The formula that is employed to find the amount of water saturating a known gas (or gas mixture) is an application of John Dalton's famous Law that says:
mol fraction of water vapor = mols water vapor/total gas mols = partial pressure water/total system pressure
Dalton's Law is applied assuming that the gas (or gas mixture) is in equilibrium with condensed water. Since it is assumed that the mixture is saturated with water vapor (since it is in equilibrium), then the vapor pressure of water at its temperature is equal to the partial pressure of the same water. Hence, Dalton's Law.
This concept applies Dalton's relationship as it theoretically exists. You have not allowed for compressibility and mutual attraction effects (empirical deviations from Dalton) and your engineering experience should tell you that you must allow for a contingency in such calculations. This is where pure science is separated from real life, practical engineering. You can expect an error of at least 10-15% in the theoretical calculation using Dalton's Law - depending on the temperatures and pressures involved. This degree of error, in hard-core process design is to be expected and is always subjected to experience and expertise in the final design phase.
If you know the volumetric composition of your gas mixture, you know the mol% of each component (& their partial pressures) - except the water of saturation. That's what you solve for.
Don't forget that all pressures in the equation are absolute.
There are correlations -as that of Bucacek- and computer programs that try to reduce the deviations from Dalton's Law as explained by Montemayor. However, the practical advice given by zdas04 is in order.
