we need [tex]\(\frac{12}{2} = 6\)[/tex] molecules of [tex]\(\mathrm{O_2}\)[/tex]: [tex]\[\mathrm{C_6H_{12}O_6} + 6\mathrm{O_2} \rightarrow 6\mathrm{CO_2} + 6\mathrm{H_2O}\][/tex]
Hence, the sequence of coefficients that balance the equation is [tex]\(1, 6, 6, 6\)[/tex].
Therefore, the correct answer is: [tex]\(1, 6, 6, 6\)[/tex]
