1. The Ideal Gas Law

2. A combination of laws: Boyle’s Law Charles’ Law Avogadro’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.

3. Ideal Gas Law Equation:
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 = L atm/K mol
Ideal Gas Law Equation:
PV = nRT

4. 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
Set up the Equation:
PV = nRT
PV = nRT
RT RT
n = PV RT
Convert units if needed:
T = 0 oC = = 273 K
Solve:
n = (1.5 atm)(8.56 L)
( LK atm mol)(273 K)
n = 0.57 mol

5. Sample Problem #2
Suppose we have a 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
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 P2 = P1V1 V2
Identify the Variables:
P1 = 1.68 atm P2 = ?
V1 = 3.5 L V2 = 1.35 L
n1 = mol n2 = mol
T1 = 25 oC T2 = 25 oC
*n and T are constant
Convert units if needed:
T = 25 oC = = 298 K
Solve:
P2 = (1.68 x 3.5) ÷ (1.35)
P2 = 4.4 atm

6. Ideal Gas Practice Problems
Given the following sets of variables, calculate the unknown quantity using the Ideal Gas Law:
P = mm Hg; V = ?; n = mol; T = 26.2 oC
P = ? mm Hg; V = 27.5 mL; n = mol; T = 16.6 oC
P = atm; V = 45.2 mL; n = mol; T = ? oC
Calculate the mass (g) of argon gas required to fill a L 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 L 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?