THE IDEAL GAS LAW
A COMBINATION OF LAWS:
 Boyle’s
•
Law
k = PV at constant T and n
 Charles’
•
Law
V = bT at constant P and n
 Avogadro’s
•
Law
V = an at constant P and T
 These
laws show how the volume of a gas
is dependent on the temperature,
pressure, and number of moles present
 The ideal gas law can be used to solve
almost any gas problem.
THE IDEAL GAS LAW
 Defines


the ideal behavior of a gas
Pressures less than or equal to 1 atm
Temperatures greater than or equal to 0 oC
 Units
must be in L, atm, K, and mol.
 The Universal Gas Constant:
R = 0.08206 L atm/K mol
Ideal Gas Law Equation:
PV = nRT
SAMPLE PROBLEM #1
A sample of hydrogen gas, H2, has a volume of 8.56 L at a
temperature of 0 oC and a pressure of 1.5 atm. Calculate the
number of moles of H2 present in this gas sample.
Identify the Variables:
P = 1.5 atm
n = ???
V = 8.56 L
T = 0 oC
Convert units if needed:
T = 0 oC = 0 + 273 = 273 K
Set up the Equation:
PV = nRT
PV = nRT
RT
RT
n = PV
RT
Solve:
n = (1.5 atm)(8.56 L)
(0.08206 LK atm mol)(273 K)
n = 0.57 mol
SAMPLE PROBLEM #2
Suppose we have a 0.240-mol sample of ammonia gas at 25 oC with
a volume of 3.5 L at a pressure of 1.68 atm. The gas is compressed
to a volume of 1.35 L at 25 oC. Use the ideal gas law to calculate
the final pressure
Identify the Variables:
P1 = 1.68 atm
P2 = ?
V1 = 3.5 L
V2 = 1.35 L
n1 = 0.240 mol n2 = 0.240 mol
T1 = 25 oC
T2 = 25 oC
*n and T are constant
Convert units if needed:
T = 25 oC = 25 + 273 = 298 K
Set up the Equation: PV = nRT
*Set it up so that the variables that change
are on one side and the constants are on
the other.
P1V1 = nRT and P2V2 = nRT
Because nRT is constant, we can
write:
P1V1 = P2V2 or
Solve:
P2 = (1.68 x 3.5) ÷ (1.35)
P2 = 4.4 atm
P2 = P1V1
V2
IDEAL GAS PRACTICE PROBLEMS
Given the following sets of variables, calculate the unknown
quantity using the Ideal Gas Law:
1.
P = 782.4 mm Hg; V = ?; n = 0.10121 mol; T = 26.2 oC
2.
P = ? mm Hg; V = 27.5 mL; n = 0.007812 mol; T = 16.6 oC
3.
P = 1.045 atm; V = 45.2 mL; n = 0.002241 mol; T = ? oC
4.
5.
6.
7.
8.
Calculate the mass (g) of argon gas required to fill a 20.4L container to a pressure of 1.09 atm at 25 oC.
What volume does 2.25 g of nitrogen gas, N2, occupy at
273 oC and 1.02 atm?
What mass of helium gas is needed to pressurize a 100.0L tank to 255 atm at 25 oC?
What mass of oxygen gas would be needed to pressurize
the same gas tank?
At what temperature will a 1.0-g sample of neon gas exert
a pressure of 500 torr in a 5.0-L container?