To derive the overall chemical equation from the given intermediate chemical reactions, we will follow these steps:
1. List the given intermediate reactions:
[tex]\[
\begin{aligned}
1. & \quad CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) \\
2. & \quad 2 H_2O(g) \rightarrow 2 H_2O(l)
\end{aligned}
\][/tex]
2. Sum the intermediate reactions:
We need to add up all the reactants and products from both equations. Notice that [tex]\(2 \, H_2O(g)\)[/tex] appears as a product in the first reaction and as a reactant in the second reaction. According to the law of conservation of mass, these will cancel out.
3. Write the sum of the reactants and products:
[tex]\(\text{Reactants:}\)[/tex] [tex]\( CH_4(g) + 2 O_2(g) \)[/tex]
[tex]\(\text{Products:}\)[/tex] [tex]\( CO_2(g) + 2 H_2O(l) \)[/tex]
When we combine these steps, the [tex]\(2 \, H_2O(g)\)[/tex] on both sides cancel out.
4. Write the overall equation:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
Thus, the overall chemical equation obtained by combining the given intermediate reactions is:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
So, among the given options, the correct overall chemical equation is:
[tex]\[
\boxed{CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)}
\][/tex]
