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

Answer:

#M = 80.0 g/(mol)#

Explanation:

For this solution one would use the variation of the Ideal Gas Law
#PM = dRT#
#P = Pressure# in #atm#
#M = Molar Mass# in #g/(mol)#
#d = Density# in #g/L#
#R = 0.0821 (atmL)/(molK)# the gas law constant
#T = Temperature# #K#

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

#d = (mass)/(volume) = g/L#

#mass = 40.0 g#
#volume = 11.2 L#

#d = (40.0g)/(11.2 L)#
#d = 3.57 g/L#

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

#P = 1 atm#
#M = ?#
#d = 3.57 g/L#
#R = 0.0821 (atmL)/(molK)#
#T = 273K#

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