A room has a volume of 50 m ^3 , where the temperature is 300 K and the relative humidity is 20 % . Given that the saturation vapour pressure at 300 K is 3.3 kPa , determine the mass of the water vapour contained within the room.

Step-by-step solution

Relative humidity is the ratio of partial pressure of water vapour to the saturation vapour pressure at the same temperature. RH = P P_ s 0.20 = P 3.3 10³ P = 0.20 3.3 10³ = 660 Pa Using the ideal gas equation, PV = nRT = m M RT m = PVM RT Substituting V = 50 m ³ , M = 18 g mol ⁻¹ , R = 8.314 J mol ⁻¹ K ⁻¹ and T = 300 K : m = 660 50 18 8.314 300 m = 594000 2494.2 238 g