45.4 L of dinitrogen reacted with 22.7 L of dioxygen and 45.4 L of nitrous oxide was formed. The reaction is

$2N_2\left(g\right)+O_2\left(g\right)\to 2N_{2}O\left(g\right)$

Reaction given:

$2N_2\left(g\right)+O_2\left(g\right)\to 2N_{2}O\left(g\right)$

Volume- 45.4 L 22.7 L 45.4 L

Here 45.4L of $N_2$ is reacting with 22.7L of $O_2$ to give 45.4L of $N_{2}O$.

Ratio of volume of gases reacted and produced:

$V_{N_2}:V_{O_2}:V_{N_{2}O}$

45.4: 22.7: 45.4

2: 1: 2

This is a simple whole number ratio.

Thus, Gay Lussac's law is obeyed in this experiment.

Gay – Lussac’s Law- According to this law, gases combine or are produced in a chemical reaction in a simple ratio by volume, provided that all gases are at same temperature and pressure.

Hence, when 45.4L of $N_2$ reacted with 22.7L of $O_2$ and 45.4L of $N_{2}O$ was formed. Gay-Lussac's law is being obeyed in the reaction.