How to determine the mass of water that needs to be evaporated so that the relative humidity in the room increases by 10%?

Room volume V = a * b * h (width * length * height). The density of saturated water vapor at the current temperature ρн – according to the reference book. Relative humidity ϕ: ϕ = (ρa / ρн) * 100%, where ρa is the absolute density of water vapor, Humidity ϕ1 = ϕ + 10%: ϕ1 = (ρa1 / ρн) * 100%; ϕ1 – ϕ = 10%; (ρa1 / ρн) * 100% – (ρa / ρн) * 100% = 10%; (ρa1 – ρa) / ρн = 1/10; ρa1 – ρa = ρн / 10 The density should increase by ρн / 10. The mass of water to be evaporated: m = (ρн / 10) * V = 0.1ρнV. The formula is applicable for ϕ <90%.
Answer: The volume of the room V is multiplied by 0.1ρн.