1. Ideal Gas Law
PV = nRT
re-arrange n
= P V RT
n =
mol gas
= mass gas (g)
molar mass (g/mol)
mass of sample
= P V
x molar mass RT
mass
= density
density = P
x molar mass V RT

2. A colorless liquid is isolated as a product in a reaction.
It might be cyclohexane, C6H12.
volume of flask = 213 mL
mass of flask = g
T = 100.0oC
P = 754 torr
mass of flask + gas = g
0.582 g
= atm
x molar mass
0.213 L x
density = P
x molar mass RT
molar mass = 84.4 g/mol

3. Dalton’s Law of Partial Pressures
Ptotal =
Pdry air
+ Pwater vapor
Ptotal
= P1 +
P2 +
P3+ …
partial pressures
In a mix of two gases, A and B
PA = nA RT
PB = nB RT
PT = V nA RT + V nB RT V V
PT = RT (nA + nB) PA
= nA
= XA
mol fraction V
nA + nB PT
Pi = Xi PT

4. Kinetic Molecular Theory of Gases
1. Gases consist of a large number of molecules.
Vmolecules
<< Vcontainer
Ideal gases have mass, but no volume
2. Gas molecules are in constant, random motion.
collisions with wall = Pressure
3. Attractive and repulsive forces negligible.
4. Energy transferred during collisions.
average KE does not change, at fixed T
5. Average KE is proportional to temperature (K)
all gases have same average KE at same T

5. Kinetic Molecular Theory of Gases
average KE same for all particles at T
distribution of molecular velocity, u
most probable u increases with T
5. Average KE is proportional to temperature (K)
all gases have same average KE at same T

6. Boyle’s Law
V 1/P
Charles’ Law
V T
Avogadro’s Law
V  n
Dalton’s Law
Ptotal= P1+ P2+ P3+ …

7.  root mean square velocity urms urms = 3RT/M M = molar mass (kg) R
= J/K mol
KE = ½ mu2
m = mass
u = average velocity
(2.01 g/mol)
urms =
1926 m/s
= H2
urms =
= UF6
(352 g/mol)
145 m/s
Dalton’s Law
Ptotal= P1+ P2+ P3+ …

8.  Graham’s Law of Effusion escape of gases through a small hole
rate1 = 
M2 / M1
rate2
diffusion
mixing of gases
mean free path
1 atm
6 x 10-9 m
space
3 x 1010 m

9. Real Gases n
= PV RT
need to correct V for Vgas
1. Gases consist of a large number of molecules.
Vmolecules
<< Vcontainer
Ideal gases have mass, but no volume

10. Real Gases
n = PV RT
need to correct V for Vgas
need to correct P for interactions P
+ n2a
V - nb
= nRT V2
3. Attractive and repulsive forces negligible.

11. van der Waals Equation P
+ n2a
V - nb
= nRT V2
a, b experimental a
related to Intermolecular Forces
molecular complexity b
related to molecular volume

12. acetylene (C2H2) produced in reaction
CaC2 (s) + 2H2O (l)  C2H2 (g) + Ca(OH)2 (aq)
gas collected over water
PT = 738 torr
V = 523 mL
How many grams of C2H2
T = 23oC
Pwater at 23oC = 21 torr
PT = Pwater + Pacetylene
738 =
21 +
Pacetylene
Pacetylene =
717 torr
= .943 atm
nacetylene =
.943
x L =
0.0821
x 296
Pi = Xi PT
mol
x g/mol
= g