To balance the chemical equation:
[tex]\[ \text{C}_2\text{H}_4\text{O}_2 (g) + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) + \text{H}_2\text{O} (g) \][/tex]
we need to ensure that the number of atoms of each element is the same on both sides of the equation. Specifically, we need to balance the carbon (C), hydrogen (H), and oxygen (O) atoms.
1. Balance Carbon:
- On the left side, there are 2 carbon atoms in [tex]\(\text{C}_2\text{H}_4\text{O}_2\)[/tex].
- On the right side, carbon is present in [tex]\(\text{CO}_2\)[/tex]. To balance the carbons, we need 2 molecules of [tex]\(\text{CO}_2\)[/tex]. Therefore, we place a coefficient of 2 in front of [tex]\(\text{CO}_2\)[/tex]:
[tex]\[ \text{C}_2\text{H}_4\text{O}_2 (g) + \text{O}_2 (g) \rightarrow 2\text{CO}_2 (g) + \text{H}_2\text{O} (g) \][/tex]
2. Balance Hydrogen:
- On the left side, there are 4 hydrogen atoms in [tex]\(\text{C}_2\text{H}_4\text{O}_2\)[/tex].
- On the right side, hydrogen is present in [tex]\(\text{H}_2\text{O}\)[/tex]. To balance the hydrogens, we need 2 molecules of [tex]\(\text{H}_2\text{O}\)[/tex]. Therefore, we place a coefficient of 2 in front of [tex]\(\text{H}_2\text{O}\)[/tex]:
[tex]\[ \text{C}_2\text{H}_4\text{O}_2 (g) + \text{O}_2 (g) \rightarrow 2\text{CO}_2 (g) + 2\text{H}_2\text{O} (g) \][/tex]
3. Balance Oxygen:
- On the left side, there are 2 oxygen atoms from [tex]\(\text{C}_2\text{H}_4\text{O}_2\)[/tex].
- On the right side, there are a total of 6 oxygen atoms (4 from [tex]\(\text{CO}_2\)[/tex] and 2 from [tex]\(\text{H}_2\text{O}\)[/tex]).
- The equation now looks like this:
[tex]\[ \text{C}_2\text{H}_4\text{O}_2 (g) + \text{O}_2 (g) \rightarrow 2\text{CO}_2 (g) + 2\text{H}_2\text{O} (g) \][/tex]
- We already have 2 oxygen atoms on the left from [tex]\(\text{C}_2\text{H}_4\text{O}_2\)[/tex], so we need 4 more oxygen atoms to balance the equation. These will come from [tex]\(O_2\)[/tex].
- Since each [tex]\(O_2\)[/tex] molecule consists of 2 oxygen atoms, we need 2 molecules of [tex]\(\text{O}_2\)[/tex]. Thus, we place a coefficient of 2 in front of [tex]\(\text{O}_2\)[/tex]:
[tex]\[ \text{C}_2\text{H}_4\text{O}_2 (g) + 2\text{O}_2 (g) \rightarrow 2\text{CO}_2 (g) + 2\text{H}_2\text{O} (g) \][/tex]
Now, the equation is balanced with the coefficients being:
[tex]\[ 1, 2, 2, 2 \][/tex]
Thus, the coefficient in front of [tex]\(\text{O}_2\)[/tex] when balanced is [tex]\(2\)[/tex].
