Detemining the mass of water vapour in air (Ideal gas law)

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SUMMARY

The calculation of the mass of water vapor in one cubic meter of air at 20°C with a relative humidity of 80% can be performed using the formula p[v] = (eM[w]) / (RT). Here, p[v] represents vapor density, e is the water vapor pressure, M[w] is the molar mass of water, R is the gas constant (8.314 J/(mol*K)), and T is the temperature in Kelvin (293.15 K). The vapor density should be measured in kg/m³, and pressure should be expressed in Pascals (Pa) for consistency with SI units.

PREREQUISITES
  • Understanding of the Ideal Gas Law
  • Knowledge of relative humidity and its implications
  • Familiarity with SI units, particularly for pressure and density
  • Basic concepts of thermodynamics related to gases
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  • Research the calculation of water vapor pressure using relative humidity
  • Learn about the molar mass of water and its significance in gas calculations
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1. I am supposed to calculate the mass of water vapour in one cubic meter of air that has a relative humidity of 80% at 20°C.






2. p[v] = (eM[w]) / (RT)

Where:
p[v] = vapour density
e = water vapour pressure
M[w] = molar mass of water
R = gas constant (8,314 J / (mol*K)
T = temperature (293,15°K)


3. I am struggling with in what unit the vapour density should be measured, as well as the pressure, Pascal? I know this problem is embarrassingly easy, but I've been trying to get the answer for several days, reading up on it online... I miss my old physics-book!

Help would be sincerely appreciated!
 
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Probably it's best if you use SI units. You can take ρ = \frac{m}{V} in \frac{kg}{m^3} and pressure in Pascals.
 

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