To determine the overall chemical equation from the given intermediate chemical equations, we need to follow these steps carefully:
1. List the intermediate chemical equations:
[tex]\[
\begin{array}{l}
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) \\
2 H_2O(g) \rightarrow 2 H_2O(l)
\end{array}
\][/tex]
2. Combine the equations:
When combining, it is vital to ensure that any intermediate species (like [tex]\( H_2O(g) \)[/tex]) cancel out correctly. Let's analyze both sides of the combined equation:
The first equation is: [tex]\( CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) \)[/tex]
The second equation is: [tex]\( 2 H_2O(g) \rightarrow 2 H_2O(l) \)[/tex]
3. Cancel out the intermediate species:
We see that [tex]\( 2 H_2O(g) \)[/tex] appears as a product in the first equation and as a reactant in the second equation. These can cancel out:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g)
\][/tex]
[tex]\[
2 H_2O(g) \rightarrow 2 H_2O(l)
\][/tex]
Canceling out [tex]\( 2 H_2O(g) \)[/tex], we get:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
4. Write the overall equation and check:
The remaining species give us the overall reaction:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
This combines the initial reactants [tex]\( CH_4 \)[/tex] and [tex]\( O_2 \)[/tex] directly to form [tex]\( CO_2 \)[/tex] and [tex]\( H_2O \)[/tex] in its liquid state, eliminating any intermediates.
Among the given choices, the correct overall chemical equation is:
[tex]\[ CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l) \][/tex]
Thus, the overall chemical equation is indeed [tex]\( CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l) \)[/tex], corresponding to the index 0 in the list of equations provided.
