To determine how many O[tex]\(_2\)[/tex] molecules are needed to form one P[tex]\(_4\)[/tex]O[tex]\(_{10}\)[/tex] molecule, we follow these steps:
1. Write down the given chemical equation:
[tex]\[
P_4(s) + x O_2(g) \rightarrow P_4O_{10}(s)
\][/tex]
2. Determine the number of oxygen atoms in P[tex]\(_4\)[/tex]O[tex]\(_{10}\)[/tex]:
- A single molecule of P[tex]\(_4\)[/tex]O[tex]\(_{10}\)[/tex] contains 10 oxygen atoms.
3. Recall that each O[tex]\(_2\)[/tex] molecule contains 2 oxygen atoms:
- We need O[tex]\(_2\)[/tex] molecules to supply the oxygen atoms required to form P[tex]\(_4\)[/tex]O[tex]\(_{10}\)[/tex].
4. Calculate the number of O[tex]\(_2\)[/tex] molecules required:
- To get the 10 oxygen atoms needed, we divide the total number of oxygen atoms required by the number of atoms contained in each O[tex]\(_2\)[/tex] molecule.
[tex]\[
\frac{10 \text{ oxygen atoms}}{2 \text{ oxygen atoms per O}_2} = 5 \text{ O}_2 \text{ molecules}
\][/tex]
5. Conclusion:
- Therefore, 5 molecules of O[tex]\(_2\)[/tex] are needed to form one molecule of P[tex]\(_4\)[/tex]O[tex]\(_{10}\)[/tex].
The balanced equation is:
[tex]\[
P_4(s) + 5 O_2(g) \rightarrow P_4O_{10}(s)
\][/tex]
