The absolute humidity of the air (habs) is calculated by dividing the mass of water contained in the air by the volume occupied by the quantity of air concerned. Absolute humidity is generally expressed in g / m³. Relative humidity can be changed in two ways. One is by adding or subtracting water vapour. The second is by changing the air's temperature.

Question: How can you convert the relative humidity of stack gas to its absolute humidity?

Answer: For simplicity let's talk about a system at one atmosphere pressure. The Absolute Humidity of a sample of (moist) air may be described as the actual grams of water present per liter of that sample. It we take that sample of moist air and cool it at some point the water will start condensing on the walls or (in a large container) as a fog. At that temperature the sample's grams of water per liter is the Absolute Humidity for saturation. Every temperature below the boiling point has a different Absolute Humidity for saturation.

The Percent Relative Humidity of that sample may be described as 100 times the grams of water present in a liter of that sample (at its specified T and P) to the grams of water that would be present if the stack gas were completely saturated with water. As the temperature increases the vapor pressure of water rises close to exponentially.

A simple formula for Percent Relative Humidity for air is

PctRelHum = 100% * AbsHum_actual / AbsHum_sat

You may rearrange this the formula to get the answer you are seeking as

AbsHum_actual = AbsHum_sat * PctRelHum / 100%

The Absolute Humidity of water in air is available from steam tables.

However, there are two problems with using this for dusty flue gas:

#1. Dust-free flue gas has gaseous components that may attract water vapor strongly and thus allow a higher amount of water to be present in the gas phase before condensation occurs, thus raising the AbsHum_sat for stack gas vs air.

#2. The dust in the stack gas may adsorb water vapor (on its outer surface and pores) and thus increase the amount of water present in a dusty air sample compared with a dust-free stack gas. However ,if the water content of the gas alone is determined on a filtered sample of the stack gas (say, by capacitance or or spectroscopy) you can determine the absolute humidity of the dust-free stack gas from its Percent Relative Humidity with only #1 as a consideration.

Best wishes for working with this complex problem.