Final answer:
To calculate the mass of water needed to saturate a room at 19ºC, the equilibrium vapor pressure is used in conjunction with the room's volume and the ideal gas law. Once the room reaches 100% relative humidity, it is at saturation and cannot hold additional water vapor without condensation.
Step-by-step explanation:
When considering the mass of water that has to pass into the air to reach saturation, the concept of relative humidity is crucial. Relative humidity is a measure of how much water vapor is present in the air compared to the maximum amount that the air can hold at a given temperature. At 100% relative humidity, the air is saturated, meaning it cannot hold any more water vapor without some of it condensing out.
At a temperature of 19ºC, the equilibrium vapor pressure of water is 0.02168 atm. Using this information, along with the volume of the room where the humidifier is placed and the initial conditions (no water vapor initially present), the mass of water that needs to evaporate to saturate the air can be calculated. This involves using the ideal gas law in conjunction with the vapor pressure to determine the total mass of water vapor that the air can hold at saturation.