A 0.75 L bottle is cleaned, dried, and closed in a room where the air is 22°C and 47% relative humidity (that is, the water vapor in the air is 0.47 of the equilibrium vapor pressure at 22°C). The bottle is brought outside and stored at 0.0°C.
My question is what does the relative humidity got to do with the problem?
See your earlier post. Note I solved the problem for 0C and not 10C.
The relative humidity plays a role in determining the amount of water vapor present in the air. It represents the amount of moisture the air is currently holding compared to the maximum amount it can hold at a given temperature.
In this problem, the relative humidity is mentioned to provide information about the water vapor content in the room where the bottle is initially closed. Specifically, it states that the relative humidity is 47%, which means that the air in the room contains 47% of the maximum amount of water vapor that it can hold at 22°C.
The relative humidity is relevant in this case because when the bottle is brought outside and stored at a lower temperature (0.0°C), the air inside the bottle will cool down. As the air cools, its capacity to hold water vapor decreases, and if there is excess moisture present, it will start to condense into liquid water. This is the phenomenon known as condensation.
Knowing the relative humidity in the room allows us to estimate the initial amount of moisture present in the air, which can help predict the occurrence of condensation when the bottle is moved to a colder environment.