Molecular Composition
of Gases
The Ideal Gas Law
Objectives:
1. State the ideal gas equation.
2. Derive the ideal gas constant and state its units.
3. Use the ideal gas equation to calculate the amount of
gas at any condition of temperature and pressure.
4. Use the ideal gas equation to calculate the molar
mass of a gas given its density.
5. Reduce the ideal gas law to Boyle’s, Charles’, GayLussac’s, or Avogadro’s Law.
The Ideal Gas Law
•Mathematical relationship between pressure,
volume, temperature, and the number of moles of
gas.
Ideal Gas Law
Calculate the value of R for 1 mole of gas at STP.
(1 atm)( 22.4 L)
L * atm
 0.0821
(1 mole)( 273 K )
mol * K
• The value of “R” depends on the units used for P, V,
and T.
• The ideal gas law can be reduced to any of the
previously studied gas laws when certain variables
are held constant.
Sample Problems
1. A 2.07 L cylinder contains 2.88 mol of helium gas at
22oC. What is the pressure in atmospheres of the gas in
the cylinder?
2. A tank of hydrogen gas has a volume of 22.9 L and
holds 14.0 mol of the gas at 12oC. What is the reading
on the pressure gauge in atmospheres?
3. A reaction yields 0.00856 mol of O2 gas. What volume
will this occupy if it is collected at 43oC and 0.926 atm
pressure?
4. What mass of ethene gas, C2H4 is contained in a 15.0 L
tank that has a pressure of 4.40 atm at a temperature of
305 K?
Ideal Gas Law and Molar Mass
A chemist determines the mass of a sample of gas to be
3.17 g. Its volume is 942 mL at a temperature of
14oC and a pressure of 1.09 atm. What is the molar
mass of the gas.

1L 
L  atom
  n  (0.0821
)(14 o C  273)
mol  K
 1000 mL 
1.09 atm942 mL
n  0.0436 moles
3.17 g
mass
M 

 72.7 g
mol
moles 0.0436 mol
Ideal Gas Law and Molar Mass
mass
Since " n" 
Molar mass
m
PV 
RT
M
mRT
M 
PV
or....
Ideal Gas Law and Density
Knowing that density is mass/volume, what is the
density of a sample of ammonia, if the pressure is
0.928 atm and the temperature is 63.0oC?
0.928 atm
n
P


 0.0336 mol
L
L  atm 
V RT 
o
 0.0821
 63.0 C  273
mol  K 



 17.0305 g 
mol
  0.572 g
(0.0336
)  
L
L
1
mol


Ideal Gas Law and Density
mRT DRT
M 

PV
P
MP
or... D 
RT