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) (a) What mass of water condenses inside the bottle?

Answer 1

Vapour Presure of H2O @ 22 deg C =19.8 mmHg

Vapour Presure of H2O @ 0 deg C = 4.6 mmHg

Water present in bottle at 20 deg C = 19.8*0.44

= 8.71 mmHg

No. of Moles at 25 deg C n=PV/RT

n=(8.71*0.75)/(760*0.08206*295)

=0.00035274

No. of Moles after cooling to 0 deg C n=PV/RT

n=(4.6*0.75)/(760*273*0.08206)
=0.0002026

No. of moles is more in outside temperature so there will be some condensed water.

No. of moles condensed water inside the bottle at 0 deg C

i.e 0.00035274-0.0002026=0.0001501

Mass of water condensed inside the bottle is 'n'*molar mass of water

=0.0001501*2

=0.0003002g=0.0003002*1000

=0.3002mg