Respuesta :
Answer:
Mass of water = 6251. 706g or 6.25Kg
Explanation:
Relative humidity = (actual vapor pressure/saturation vapor pressure) * 100%
Actual vapor pressure, Pw = relative humidity * saturation vapor pressure
Pw = 60% * (35.6 *0.001)atm = 0.0216atm
Note: 1mbar = 0.001atm
Using the ideal gas equation: PV=nRT; where P = Pw= 0.02136atm, V= (400
* 1000)dm^3, R= 0.082 atmdm^3/kmol, T= (27+273)K, n = number of moles
Note: 1m^3 = 1000dm^3,R is the molar gas constant.
Making n subject of the formula, n = PV/RT
n= (0.02136 * 400000)/(0.082 * 300) = 347.317 moles
Mass (g) = number of moles (n) * molar mass
molar mass of water=18g
Mass of water = 347.317 * 18 = 6251. 706g or 6.25Kg
The relative humidity is given as the ratio of the actual vapor pressure and the saturation vapor pressure. The mass of the water vapor is 6.25 kg.
What is humidity?
The humidity is given as the mass of the water vapor present in the air.
The vapor pressure of the water in the air is calculated as:
[tex]\rm Vapor\;pressure=Realtive\;humidity\;\times\;saturation\;vapor\;oressure\\Vapor\;pressure=60\;\times\;(35.6\;mbar\;\times0.001)atm\\Vapor\;pressure=0.0216\;atm[/tex]
The moles of the water has been calculated by the ideal gas equation as:
[tex]\rm PV=nRT\\0.0216\;\times\;400000\;dm^3=n\;\times\;0.0821\;atm.dm^3/mol.T\;\times\;300\;K\\n=347.317 \;mol[/tex]
The molar mass of water is 18 g/mol, the mass of water vapor in 347.317 moles is:
[tex]\rm Mass=Molar\;mass\;\times\;Moles\\Mass=18\;g./mol\;\times\;347.317\;mol\\Mass=6251.706\;g\\Mass=6.25\;kg[/tex]
The mass of water vapor in the air is 6.25 kg.
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