Let's solve the problem step-by-step.
The balanced chemical equation would distribute the four atoms of oxygen among water (\( H_2O \)) and oxygen gas (\( O_2 \)).
To determine the correct coefficients, we need to balance the atoms of oxygen in the reactants and the products.
First, let's check each provided option:
1. 2 in front of water and 2 in front of oxygen:
[tex]\[
2 H_2O + 2 O_2 \rightarrow Products
\][/tex]
Water (\( H_2O \)) has 1 oxygen per molecule and Oxygen gas (\( O_2 \)) has 2 oxygen atoms per molecule.
Total oxygen atoms:
[tex]\[
2 \times 1 + 2 \times 2 = 2 + 4 = 6 \text{ atoms of oxygen}
\][/tex]
This doesn't match the 4 atoms we need.
2. 1 in front of water and 2 in front of oxygen:
[tex]\[
1 H_2O + 2 O_2 \rightarrow Products
\][/tex]
Total oxygen atoms:
[tex]\[
1 \times 1 + 2 \times 2 = 1 + 4 = 5 \text{ atoms of oxygen}
\][/tex]
This also doesn't match.
3. 1 in front of water and 1 in front of oxygen:
[tex]\[
1 H_2O + 1 O_2 \rightarrow Products
\][/tex]
Total oxygen atoms:
[tex]\[
1 \times 1 + 1 \times 2 = 1 + 2 = 3 \text{ atoms of oxygen}
\][/tex]
This still doesn't match.
4. 2 in front of water and 1 in front of oxygen:
[tex]\[
2 H_2O + 1 O_2 \rightarrow Products
\][/tex]
Total oxygen atoms:
[tex]\[
2 \times 1 + 1 \times 2 = 2 + 2 = 4 \text{ atoms of oxygen}
\][/tex]
This matches the 4 atoms we have.
Thus, the correct coefficients that balance the oxygen atoms in the reactants and products are 2 in front of water and 1 in front of oxygen.
The correct choice is:
[tex]\[
\boxed{4}
\][/tex]
