According to the ideal-gas law, number concentration of water vapor nH2O(molecules/m3) is:
nH2O=nA*pH2O/(RT)
From the definition of relative humidity, RH,:
pH2O=pH2O_sat(T)*RH
where pH2O_sat(T) is given by different functions. For example, pH2O_sat(T) in mbar can be calculated with :
pH2O_sat(T)=1013.25exp[13.3185a-1.97a^2-0.6445a^3-0.1299a^4] with a=1-373.15/T
Example:
The number concentration of water vapor for RH=5
pH2O_sat(298)=31.387mbar=31.387*10^2 N/m2
nH2O=(6.022*10^23*31.387*10^2*50/100.)/(8.314*298)= 3.81*10^23 molecules/m3
nH2O= nH2O(molecules/m3)*10^(-6)=3.81*10^17 molecules/cm3
Volume mixing ratio:
vmr=pH2O/p_air
At 5
vmr=31.387*10^2*50/10^5=1.569 (which means 1.569%. Tipically is 1%\ in atmosphere)
vmr(ppm)=1.569e6 ppm for 50%\ RH
Saturation mixing ratio is:
vmr(ppm)=3.138e4 ppm for T=298 K
Mass mixing ratio:
mmr=vmr*mH2O/m_air in kg/kg
mmr=1.569*0.622=6.16e-3 kg/kg