This is very confusing: "The relative humidity is 80%." How do you know that? The thermodynamic values are in 

https://en.wikipedia.org/wiki/Vapour_pressure_of_water

 Thanks for the reply. Actually I did this experiments in a day that the relative humidity reported by meteorology was 80%. I do not have any idea how pumping the chamber down would affect the relative humidity level and how I can calculate the amount of vapor molecules inside.

I would suggest the following procedure. Put 2 mL of water (0.11 mole of water)  into your chamber ( which has 0.04 mole of air), turn on the pump and reach a desired  pressure. You are expected to have only water molecules in the chamber.  Amount of gas i(water) n the chamber is N(moles)=PV/RT

You will not be able to keep the ratio water/air constant while pumping gas from your chamber. 

 Well, unfortunately I do not have any access to that experiment set-up any more. I just need to estimate the amount of the vapor in that specific day with the data in hand, to analyze the other experiments I did inside the chamber after pumping. Even a rough estimation also should work for my purpose. 

from relative humidity, find the partial pressure, from the partial pressure, find the no. of moles of water vapor, therefore, no. of moles of water vapor=partial pressure of water vapor/total pressure of air