Answer: Option (a) is the correct answer.
Step-by-step explanation:
The given reaction is as follows.
![CH_(4) + x(O_(2) + 3.76N_(2)) \rightarrow Products](https://img.qammunity.org/2020/formulas/chemistry/college/c5u5sn03kqw44vhubw7kgghz40ebnragxx.png)
Since, it is a combustion reaction so, nitrogen will not take part in it and hence, it will remain the same on both sides of the reaction.
Also, it is known that in a combustion reaction oxygen reacts with a hydrocarbon and results in the formation of carbon dioxide and water. Therefore, for the above reaction we write the complete reaction equation as follows.
![CH_(4) + x(O_(2) + 3.76N_(2)) \rightarrow CO_(2) + H_(2)O + 3.76 N_(2)](https://img.qammunity.org/2020/formulas/chemistry/college/dbtx0ocfg6q97745q5667xs80ohvj82dqr.png)
or,
as nitrogen is not taking part in the reaction.
Number of atoms on reactant side are as follows.
C = 1
H = 4
O = 2
Number of atoms on product side are as follows.
C = 1
O = 3
H = 2
Therefore, to balance this equation we multiply oxygen on reactant side by 2. Also, we multiply water on product side by 2. Hence, the complete balanced chemical equation is as follows.