To balance the chemical equation involving acetylene ([tex]\(C_2H_2\)[/tex]) and oxygen ([tex]\(O_2\)[/tex]), we need to ensure that the number of atoms for each element is the same on both sides of the equation. The balanced chemical equation will allow us to find the requested coefficient for [tex]\(CO_2\)[/tex].
The unbalanced equation is:
[tex]\[ C_2H_2(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g) \][/tex]
We need to balance the number of carbon (C), hydrogen (H), and oxygen (O) atoms on both sides of the equation.
1. Balance carbon atoms:
- On the left-hand side, there are 2 carbon atoms in [tex]\(C_2H_2\)[/tex].
- Therefore, we need 2 molecules of [tex]\(CO_2\)[/tex] to balance the carbon atoms on the right side:
[tex]\[ C_2H_2 + O_2 \rightarrow 2 CO_2 + H_2O \][/tex]
2. Balance hydrogen atoms:
- On the left-hand side, there are 2 hydrogen atoms in [tex]\(C_2H_2\)[/tex].
- Therefore, we need 1 molecule of [tex]\(H_2O\)[/tex] to balance the hydrogen atoms on the right side:
[tex]\[ C_2H_2 + O_2 \rightarrow 2CO_2 + H_2O \][/tex]
3. Balance oxygen atoms:
- On the right-hand side, we have:
- [tex]\(2 \times 2 = 4\)[/tex] oxygen atoms from [tex]\(2CO_2\)[/tex]
- [tex]\(1 \times 1 = 1\)[/tex] oxygen atom from [tex]\(H_2O\)[/tex]
- This totals 5 oxygen atoms.
- On the left-hand side, each [tex]\(O_2\)[/tex] molecule contains 2 oxygen atoms. So, we need:
- [tex]\(5 / 2 = 2.5\)[/tex] molecules of [tex]\(O_2\)[/tex]
- To avoid fractional coefficients, we can multiply all the coefficients by 2:
[tex]\[ 2C_2H_2 + 5O_2 \rightarrow 4CO_2 + 2H_2O \][/tex]
Thus, the balanced equation is:
[tex]\[ 2C_2H_2(g) + 5O_2(g) \rightarrow 4CO_2(g) + 2H_2O(g) \][/tex]
The coefficient of [tex]\(CO_2\)[/tex] is 4.
