Kinetic Theory
Kinetic Theory - All molecules and atoms
Kinetic Energy - The energy an object has
1. All gases consist
2. The molecules of a gas
move in
Kinetic Theory (con’t)
3. The collisions that occur with other molecules are
4. The particles are separated from each other
1
Pressure
Gas Pressure - Occurs from the
Atmospheric Pressure - Occurs from the
Measuring Pressure
Pressure is
The SI unit of
The SI unit of
One Newton of
1 Newton = 1 Pa
meter2
2
Measuring Pressure (con’t)
1 ATM pressure is defined as
1 atm =
1 atm =
Pressure Instruments
Barometer – an instrument used to
The weight of the
3
Pressure Instruments (con’t)
If in one inch there are
, then how many inches
of Mercury =
of pressure?
Pressure Instruments (con’t)
Manometer – an instrument used to
4
Dalton’s Law of Partial Pressure
The total pressure of a container of gases is equal to the
This can be written mathematically as:
Example: You have a mixture of gases, A + B, in a
container. Gas A has a pressure of
Gas B has
pressure of
The total pressure of the gasses in
the container is the
Sample Problem #1
If the partial pressures of N2 is
, O2 is
and Ar is
in a closed container, what is the total
pressure of the container?
5
Sample Problem #2
If the total pressure of a container is
and the oxygen is
of the gas by moles in the container what is the partial
pressure of the oxygen?
Sample Problem #3
If a container contains equal amounts of Nitrogen, Oxygen,
Carbon Dioxide, Carbon Monoxide, and Neon with a total
pressure of
, what is the Partial Pressure of the
Nitrogen in Pascals?
6
Boyle’s Law for Pressure–Volume Changes
At a constant temperature, volume of a gas varies
This is true as
long as the other
Sample Problem #1
If you need to fill a
tank with Helium at
pressure, what volume of Helium at
pressure do you need?
Plug and Chug
7
Sample Problem #2
At constant temperature, a container is increased in volume from
If the initial pressure is
what
is the final pressure in Pascals?
Plug and Chug
Sample Problem #3
You are in charge of the orders for the student council balloon
sale. Each tank of Helium gas is
in volume at a
pressure of
If each balloon is
in volume
when filled at
pressure and
balloons have been
ordered, how many tanks will you need?
8
Charles’ Law for Temperature–Volume Changes
At constant pressure, the volume of a gas is
The proportionality between Volume and Temperature can be
expressed mathematically as:
Charles’ Law for Temperature–Volume Changes
Jacques Charles
made
9
Sample Problem #1
The initial temperature is
and the initial volume is
If the final temperature is
what is the final volume?
Plug and Chug
Sample Problem #2
A hot-air balloon has a final total volume of
and the initial temperature is
The balloon is filled
initially to
capacity. To what final temperature in
does the temperature of the gas have to be raised
in order to fill the entire balloon?
Note: The gas calculations must be done in
10
Sample Problem #2 (con’t)
Step 2- Plug and Chug
Gay-Lussac’s Law for TemperaturePressure Changes
The proportionality between Pressure and Temperature
11
The Combined Gas Law
Charles’s Law =>>
Boyle’s Law =>>
Gay-Lussac’s Law =>>
Combining these three laws you get the combined gas law:
This can be expressed as the following equation:
Sample Problem #1
A sample of oxygen gas has a volume of
at a pressure
of
and a temperature of
What will the
volume of the gas be if the pressure is changed to
and
the temperature is changed to
First, convert both
Plug and Chug
12
Sample Problem #1 (con’t)
Sample Problem #2
Freon-12, dichlorodifluoromethane, was a widely used
refrigerant. Consider a
sample of Freon-12 at a
pressure of
and a temperature of
Calculate
the Temperature
of the gas when the gas is
used at the factory to fill refrigerator cooling systems with a total
volume of
at a total final pressure of
Convert the
13
Sample Problem #2 (con’t)
Now Plug and Chug
The Ideal Gas Law
According to Charles’s Law when the temperature reaches 0 K
then the
Ludwig Boltzman and James Maxwell (1860) proposed the
14
The Ideal Gas Law
1. The molecules of an ideal gas are
2. The molecules of a gas move
3. The collisions that occur with other molecules are
A real gas behaves as an ideal gas as long as
The Ideal Gas Law
Charles’s, Boyle’s, Gay-Lussac’s and Avogadro’s Laws relate
two of the gas variables while holding the other constant. If we
combine all of these relationships we can derive a law that
summarizes them. It is called
15
The Ideal Gas Law
The ideal gas law
can be used to solve any of the gas
law problems, since you can write this as:
At constant number of moles and Temperature:
At constant number of moles and Pressure:
At constant number of moles and Volume:
At constant Volume and Temperature:
Value of R
Solving R at STP for one mole of gas:
16
Sample Problem #1-Finding Pressure
What pressure is exerted by
container at
First convert
of gas in a
Plug and Chug
Sample Problem #2-Finding Volume
What volume would be occupied by
temperature of
and a pressure of
First convert
at a
Plug and Chug
17
Sample Problem #3-Finding Moles
How many
flask at a temperature of
First convert
can be contained in a
and a pressure of
Plug and Chug
Sample Problem #4 – Finding Temp.
What temperature in degrees Celsius is
occupies a volume
at a pressure of
First convert
if it
Plug and Chug
18
Diffusion and Graham’s Law
Diffusion - The movement of molecules and ions
Graham’s Law - The rate of diffusion of a gas is
The temperature of a gas is a measurement of the
Diffusion and Graham’s Law #2
Not all the molecules of a gas are
As the temperature increases
19
Deriving Graham’s Law
Maxwell and Boltzman found that the
If two different gases have the same temperature, are their
molecules moving
Deriving Graham’s Law #2
Divide both sides by
Next take the
20
Sample Problem #1
What is the molar mass of an unknown gas that diffuses
Sample Problem #2
The rate of diffusion of an unknown gas that is made of a single
element is
Identify the
unknown gas?
21