Question

A 0.75L bottle is cleaned, dried and closed in a room where the air is 22C and 35% relative humidity (that is the water vapor in the air is 0.35 of the equilibrium vapor pressure at 22C. The bottle is brought outside and stored at 0.0C. what mass of liquid water condenses inside the bottle? __grams

Answer 1

Use ideal gas PV = nRT to calculate mass at 22deg

From your table, PH2O = 19.8 torr @ 22 deg C

R = gas constant = 62.3636 L torr / (deg K * mol)

n = PV/RT = (19.8 torr)(0.75 L)/(62.3636 L torr/[deg K*mol])(273 + 22 K) = 8.07185e-4 mol

This would be for 100% relative humidity, but we have 35% RH, so it is 8.07185e-4 mol * 0.35 = 2.8251475e-4 mol

So the vapor pressure falls to 4.6 torr at 0 deg. What is the mol of water that can be held in gas phase at 100% humidity?

n = PV/RT = (4.6 torr)(0.75 L)/(62.3636 L torr/[deg K*mol])(273 + 0 K) = 2.0264004e-4 mol

This means that (2.8251475e-4 - 2.0264004e-4 mol) = 0.00007987 mol

Since there are 18.02 g H2O / mol H2O, = 0.001439 g = 1.44 mg of liquid should form.