Question

An apartment has the dimensions 20 m by 10 m by 7 m. The temperature is 30°C, and the relative humidity is 52 percent. What is the total mass (in kg) of water vapor in the air in the apartment?

Answer 1

The mass of the water vapor in the apartment would be 22.1 kg

Step-by-step explanation:

The ideal gas equation would be used to obtain the total mass and is expressed as;

P V = n R T .............1

but n = m/M

Substituting into equation 1 we have;

P V = (m/M)RT

Making m the subject formula we have;

m = M P V / R T ..............................3

Where M is the molar mass of water = 18 g/ mol

NB the pressure of water at
`30^(0)`C from the saturation table is 4250 Pa

P is the pressure at 52% relative humidity = 0.52 x 4250 =2210 Pa

V is the volume = 20 x 10 x 7 = 1400
`m^(2)`

T is the temperature, T =
`30^(0)`C + 273.15 = 303.15 K

R is the ideal gas constant = 8.3245 J/mol/K

m = (18 g/ mol x 2210 Pa x 1400
`m^(2)` )/ (8314 J x 303.15 K)

m = 55692000 / 2520.3891

m =22096.58 g

m = 22096.58/1000

m = 22.1 kg

Therefore the mass of the water vapor in the apartment would be 22.1 kg