To determine the overall equation for the reaction that produces \(P_4O_{10}\) from \(P_4O_6\) and \(O_2\), we need to follow these steps:
1. Identify the Given Equations:
[tex]\[
\begin{array}{l}
P_4(s) + 3 O_2(g) \rightarrow P_4O_6(s) \\
P_4(s) + 5 O_2(g) \rightarrow P_4O_{10}(s)
\end{array}
\][/tex]
2. Determine the Chemical Equation to Combine:
We need \(P_4O_6\) and \(O_2\) as reactants, resulting in \(P_4O_{10}\) as a product. To do so, we should subtract the first equation from the second one.
3. Balance the Reactants and Products:
On subtracting the first equation from the second:
Cancel out the common reactant \(P_4(s)\)
Adjust the \(O_2(g)\) molecules and the corresponding products.
First reaction:
[tex]\[
P_4(s) + 3 O_2(g) \rightarrow P_4O_6(s)
\][/tex]
Second reaction:
[tex]\[
P_4(s) + 5 O_2(g) \rightarrow P_4O_{10}(s)
\][/tex]
Subtract the coefficients of the first reactants from the reactants of the second:
[tex]\[
P_4(s) + 5 O_2(g) \rightarrow P_4O_{10}(s)
\][/tex]
Minus:
[tex]\[
P_4(s) + 3 O_2(g) \rightarrow P_4O_6(s)
\][/tex]
This gives:
[tex]\[
(5 O_2(g) - 3 O_2(g)) \rightarrow P_4O_{10}(s) - P_4O_6(s)
\][/tex]
Simplifies to:
[tex]\[
2 O_2(g) + P_4O_6(s) \rightarrow P_4O_{10}(s)
\][/tex]
4. Conclusion:
The overall chemical equation that produces \(P_4O_{10}\) from \(P_4O_6\) and \(O_2\) becomes:
[tex]\[
P_4O_6(s) + 2 O_2(g) \rightarrow P_4O_{10}(s)
\][/tex]
Therefore, the correct equation is:
[tex]\[
P_4O_6(s) + 2 O_2(g) \rightarrow P_4O_{10}(s)
\][/tex]
