Kinetic Molecular Theory
• Particles in an ideal gas…
–
–
–
–
–
have no volume.
have elastic collisions.
are in constant, random, straight-line motion.
don’t attract or repel each other.
have an avg. KE directly related to Kelvin temperature.
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Molecular Velocities
molecules sorted by speed
Fractions of particles
many different molecular speeds
the Maxwell speed distribution
speed
http://antoine.frostburg.edu/chem/senese/101/gases/slides/sld016.htm
Real Gases
• Particles in a REAL gas…
– have their own volume
– attract each other
• Gas behavior is most ideal…
– at low pressures
– at high temperatures
– in nonpolar atoms/molecules
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Characteristics of Gases
Gases expand to fill any container.
– random motion, no attraction
Gases are fluids (like liquids).
– no attraction
Gases have very low densities.
– no volume = lots of empty space
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Characteristics of Gases
• Gases can be compressed.
– no volume = lots of empty space
• Gases undergo diffusion & effusion.
– random motion
Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem
Properties of Gases
Gas properties can be modeled using math.
Model depends on:
V
T
P
n
=
=
=
=
volume of the gas (liters, L)
temperature (Kelvin, K)
pressure (atmospheres, atm)
amount (moles, mol)
Pressure - Temperature - Volume
Relationship
P T V
Charles
1
P
V
VaT
Gay-Lussac’s
PaT
Boyle’s
a ___
Pressure - Temperature - Volume
Relationship
P T
n V
1
V
a ___
Boyle’s
P
Charles
VaT
Gay-Lussac’s
PaT
Robert Boyle
Boyle: His Life
•Born on January 25, 1627 in Ireland
•His father was the wealthiest man in the British Isles
•Youngest of fourteen children
•Boyle was a very shy, devoutly religious man
•He was once offered a position in the clergy, but turned
it down because he was more interested in the sciences.
•He died on December 30, 1691, and left the gist of his
estate to charitable organizations.
Robert Boyle
Boyle:His Scientific Career
•Known as the “Father of Modern Chemistry”
•First scientist to perform controlled experiments and
publish his reports and work.
•Responsible for Boyle’s Law, which states that at
constant temperature, the pressure and volume of a
gas are inversely proportional to each other.
Robert Boyle
Boyle: His Law Explained
At constant temperature, the volume of a gas is inversely
proportional to pressure. In other words, when temperature
remains the same, as pressure is increased, the volume of the
gas will decrease. This is an INVERSE relationship.
The Formula is:
P1V1=P2V2
P1=original pressure
P2= New pressure
V1= Original volume
V2= New Volume
Robert Boyle
Example:
The Volume of a gas is 50 ML at a pressure of 1 atm.
If the volume increases to 100 ML, and the temperature remains
constant,
what will the new pressure be?
P1=1 atm.
P2= ?
V1= 50 ML. V2= 100 ML
Put the numbers in the equation:
1atm(50 ML)= P2(100 ML)
Divide both sides by 100.
100 (P2)
------------------------------
100
50
=
------------------------------
100
The New Pressure is .5 atm.
P2= 0.5 atm.
Robert Boyle
Boyle’s law is important to Scuba Divers. They need
to ascend slowly, because as they come closer to the
surface, the pressure exerted by the water decreases,
which means the volume of air in their lungs
increases. If a diver were to ascend very quickly, the
pressure would decrease rapidly, causing the air in
the lungs to increase rapidly, resulting in the Diver
“exploding.”
Jacques Charles
Charles: His Life
•Charles was born on November 23, 1746 in Beaugency,
France.
•As a child, he learned only basic math and hardly any
science.
•Charles became interested in science after the
ambassador from the United States, Benjamin Franklin,
visited Paris.
•Although he is responsible for “Charles Law,” it was not
published until 15 years after his initial discovery, by
Josepgh Gay-Lussac.
Jacques Charles
Charles: His Scientific Career:
•Although Charles is well known for his gas law, he was better known
for his aeronautic research.
•In 1783, he realized that Hydrogen was lighter than air and made the
first balloon using hydrogen gas.
• On August 27, 1783, Charles’s balloon ascended nearly 3,000 feet.
Upon witnessing this, hordes of angry peasants destroyed the balloon
after it landed, believing it was some type of evil or witchcraft.
•In 1787, Jacques Charles discovered the relationship between the
volume of gas and temperature (Charles’s law.)
Jacques Charles
Charles: His Law Explained:
At Constant pressure, the Volume of a gas is directly proportional
to temperature (must be in Kelvin.) In other words, as temperature
increases, so too, does volume.
Notice that it’s absolutely imperative that the temperature is in degrees Kelvin (K=C+273)
The Formula is:
V1
---------T1 (Kelvin)
=
V2
----------T2 (Kelvin)
Jacques Charles
Example:
At 200K, the volume of a gas is 100 ML. The temperature is raised to
300K, what will the new volume be?
V1=100 ML
V2= ?
T1 =200K
T2=300K
Substitute the numbers in the Equation: 100
------200
Cross Multiply: 200 (V2)= 30,000
Divide Both Sides By 200:
200 V2
30,000
------------- = -----------V2 =
200
200
The New Volume is 150 ML.
30,000
---------- = 150
200
=
V2
------300
Amedeo Avogadro
Avogadro: His Life:
•Avogadro was born on August 9, 1776 in Turin, Italy.
•He was born into a family of respected lawyers, and he
intended to carry the family tradition, graduating with a
degree in law at the age of twenty. He became interested in
the sciences, however, and in 1800, he began studies in math
and science.
•He had six children and was very religious.
Amedeo Avogadro
Avogadro: His Scientific Career:
•While employed as a teacher in Vericelli, Avogadro wrote a note, declaring the
hypothesis, now known as Avogadro’s law.
•His hypothesis wasn’t accepted until after his death, in 1858.
•Avogadro is responsible for resolving the confusion surrounding atoms and
molecules.
•He believed that particles were composed of molecules, and that molecules were
made up of smaller units; atoms.
•Avogadro is also responsible for discovering the number of molecules in one
mole. (6.02 x 10 23)
Translation: (Good thing I take
Italian)
“Equal volumes of gas in the
same conditions of
temperature and pressure
contain the same number of
molecules”
Amedeo Avogadro
Avogadro: His Law Explained:
Equal Volumes of gases under the same conditions of
temperature and pressure have the same number of molecules
Therefore, if more gas is added, the number of molecules will
increase, as well, which will cause the volume to increase.
One mole has 6.02 x 10 23 particles, and one mole of gas
occupies 22.4 L.
.
Example:
Amedeo Avogadro
How many molecules are in 11.2 liters of a gas at STP?
Since one mole of gas contains 22.4 L, 11.2 L is exactly half
of that. Therefore, if one mole contains 6.02 x 1023
particles, than half of that is 3.01 x 1023.
There are approximately 3.0 x 1023 molecules in 11.2 L. of a
gas at STP.
John Dalton
John Dalton: His Life:
•John Dalton was born in 1766, in Cumberland, England
•For most of his life, Dalton was employed as a teacher and public lecturer.
•He was very interested with weather, and kept daily weather records from 1787
until his death.
•Dalton was a Quaker, meaning he believed in nonviolence.
•He led a very modest life, although he received many honors for his
accomplishments.
John Dalton
John Dalton: His Scientific Career:
•Known as one of the fathers of modern physical science.
•Developed the atomic theory of matter.
•Devised a system of chemical symbols
•formulated the theory that a chemical combination of different elements occurs in
simple numerical ratios by weight.
•Discovered Butylene and determined the composition of ether
•Developed an atomic theory, stating that all elements are composed of tiny,
indestructible particles called atoms that are all alike and have the same atomic
weight.
John Dalton
Dalton: His Law Explained
Dalton’s Law of partial pressures states that the sum of the partial
pressures of all the components in a gas mixture is equal to the
total pressure of the gas mixture.
Pt= Pa+Pb+Pc
Pt=The total pressure of a gas mixture.
Pa+Pb+Pc= the individual pressures of each component
Joseph Louis GayLussac
Lussac:His Life:
•Born in 1778, in France.
•Grew up during the French Revolution.
•His father was a very successful lawyer, who, during the
revolution was imprisoned.
•selected to attend the École Polytechnique, an exclusive
institution designed to create scientific and technical
leadership.
Joseph Louis GayLussac
Lussac:His Scientific Career:
•Lussac’s study of gasses led him to make several trips
nearly 7,000 meters above sea level in a Hydrogen balloon.
•Gay-Lussac also participated in early electrochemical
research.
•With the help of other scientists, he decomposed boric
acid by using fused potassium, thus discovering the
element boron.
Joseph Louis GayLussac
Lussac: His Law Explained:
As Temperature increases, Pressure increases, when volume
remains constant.
P1
------- =
T1
P2
--------T2
Combined Gas Law
P1 V1
---------T1
P2 V2
=
----------T2
Ideal Gas
Ideal Gases follow all laws perfectly.
How to get a gas to behave like an ideal gas:
LOW PRESSURE,
so the molecules have
lots of room to spread out.
HIGH TEMPERATURE,
They want a lot of
kinetic energy to
overcome
Intermolecular forces
Gas Law Calculations
Boyle’s Law
Graham’s Law
P1V1 = P2V2
v1
m2

v2
m1
Charles’ Law
diffusion vs. effusion
Combined
V1 = V2
T1 = T2
P1V1 = P2V2
T1 = T2
Density
P1 = P2
T1D1 = T2D2
1 atm = 760 mm Hg = 101.3 kPa
R = 0.0821 L atm / mol K
PV = nRT
Dalton’s Law
Gay-Lussac
P1 = P2
T 1 = T2
Ideal
Gas Law
Partial Pressures
PT = PA + PB