AP Chemistry
Unit 5 – States of Matter
Lesson 2 – Ideal Gas Law
Book Section: 10.4-10.5
Ideal-Gas Equation
• So far we’ve seen that
• V  1/P (Boyle’s Law)
• V  T (Charles’s Law)
• V  n (Avogadro’s Law)
• Combining these, we get
nT
V
P
Ideal-Gas Equation
• To turn any proportionality into an equation,
you have to multiply by a constant.
• The constant of proportionality in this case is
known as R, the ideal-gas constant.
• R = different values depending on units of
pressure:
0.0821 L-atm/mol-K (use when P = atm)
8.314 J/mol-K
(use when P = Pa)
62.36 L-torr/mol-K (use when P = torr)
Ideal Gas Law
• The relationship
• Then becomes
• Or…
nT
V
P
nT
V R
P
• PV = nRT  Ideal Gas Law
Ideal Gas Law and Density
• If we divide both sides of the ideal gas equation by
V and by RT, we get
n
P

V RT
Ideal Gas Law and Density
• We know that
– Moles x molar mass = mass
nxM=m
(M = molar mass)
• So, multiplying both sides by the molar
mass (M) gives
m PM

V
RT
Ideal Gas Law and Density
• Mass/volume = density
• So…
PM
D
RT
• One only needs to know the molar mass,
pressure, and temperature to calculate
the density of a gas.
Molar Mass
• We can manipulate the density equation
to enable us to find the molar mass of a
gas:
DRT
M 
P
1984 MC #23
• The density of an unknown gas is 4.20
grams per liter at 3.00 atmospheres
pressure and 127 ºC. What is the
molecular weight of this gas? (R =
0.0821 liter-atm/mole-K)
A) 14.6
B) 46.0
C) 88.0
D) 94.1
E) 138
1984 MC #23
• The density of an unknown gas is 4.20
grams per liter at 3.00 atmospheres
pressure and 127 ºC. What is the
molecular weight of this gas? (R =
0.0821 liter-atm/mole-K)
A) 14.6
B) 46.0 – 75% correct, easy
C) 88.0
D) 94.1
E) 138
1994 MC #24
• A sample of 0.0100 mole of oxygen gas is
confined at 37 ºC and 0.216 atmosphere.
What would be the pressure of this sample
at 15 ºC and the same volume?
A) 0.0876 atm
B) 0.175 atm
C) 0.201 atm
D) 0.233 atm
E) 0.533 atm
1994 MC #24
• A sample of 0.0100 mole of oxygen gas is
confined at 37 ºC and 0.216 atmosphere.
What would be the pressure of this sample
at 15 ºC and the same volume?
A) 0.0876 atm
B) 0.175 atm
C) 0.201 atm – 76% correct, easy
D) 0.233 atm
E) 0.533 atm
1994 MC #37
• A sample of 3.30 grams of an ideal gas at
150.0 ºC and 1.25 atmospheres pressure has
a volume of 2.00 liters. What is the molar
mass of the gas? The gas constant, R, is
0.0821 (L-atm)/(mol-K).
A) 0.0218 gram/mole
B) 16.2 grams/mole
C) 37.0 grams/mole
D) 45.8 grams/mole
E) 71.6 grams/mole
1994 MC #37
• A sample of 3.30 grams of an ideal gas at
150.0 ºC and 1.25 atmospheres pressure has
a volume of 2.00 liters. What is the molar
mass of the gas? The gas constant, R, is
0.0821 (L-atm)/(mol-K).
A) 0.0218 gram/mole
B) 16.2 grams/mole
C) 37.0 grams/mole
D) 45.8 grams/mole – 81% correct, very easy
E) 71.6 grams/mole
Homework: 10.30, 10.34, 10.36, 10.42
• This week:
– Thursday: Partial Pressures (10.6), Problem Set 3
Due
– Friday: Kinetic-Molecular Theory (10.7)
• Due Dates:
–
–
–
–
Volume-Temperature Behavior of Gases: 11/30
States of Matter Exam: Monday, 12/6
Molar Mass of Condensable Vapor: 12/8
Problem Set 4: 12/10