To determine which gas odor you would detect first on the other side of a room, we need to consider the diffusion rates of the gases involved. The diffusion rate of a gas is inversely related to the square root of its molar mass—this is described by Graham's law of diffusion.
Let's review the molar masses of the gases involved:
1. Hydrogen Sulfide (H₂S):
- Hydrogen (H) has an atomic mass of approximately 1 g/mol.
- Sulfur (S) has an atomic mass of approximately 32 g/mol.
- Thus, the molar mass of H₂S = 2(1) + 32 = 34 g/mol.
2. Ammonia (NH₃):
- Nitrogen (N) has an atomic mass of approximately 14 g/mol.
- Hydrogen (H) has an atomic mass of approximately 1 g/mol.
- Thus, the molar mass of NH₃ = 14 + 3(1) = 17 g/mol.
Since the diffusion rate is higher for gases with lower molar mass, the gas with the lower molar mass will diffuse faster. Comparing the molar masses:
- H₂S: 34 g/mol
- NH₃: 17 g/mol
Ammonia (NH₃) has a lower molar mass than Hydrogen Sulfide (H₂S). Hence, NH₃ will diffuse faster through the room.
Therefore, you would detect the odor of ammonia (NH₃) first.
