In a room of volume 50 m ^3 , the temperature is 300 K and the relative humidity is 20 % . After the floor is washed with water, 500 g of water remains sticking to the floor. Assuming there is no communication with the surroundings, determine the relative humidity when the floor dries. Changes in temperature and pressure can be neglected. The saturation vapour pressure at 300 K is 3.3 kPa .

Step-by-step solution

Initial vapour pressure P₁ = 0.20 3.3 kPa = 0.66 kPa = 660 Pa . Number of moles of water evaporated n = 500 18 mol . Increase in vapour pressure due to evaporated water is given by the ideal gas equation: P = nRT V = 500 8.314 300 18 50 Pa 1386 Pa = 1.386 kPa . Final vapour pressure P₂ = P₁ + P = 0.66 kPa + 1.386 kPa = 2.046 kPa . Final relative humidity is: RH = P₂ P_s 100 = 2.046 3.3 100 62 % .