# Applications of the Ideal Gas Law

EXAMPLE #1:
Q:
At 28 oC and 0.974 atm, 1.00 L of gas has a mass of 5.16 grams.  What is the molar mass of this gas?

A:   P V = n R T      * given T, P, V & R is constant, we must solve for n *
n = P V =         (0.974 atm) (1.00 L)        = 0.0394 moles
R T     (0.0821 L atm/mole K) (301 K)
moles = grams
MM
MM = grams =    5.16 grams   = 131 g/mole
moles      0.0394 moles

EXAMPLE #2:
Q:
What is the molar mass of a gas if 0.427 grams of the gas occupies a volume of 125 mL at 20.0 oC
and 0.980 atm?                                                                                                         (A: 83.8 g/mole)

*Honors only
EXAMPLE 3:
Q:
What is the density of argon gas, Ar, at a pressure of 551 torr and a temperature of 25 oC?
A:
density =   mass                  P V = (mass/MM) R T
volume
P = (mass/MM) R T            P MM = mass            Density =   P (MM)
V                         R T        V                                 R T
P = 551 torr x   1 atm  = 0.725 atm                    T = 25 oC + 273 = 298 K
760 torr
D =   (0.725 atm) (39.9 g/mole)     = 1.18 g/L
(0.0821 L atm/mole K) (298 K)

EXAMPLE 4:
Q:
The density of a gas was found to be 2.0 g/L at 1.50 atm and 27 oC.  What is the molar mass of
the gas?                                                                                          (A:  33 g/mole)