Cigars are best stored in a \'humidor\' at 18 degree C and 55% relative humidity
ID: 500395 • Letter: C
Question
Cigars are best stored in a 'humidor' at 18 degree C and 55% relative humidity. This means the pressure of the water vapor should be 55% of the vapor pressure of the pure water at the same temperature (VP of pure water at 18 degree C = 16.0 mm Hg). The proper humidity can be maintained by placing a solution of glycerol (C_3H_8O_3) and water in the humidor. Calculate the percent by mass of glycerol that will lower the vapor pressure of water to the desired value. (Vapor pressure of glycerol can be considered negligible).Explanation / Answer
from Raoluts law, vapor pressure of solution =mole fraction of solvent* pure component vapor presure
16*0.55= 16*mole fraction of solvent
mole fraction of solvent =0.55 moles of solvent/ total moles =0.55
moles of solvent = 0.55*( moles of solvent + moles of glycerol)
0.45* moles of solvent = moles of glycerol
0.45* mass of water/molar mass = mass of glycerol/molar mass of glycerol
0.45*mass of water/18= mass of glycero/92
mass of water/ mass of glycerol= 18/(92*0.45)= 0.434
1+ mass of water/ mass of glycerol =1.434
(mass of glycerol+mass of water)/mass of glycerol= 1.434
mass of glycerol/mass of mixture = 1/1.434= 0.70
Mass % of glycerol= 70%
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