Consider the following intermediate chemical equations:
[tex]\[
\begin{aligned}
&CH_4 (g) + 2 O_2 (g) \rightarrow CO_2 (g) + 2 H_2O (g) \\
&2 H_2O (g) \rightarrow 2 H_2O (l)
\end{aligned}
\][/tex]

Which overall chemical equation is obtained by combining these intermediate equations?

A. [tex]\(CH_4 (g) + 2 O_2 (g) \rightarrow CO_2 (g) + 2 H_2O (l)\)[/tex]

B. [tex]\[
\begin{aligned}
CH_4 (g) + 2 O_2 (g) \rightarrow CO_2 (g) + 2 H_2O (g) \\
CH_4 (g) + 2 O_2 (g) \rightarrow CO_2 (g) + 4 H_2O (g) + 2 H_2O (l)
\end{aligned}
\][/tex]

C. [tex]\(CH_4 (g) + 2 O_2 (g) \rightarrow CO_2 (g) + 6 H_2O (g)\)[/tex]



Answer :

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]