Question

A 0.75 L bottle is cleaned, dried, and closed in a room where the air is 26°C and 41% relative humidity (that is, the water vapor in the air is 0.41 of the equilibrium vapor pressure at 26°C). The bottle is brought outside and stored at 0.0°C. (a) What mass of water condenses inside the bottle? (b) Would water condense at 10°C? yes/no?

Answer 1

Hi, we will begin with some data. The water vapor capacity of air at 26 °C is 20 g/kg of air, at 10 °C is 7.8 g/kg and 3.8 g/kg air at 0 °C. If the relative humidity is 41 % then the amount of water is 0.41*20, that is 8.2 g. If the bottle is cooled to 0 °C then 8.2-3.8 = 4.4 g of water will condense inside the bottle.

As we know the amount of water vapor in the bottle is 8.2 g which is greater than the water vapor capacity of air at 10 0 °C, so yes water would condense at 10 0 °C.