Question

A 0.75 L bottle is cleaned, dried, and closed in a room where the air is 20°C and 44% relative humidity (that is, the water vapor in the air is 0.44 of the equilibrium vapor pressure at 20°C). The bottle is brought outside and stored at 0.0°C. (See Table 5.2) vapor pressure of 20 degrees is 17.5 torr and 0 degrees is 4.6 torr

What mass of water condenses inside the bottle?

Answer 1

Step 0. Think of your problem

To find out the amount of water condensed within the bottle is necesary to use the ideal gas law to clear n, both at 20 ºC and 0 ºC: Nevertheless, calculating water vapor pressure first is mandatory.

Step 1. Link relative humidity with the vapor pressure of water mixed with the air.

where phi is the relative humidity, P* is the equilibrium vapor pressure of water at a specific temperature, and P is the vapor pressure of water in the air.

At 20 ºC P*_H2O = 17.5 torr. Given a 44% of relative humidity, we have:

At 0 ºC P*_H2O = 4.6 torr. Assuming that outdoors relative humidity is 100%,

Step 2. Get to know the formula of ideal gases and clear for n.

Since there are two different conditions, the quantity of moles of water earned by the bottle can be obtained from the difference from outdoors and indoors.

It is important to remember that the volume of the bottle remains constant and make the conversion of temperatures:

T₁ = 22 ªC = 295.15 K

T₂ = 0 ªC = 273.15 K

Then,

Step 3. Converse number of moles to grams of water.