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What is the final chemical equation from the following intermediate chemical equations?

[tex]\[
\begin{array}{l}
P_4O_6(s) \rightarrow P_4(s) + 3O_2(g) \\
P_4(s) + 5O_2(g) \rightarrow P_4O_{10}(s)
\end{array}
\][/tex]

A. [tex]\(P_4O_6(s) + 2O_2(g) \rightarrow P_4O_{10}(s)\)[/tex]

B. [tex]\(P_4O_6(s) + 8O_2(g) \rightarrow 2P_4(s) + P_4O_{10}(s)\)[/tex]

C. [tex]\(P_4O_6(s) + 15O_2(g) \rightarrow P_4(s) + P_4O_{10}(s)\)[/tex]

D. [tex]\(P_4O_6(s) + \left(\frac{5}{3}\right)O_2(g) \rightarrow P_4O_{10}(s)\)[/tex]



Answer :

GinnyAnswer
To find the final chemical equation from the given intermediate chemical equations, let's analyze each step systematically.

We are given two intermediate equations:
1. [tex]\( P_4O_6(s) \rightarrow P_4(s) + 3O_2(g) \)[/tex]
2. [tex]\( P_4(s) + 5O_2(g) \rightarrow P_4O_{10}(s) \)[/tex]

The goal is to derive the single combined chemical equation.

Step-by-Step Solution:

1. Identify the species involved in each step:
- For the first intermediate equation:
- Reactant: [tex]\( P_4O_6(s) \)[/tex]
- Products: [tex]\( P_4(s) \)[/tex], [tex]\( O_2(g) \)[/tex]

- For the second intermediate equation:
- Reactants: [tex]\( P_4(s) \)[/tex], [tex]\( O_2(g) \)[/tex]
- Product: [tex]\( P_4O_{10}(s) \)[/tex]

2. Combine the two reactions:

- The product [tex]\( P_4(s) \)[/tex] formed in the first reaction serves as the reactant in the second reaction. Therefore, we can combine the two reactions by ensuring the [tex]\( P_4(s) \)[/tex] produced is used completely.

[tex]\[ P_4O_6(s) \rightarrow P_4(s) + 3O_2(g) \][/tex]
[tex]\[ P_4(s) + 5O_2(g) \rightarrow P_4O_{10}(s) \][/tex]

3. Sum the reactions:

- By adding the two reactions together, we get:

[tex]\[ P_4O_6(s) \rightarrow P_4(s) + 3O_2(g) \][/tex]
[tex]\[ P_4(s) + 5O_2(g) \rightarrow P_4O_{10}(s) \][/tex]

When we add these reactions, the [tex]\( P_4(s) \)[/tex] cancels out from both sides:

[tex]\[ P_4O_6(s) + 5O_2(g) \rightarrow P_4(s) + 3O_2(g) + P_4O_{10}(s) \][/tex]

Simplifying further:

[tex]\[ P_4O_6(s) + (5 - 3)O_2(g) \rightarrow P_4O_{10}(s) \][/tex]
[tex]\[ P_4O_6(s) + 2O_2(g) \rightarrow P_4O_{10}(s) \][/tex]

Final Chemical Equation:

Therefore, the final chemical equation derived from the intermediate steps is:

[tex]\[ P_4O_6(s) + 2O_2(g) \rightarrow P_4O_{10}(s) \][/tex]

This is the correct and final chemical equation resulting from combining the intermediate steps given.

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