Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
Chapter 11 Part 1
Chapter 11 problems: page 390
3, 11, 14, 15, 20, 21, 22, 23, 31, 33, 34
Development of the Kinetic Theory of Gases
The KTG:
1. Gases are made up of molecules with lots of
2. Particles
-
is caused by this motion
3. Collisions are completely
4. There are no
between molecules
5. KE =
Properties of Gases resulting from the KTG:
1. Expansion - no
2. Fluidity - particles
( gases and liquids are both fluids)
3. Low Density - gases are roughly 1/1000 the density of
4. Compressibility
5. Diffusion - spontaneous mixing of 2 substances due to
6. Effusion - a gas spreads through a
between containers
- gases only behave close to ideally at
pressures and
temperatures.
A qualitative description of gases:
P=
T=
V=
n=
Combined Gas Law: Describes the relationship between
.
Formula:
STP = standard temperature and pressure:
Pressure units:
Temperature units:
kPa,
torr,
K,
Volume: if one mole is present, then
106738592
atm,
mmHg
C0 ( must use K with gas laws)
L
Page 1 of 7
Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
Boyle’s Law - (Irish - 1662)
Boyle’s Law: The volume of a gas varies
with pressure at constant
Formula:
As the applied (outside pressure) increases, the volume
.
Graph:
Ex1: If 150. ml of a sample of O2 at 720.0 mm Hg has the pressure increased to
750.0 mm Hg, what is the new volume?
106738592
Page 2 of 7
.
Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
Charle’s Law (French - late 1700’s)
Charle’s Law: The volume of a fixed mass of gas varies
constant
.
with temperature at
Formula:
As the temperature increases, the volume
. (hot air balloon)
Graph:
Ex2: If 753 ml of nitrogen at 25 C0 is heated to 50. C0, then what is the new volume?
When the graph is extrapolated to 0 K, the volume is 0. This is impossible as the gas
would have volume of all the particles with no space between them. Of course, this is
impossible to test since no gases exist at - 273 C0 (only solids and liquids).
106738592
Page 3 of 7
Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
Gay-Lussac’s Law (French)
Gay-Lussac’s Law: The pressure of a fixed mass of gas varies
at constant
.
with temperature
Formula:
As the temperature increases, the pressure
.
Page 3
Graph:
Ex3: If a gas at 3.0 atm and 25 C0 is heated to 52 C0, what is the new pressure?
Combined Gas Law
Nothing in life is ever constant, so....
add together the three previous gas laws to create......
Ex4: If a sample of gas at 22.0 C0 and 31 kPa occupies 200.0 cm3, what space will it
occupy at STP?
106738592
Page 4 of 7
Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
Dalton’s Law of Partial Pressures (English - 1802)
Dalton’s Law: The total pressure of a collection of gases in a mixture is equal to the
of the pressures that each gas would exert by itself in the same volume.
Collecting gas over water:
H2O(g)
H2O(g)
H2O(g)
Zn(s) + H2SO4(aq)  ZnSO4(aq) + H2(g)
Dalton’s Law of Partial Pressures
So, for the above drawing:
PT = P1
P
=
+ P2 .....
P
+
P
Ex5: A student collects oxygen gas over water at an atmospheric pressure of 100.0 kPa
and a temperature of 29.0 C0. What is the partial pressure of the oxygen? (see
table A-7)
At 29.0 C0 water has a pressure of ________________________
106738592
Page 5 of 7
Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
Graham’s Law of Diffusion - (English - 1824)
Graham noticed that gases with low densities diffuse
densities.
than gases with higher
Graham’s Law: Under the same conditions of temperature and pressure, gases diffuse at
a rate
proportional to the square roots of their
Formula:
or
rate of gas “A”
rate of gas “B”
density of gas “B”
density of gas “A”
=
velocity of gas “A”
velocity of gas “B”
=
molecular weight of gas “B”
molecular weight of gas “A”
Show derivation of formula from Gas A ½ mv2 = Gas B ½ mv2
Gas “A” has a kinetic energy of ½ mv2 and Gas “B” has a kinetic energy of ½ mv2.
At the same temperature, the two gases will have the same kinetic energy.
Ex6: If CO2 molecules travel at 200.0 mph, how fast do H2 molecules go?
Ex7: If He atoms travel at 800.0 mph, how fast do nitrogen molecules go?
106738592
Page 6 of 7
Accelerated Chemistry
Chapter 11 Part 1 – Gas Laws
The Kinetic Theory and the Gas Law
In Boyle’s Law, Pressure = Force/Area. So….
½ the volume means
So,
the pressure
big box
the particles
box half as small
In Charle’s Law, temperature is proportional to KE. So....
doubling temperature =
doubling KE
=
KE
pressure (
the number of collisions)
in order to keep pressure the same (constant), volume must
In Gay-Lussac’s Law, temperature is proportional to KE. So...
doubling temperature =
KE
doubling KE
pressure (
=
volume is constant, so the
the number of collisions)
does change
In Dalton’s Law of Partial Pressures, if gas A exerts a pressure of 5 collisions/second and
gas B exerts a pressure of 5 collisions/second, then the total # of collisions/second
should =
(their sum).
106738592
Page 7 of 7