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.

a. What mass of water condenses inside the bottle?

b. Would water condense at 10*C?

Answer 1

vapor pressure of water at 20 deg.c = 17.5 mm Hg and at 10 deg.c = 9.2 mm Hg vapor pressure of water at 0 deg.c = 4.6 mm Hg

Relative humidity= 44%

0.44 = partialpressure of water vapor/ vapor pressure of liquid

Partial pressure of water vapor =0.44* vapor pressure of liqudi =0.44*17.5 mm Hg= 7.7 mmHg

partail pressure of water vapor/ partial pressure of dry air = 7.7/(760-7.5) =0.010122 (1)

Eq.1 in turn will be equal to moles of water vapor/ moles of dry air

Moles of water vapor/ Moles of dry air =0.010122

Moles of dry air = Moles of water vapor/0.010122 =98.78 Moles of water vapor = (2)

total number of moles of wet air (n) at 20 deg.c can be calculated from PV= nRT

where V= volume of air =0.75L T= 20 deg.c =20+273.15= 293.15K, R =0.08206 L.atm/ mole. K P=1atm

n= PV/RT= 1*0.75/(293.15*0.08206)=0.03118

moles of water vapor + moles of dry air =0.03118 (3)

from Eq.2, 98.79 * moles of water vapor + moles of water vapor= 0.03118

moles of water vapor *99.78= 0.03118

Moles of water vapor at 20 deg.c =0.03118/99.78= 0.000312

Moles of dry air = 98.78* 0.000312=0.030819 moles

These moles will not change during condensation.

Assume that the water is sturated at 0 deg.c , where partial pressure = vapor pressure = 4.6 mm Hg

at 0deg.c

Partial pressure of water vapor/ Partial pressure of dry air = moles of water vapor/ moles of dry air

4.6/(760-4.6)= moles of water vapor/ 0.030819

Mole of water vapor at 0 deg.c = 0.006089= moles of water vapor at 10 deg.c/ 0.030819

Moles of water vapor at 0 deg.c =0.006089*0.030819 =0.000188

Moles of water vapor at 20 deg.c = 0.000312

Moles of water condensed= 0.000312- 0.000188= 0.000124

Moles of water condensed= 0.000124*18 (18 is the molecular weight of water)= 0.00232 gms of water gets condensed

b) for water to condense, partial presure at 10 deg.c = vapor pressure at 10 deg.c =9.2 mm Hg

This is more than the partial pressure of water vapor at 20 deg.c =7.7 mm Hg

Hence there will not be any condensation