Sure! Let's balance the chemical equation step by step to find the missing coefficient for [tex]\(O_2\)[/tex]:
Given the unbalanced equation:
[tex]\[ \ce{C2H4 + (?) O2 -> 2 CO2 + 2 H2O} \][/tex]
1. Balance carbon atoms:
- On the left side, ethylene ([tex]\(\ce{C2H4}\)[/tex]) contains 2 carbon atoms.
- On the right side, there are 2 molecules of carbon dioxide ([tex]\(\ce{CO2}\)[/tex]), and each [tex]\(\ce{CO2}\)[/tex] molecule contains 1 carbon atom.
- Thus, on the right side, there are 2 carbon atoms ([tex]\(2 \times 1 = 2\)[/tex]).
- The number of carbon atoms is already balanced with 2 on both sides.
2. Balance hydrogen atoms:
- On the left side, ethylene ([tex]\(\ce{C2H4}\)[/tex]) contains 4 hydrogen atoms.
- On the right side, there are 2 molecules of water ([tex]\(\ce{H2O}\)[/tex]), and each [tex]\(\ce{H2O}\)[/tex] molecule contains 2 hydrogen atoms.
- Thus, on the right side, there are 4 hydrogen atoms ([tex]\(2 \times 2 = 4\)[/tex]).
- The number of hydrogen atoms is already balanced with 4 on both sides.
3. Balance oxygen atoms:
- On the right side, there are 2 molecules of carbon dioxide ([tex]\(\ce{CO2}\)[/tex]), and each [tex]\(\ce{CO2}\)[/tex] molecule contains 2 oxygen atoms.
- Thus, there are 4 oxygen atoms coming from the carbon dioxide ([tex]\(2 \times 2 = 4\)[/tex]).
- Additionally, there are 2 molecules of water ([tex]\(\ce{H2O}\)[/tex]), and each [tex]\(\ce{H2O}\)[/tex] molecule contains 1 oxygen atom.
- Thus, there are 2 oxygen atoms coming from the water ([tex]\(2 \times 1 = 2\)[/tex]).
- Therefore, the total number of oxygen atoms on the right side is [tex]\(4 + 2 = 6\)[/tex].
- On the left side, [tex]\(\ce{O2}\)[/tex] is the source of oxygen, and each [tex]\(\ce{O2}\)[/tex] molecule contains 2 oxygen atoms.
- To balance the 6 oxygen atoms on the right side with [tex]\(\ce{O2}\)[/tex] on the left side, we need [tex]\(6 \div 2 = 3\)[/tex] molecules of [tex]\(\ce{O2}\)[/tex].
Thus, the balanced chemical equation is:
[tex]\[ \ce{C2H4 + 3 O2 -> 2 CO2 + 2 H2O} \][/tex]
Therefore, the missing coefficient in front of [tex]\(\ce{O2}\)[/tex] is [tex]\(3\)[/tex].
