Question

The relative humidity of air equals the ratio of the partial pressure of water in the air to the equilibrium vapor pressure of water at the same temperature times 100%. If the relative humidity of the air is 58% and its temperature is 68 oF , how many moles of water are present in a room measuring 12 ft x 10 ft x 8 ft? The vapor pressure of water at 68 oF is 17.54 torr. The answer is 20, but for some reason I keep getting 15.127moles

Answer 1

Conversion Factor

68F = 20C

The vapor pressure of H2O is equal to 17.54 torr

vapor pressure of air = 58/100 * 17.54 torr = 10.17132 torr

Volume of the room = Length * Breadth * Height

=> 12 ft * 10 ft * 8

=> 960 ft^3

Using the ideal gas equation

PV = nRT

1 ft^3 = 28.3168 L

Volume in Liters = 27184.2 L

Pressure in atm = 10.17132/760 = 0.0133945 atm

Pv = nRT

(0.0133945)(27184.2) = n * 0.0821 * (273+20)

n = 15.1367 moles

This is the corret answer,i am 100% sure of this answer