Final answer:
To increase the relative humidity of a room in the desert from 0% to 40% for air at 90°F (≈ 32.2°C), 1809.6 grams of water vapor must be added to the 120 m³ room volume.
Step-by-step explanation:
To calculate how much water vapor needs to be added to air in a room so that its relative humidity becomes 40%, we need to know the saturation vapor density at the given temperature and then calculate the required mass of water vapor for the desired relative humidity. Since the room is at 90°F (≈ 32.2°C), and we want to find the amount of water vapor needed for a relative humidity of 40% in the room, we need to use the concept of percent relative humidity and the saturation vapor density at the given temperature.
The volume of the room is 5 m × 6 m × 4 m = 120 m³. At 32.2°C, the saturation vapor density is approximately 37.7 g/m³ (this would be confirmed by referring to a table of saturation vapor densities at different temperatures, which is not provided here, but let's assume we know this value from such a table). To achieve 40% relative humidity, we would want the water vapor density to be 40% of 37.7 g/m³, which is 0.4 × 37.7 g/m³ = 15.08 g/m³.
With zero initial humidity, the entire 15.08 g/m³ must be added to each cubic meter of air to reach 40% humidity. Therefore, for the entire room which is 120 m³, we would need to add 15.08 g/m³ × 120 m³ = 1809.6 grams of water vapor to reach the desired humidity level.