# Why doesn't the number of $\rm H_2O$ molecules evaporated depend on the number of the other gaseous molecules?

I have a conceptual contradiction. Say we remove a partition between liquid water and gaseous nitrogen at constant volume and temperature. The average number of gaseous water molecules will increase until the partial pressure of water (PP) equals the vapor pressure of water (VP), which only depends on temperature.

$$VP = PP = \frac{N_{H^2O}}{N_{H^2O}+N_{N^2}}P_{total} = \frac{N_{H^2O}}{N_{H^2O}+N_{N^2}}\frac{RT}{V}(N_{H^2O}+N_{N^2}) = N_{H^2O}\frac{RT}{V}$$

So $$N_{H^2O} = VP\frac{V}{RT}$$, which doesn't depend on the number of nitrogen molecules. But shouldn't increasing the number of nitrogen molecules put more pressure on the liquid water surface and thus decrease the number of molecules that leave the gas? Thank you

• The vapor pressure of the liquid changes with pressure and adding a gas to a liquid can cause the liquid to evaporate due to an increase of the vapor pressure, see Poynting effect. This answer at chemistry stack exchange contains a good explanation what happens, chemistry.stackexchange.com/q/122727/64200 Commented Oct 18, 2022 at 14:26