Sure, let's determine the overall reaction step-by-step for the given chemical equations.
We are given two chemical equations:
1. [tex]\( CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g) \)[/tex]
2. [tex]\( 2 H_2O(g) \rightarrow 2 H_2O(l) \)[/tex]
To find the overall reaction, we need to add these two equations together. When adding chemical equations, we need to sum the reactants on one side and the products on the other side. Also, we should cancel out any species that appear on both sides of the resulting equation.
Let's write them down step by step.
1. The first equation:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(g)
\][/tex]
2. The second equation:
[tex]\[
2 H_2O(g) \rightarrow 2 H_2O(l)
\][/tex]
Now, let's add them together:
- On the reactants side, we have: [tex]\( CH_4(g) + 2 O_2(g) + 2 H_2O(g) \)[/tex]
- On the products side, we have: [tex]\( CO_2(g) + 2 H_2O(g) + 2 H_2O(l) \)[/tex]
We notice that [tex]\( 2 H_2O(g) \)[/tex] on the reactants side appears on the products side as well. So we can cancel out [tex]\( 2 H_2O(g) \)[/tex] from both sides.
After canceling [tex]\( 2 H_2O(g) \)[/tex]:
- On the reactants side, we are left with: [tex]\( CH_4(g) + 2 O_2(g) \)[/tex]
- On the products side, we are left with: [tex]\( CO_2(g) + 2 H_2O(l) \)[/tex]
So, the overall reaction is:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
Thus, the equation for the overall reaction obtained by adding the given equations is:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
Hence, the correct answer is:
[tex]\[
CH_4(g) + 2 O_2(g) \rightarrow CO_2(g) + 2 H_2O(l)
\][/tex]
