Hint: The law of conservation of mass states that mass is neither created nor destroyed in a chemical reaction.

Explanation:

Step 1: The complete reaction is: 

          \(2N_2(g) \ \ + \ \ O_2(g) \ \ \rightarrow\ \ 2N_2O(g)\)
          45.4 L          22.7L          45.4 L

So, the ratio of the volume of gases is:

 \(V_{N_2} : V_{O_2} : V_{N_2O} \) = \(2:1:2\)

Step 2: The gases are present in a simple whole number ratio. According to Gay Lussac's law, gases combine or are produced in a chemical reaction in a simple ratio by volume, provided that all gases are at the same temperature and pressure.

Hence, the given reaction follows Gay Lussac's law. 

Step 3: This reaction does not violate the law of conservation of mass. As per the stoichiometry, one mole of \(O_2\) reacts with two moles of \(N_2\) to form two moles of \(N_2O\).

Thus, the volume of product formed is not equal to the volume of \(O_2\) consumed. 

Therefore, option 1 is the correct answer.