On a given day, the temperature and humidity of air are 27^ C and 50 % . Determine the amount of vapour that must be added to 1 cubic metre of air to saturate it. The saturation vapour pressure at 27^ C is 3600 Pa .

Step-by-step solution

Relative humidity is given as 50 % . Initial vapour pressure P₁ = 0.50 3600 = 1800 Pa . To saturate the air, the vapour pressure must reach the saturation vapour pressure P_ s = 3600 Pa . Additional vapour pressure required is P = 3600 - 1800 = 1800 Pa . Using the ideal gas equation, P V = m M R T , where V = 1 m ³ , T = 300 K , and M = 18 g/mol is the molar mass of water. m = P V M R T m = 1800 1 18 8.314 300 g m = 108 8.314 13 g