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Consider the following intermediate chemical equations:

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

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

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

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

C. [tex]\( CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 4H_2O(g) + 2H_2O(l) \)[/tex]

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



Answer :

GinnyAnswer
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.

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