Question

8. How many grams of water vapor are there in a room with temperature 27°C and dimensions 4 meters x 3 meters x 2.5 meters? Assume that the room is saturated with water vapor – in other words, the partial pressure of water vapor in the room equals the vapor pressure of water at 27°, which is 26.7 mmHg. A) 42.8 grams B) 771 grams C) 1339 grams D) 24,100 grams E) 30,000 grams

Answer 1

From gas law;

PV=nRT

Here P = 26.7 mmHg

1 atm = 760 mmHg

26.7 mmHg / 760 mmHg * 1 atm = 0.035 atm

T = 27+237= 300 K

R = 0.0821 L atm / K mol

Volume = 4 meters x 3 meters x 2.5 meters=30 m^3

1. m^3 = 1000 L

30 m^3= 30,000 L

Now calcualte the n as follows:

n= PV/RT

n= 0.035 atm * 30,000 L/0.0821 L atm / K mol* 300K

n= 42.63 moles

now convert it into mass as follows:

molar mass of H2O = 18.02 g/mol

42.63 moles*18.02 g/mol = 768.20 g

Hence the correct answer is B) 771 grams