What is the molar mass of a gas if a 40.0-gram sample of the gas occupies 11.2 liters of space at STP?

1 Answer
Mar 11, 2016

M = 80.0 g/(mol)M=80.0gmol

Explanation:

For this solution one would use the variation of the Ideal Gas Law
PM = dRTPM=dRT
P = PressureP=Pressure in atmatm
M = Molar MassM=MolarMass in g/(mol)gmol
d = Densityd=Density in g/LgL
R = 0.0821 (atmL)/(molK)R=0.0821atmLmolK the gas law constant
T = TemperatureT=Temperature KK

The density can be found by dividing the mass by the volume.

d = (mass)/(volume) = g/Ld=massvolume=gL

mass = 40.0 gmass=40.0g
volume = 11.2 Lvolume=11.2L

d = (40.0g)/(11.2 L)d=40.0g11.2L
d = 3.57 g/Ld=3.57gL

The STP values (standard temperature and pressure) are 1 atm and 273 K.

P = 1 atmP=1atm
M = ?M=?
d = 3.57 g/Ld=3.57gL
R = 0.0821 (atmL)/(molK)R=0.0821atmLmolK
T = 273KT=273K

PM=dRTPM=dRT
(1 atm)(M)=(3.57g/L)(0.0821 (atmL)/(molK))(273K)(1atm)(M)=(3.57gL)(0.0821atmLmolK)(273K)
(M)=((3.57g/cancel(L))(0.0821 (cancel(atm)cancel(L))/(molcancel(K))(273cancelK)))/(1 cancel(atm))(M)=(3.57gL)(0.0821atmLmolK(273K))1atm
M = 80.0 g/(mol)M=80.0gmol