Sure, I can help you balance the given chemical equation step-by-step:
Equation: [tex]\(C_{12}H_{22}O_{11} + O_2 \longrightarrow CO_2 + H_2O\)[/tex]
### Step 1: Balance Carbon Atoms
- The left side of the equation has 12 carbon atoms in one molecule of [tex]\(C_{12}H_{22}O_{11}\)[/tex].
- To balance the carbons, you need 12 molecules of [tex]\(CO_2\)[/tex] on the right side since each [tex]\(CO_2\)[/tex] contains one carbon atom.
The equation now looks like:
[tex]\[C_{12}H_{22}O_{11} + O_2 \longrightarrow 12CO_2 + H_2O\][/tex]
### Step 2: Balance Hydrogen Atoms
- The left side of the equation has 22 hydrogen atoms in one molecule of [tex]\(C_{12}H_{22}O_{11}\)[/tex].
- To balance the hydrogens, you need 11 molecules of [tex]\(H_2O\)[/tex] on the right side since each [tex]\(H_2O\)[/tex] contains two hydrogen atoms.
The equation now looks like:
[tex]\[C_{12}H_{22}O_{11} + O_2 \longrightarrow 12CO_2 + 11H_2O\][/tex]
### Step 3: Balance Oxygen Atoms
- On the left side, there are 11 oxygen atoms from [tex]\(C_{12}H_{22}O_{11}\)[/tex] and the rest need to come from [tex]\(O_2\)[/tex].
- On the right side, we have:
- 12 molecules of [tex]\(CO_2\)[/tex] contributing [tex]\(12 \times 2 = 24\)[/tex] oxygen atoms.
- 11 molecules of [tex]\(H_2O\)[/tex] contributing [tex]\(11 \times 1 = 11\)[/tex] oxygen atoms.
So, in total, the right side has [tex]\(24 + 11 = 35\)[/tex] oxygen atoms.
- On the left side, we already have 11 oxygen atoms from [tex]\(C_{12}H_{22}O_{11}\)[/tex]. Therefore, the remaining [tex]\(35 - 11 = 24\)[/tex] oxygen atoms need to come from [tex]\(O_2\)[/tex].
- Each molecule of [tex]\(O_2\)[/tex] provides 2 oxygen atoms, so we need [tex]\( 24 / 2 = 12 \)[/tex] molecules of [tex]\(O_2\)[/tex].
The balanced equation is:
[tex]\[C_{12}H_{22}O_{11} + 12O_2 \longrightarrow 12CO_2 + 11H_2O\][/tex]
### Final Balanced Equation:
[tex]\[\boxed{C_{12}H_{22}O_{11} + 12O_2 \longrightarrow 12CO_2 + 11H_2O}\][/tex]
This is the balanced equation with the lowest whole-number coefficients.
