Wonder if there is any easy formula out there:
Suppose you take a liquid (say, 1 liter of water,) pour it into a hot and completely dry room containing 1000 cubic meters of air and it all evaporates. What is the formula for determining how many parts per million (ppm) of the new room atmosphere is comprised of water vapor?
Air is roughly 1.225 kg/m^3 at standard temperature and pressure. 1000 m^3 is therefore 1225 kg. 1 l of water weighs 1 kg. Therefore the water is 1/(1225+1) = 0.000815 of the total. Multiply by a million to get 815 ppm.
What Dr. Strangelove did except maybe he forgot that ppm in gases usually refers to volume percents (or mole percents).
So moles of air = 1225/28.97 = 42.3
Moles of water = 1/18 = 0.056
So percent of water in air = 100 * .056 / (42.3 +0.056)=0.1312% which is 1312 ppm
Also I checked that dry air at 25 C indeed can accommodate 1 liter of water. However, there is about a 2 deg C drop when it absorbs the water due to the heat of vaporization.
Didn’t realize that ppm was usually by volume instead of by mass for gases–thanks for the correction. Of course, the OP should double check that that’s what he wants, since it does depend on the application.
The term “ppm” is ambiguous. I might refer to dimensionless quantities such as mass fraction, mole fraction, volume fraction, and perhaps others. It is also sometimes used for quantities with dimensions such as mg/liter (but usually not with gasses). Before we can answer your question, we must know exactly what you mean by “ppm”.
Agree it is ambiguous but it is also very commonly used. For example here is a Climate change paper talking about CO2 ppm in air :