To determine which gas you would detect first after opening a container in a corner of a large room, we need to consider the properties of the gases involved, specifically their molecular weights. The rate at which a gas diffuses is inversely proportional to the square root of its molecular weight (this is described by Graham's Law of Diffusion).
Let's look at the molecular weights of the given gases:
- Hydrogen sulfide ([tex]\( H_2S \)[/tex]) has a molecular weight of approximately 34 g/mol.
- Ammonia ([tex]\( NH_3 \)[/tex]) has a molecular weight of approximately 17 g/mol.
According to Graham's Law, the gas with the lower molecular weight will diffuse faster.
Given these molecular weights:
- [tex]\( H_2S \)[/tex] (Hydrogen sulfide) with a molecular weight of 34 g/mol.
- [tex]\( NH_3 \)[/tex] (Ammonia) with a molecular weight of 17 g/mol.
Since ammonia ([tex]\( NH_3 \)[/tex]) has a lower molecular weight than hydrogen sulfide ([tex]\( H_2S \)[/tex]), it will diffuse faster. Therefore, you would detect the odor of ammonia ([tex]\( NH_3 \)[/tex]) first on the other side of the room.
Thus, the answer is:
[tex]\( NH _3 \)[/tex].
