Kinetic Theory
Kinetic Theory - All molecules and atoms are in
Kinetic Energy - The energy an object has because of
1. All gases consist of
2. The molecules of a gas
move in
Kinetic Theory (con’t)
3. The collisions that occur with other molecules are perfectly
4. The particles are separated from each other by
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Gas Properties
1. Amount of a gas –
2. Volume – The SI Unit of volume is the
3. Temperature – SI unit of temperature is
4. Pressure – Collisions of the gas with
Pressure
Gas Pressure - Occurs from the
Atmospheric Pressure - Occurs from the
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Measuring Pressure
Pressure is
The SI unit of force is the
The SI unit of Pressure is the
One Newton of force/meter2 equals
Measuring Pressure (con’t)
1 ATM pressure is defined as
1 atm =
1 atm =
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Pressure Conversions
If in one inch there are 25.4 mm, then how many inches
of Mercury =
Barometer
An instrument used to
The weight of the
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Manometer
An instrument used to measure pressure
Manometer Problem #1
What happens to the height of the column of Hg on the open
side of the manometer when
Manometer Problem #2
If the Hg on the closed side of the manometer is
lower
and the atmospheric pressure is
, what is the
pressure inside the container?
Note:
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Manometer Problem #3
If the atmospheric pressure is
and the Hg on the open
side of the manometer is
Hg higher than the on the closed
side, what is the pressure of the gas in the monometer in ATM?
Dalton’s Law of Partial Pressure
The total pressure of a container of gases is equal to the
This can be written mathematically as:
PT =
Example: You have a mixture of gases, A + B, in a
container. Gas A has a pressure of
Hg. Gas B has
pressure of
Hg. The total pressure of the gasses in
the container is the
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Sample Problem #1
If the partial pressures of N2 is
Hg, O2 is
Hg
and Ar is
Hg in a closed container, what is the total
pressure of the container?
PT =
PT =
PT =
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?
PO2 =
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Sample Problem #3
If a flask 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?
Boyle’s Law for Pressure–Volume Changes
At a constant temperature, volume of a gas varies
PV = K (a constant) ------>
This is true as
long as the other
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Sample Problem #1
If you need to fill a
liter tank with Helium at
atmosphere pressure, what volume of Helium at 0.4000 atm
pressure do you need?
Plug and Chug
P1V1 = P2V2
Sample Problem #2
At constant temperature, a container is increased in volume from
If the initial pressure is
Hg, what
is the final pressure in Pascals?
Plug and Chug
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Sample Problem #3
You are in charge of the orders for the student council balloon
sale. Each tank of Helium gas is
liters in volume at a pressure
of
atm. If each balloon is
liters in volume when filled at
atm pressure and
balloons have been ordered, how
many tanks will you need?
Charles’ Law
Jacques Charles
made graphs of the
relationship between
a gas’s
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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:
V
T
=
k
Sample Problem #1
The initial temperature is
If the final temperature is
K and the initial volume is
K what is the final volume?
Plug and Chug
V1 = V2
T1
T2
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Sample Problem #2
If a container is reduced in volume from
and the initial temperature of the container is
what will be
the final temperature of the container in degrees Celsius?
Note: Remember to do the gas calculations in Kelvin and
then convert back to Celsius to give the final answer.
Sample Problem #3
A hot-air balloon has a final total volume of
cubic meters
and the initial temperature is
The balloon is filled
initially to three-fourths capacity. To what final temperature in
degrees Celsius does the temperature of the gas have to be raised
in order to fill the entire balloon?
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Problem #3 (con’t)
Step 2- Plug and Chug in the Charles Law Equation
Gay-Lussac’s Law for TemperaturePressure Changes
P/T = k therefore,
The proportionality between Pressure and Temperature
can be expressed mathematically as:
P
T
=
k
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The Combined Gas Law
Charles’s Law =>> V = k Boyle’s Law =>> PV = k
T
Gay-Lussac’s Law =>> P = k
T
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
kPa and a temperature of
What will the volume of
the gas be if the pressure is changed to
and the
temperature is changed to
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Problem #1 (con’t)
Sample Problem #2
Freon-12, dichlorodifluoromethane, was a widely used
refrigerant. Consider a
Liter sample of Freon-12 at a
pressure of
kPa and a temperature of 5.5°C. Calculate
the Temperature in degrees Celsius 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
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Problem #2 (con’t)
Avogadro’s Principle
Avogadro hypothesized that equal
Therefore, as the number of gas particles
P = k
n
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The Ideal Gas Law
According to Charles’s Law when the temperature reaches 0 K
then the volume of the gas will be zero. Volume can not be
Ludwig Boltzman and James Maxwell (1860) proposed the
Molecular Theory of Ideal Gases
1. The molecules of an ideal gas are
2. The molecules of a gas move in
3. The collisions that occur with other molecules are perfectly
4. The molecules of an ideal gas do not exert
A real gas behaves as an ideal gas as long as the conditions of
temperature and pressure are
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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 the
Using The Ideal Gas Law
The ideal gas law PV = nRT can be used to solve any of the gas
law problems, since you can write this as:
R =
PV At constant number of
nT
At constant number of
At constant number of
At constant
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Value of R
Solving R at STP for one mole of gas:
R = PV
nT
Sample Problem #1-Finding Pressure
What pressure is exerted by
moles of gas in a 19800 mL
container at
First convert Temp to Kelvin and Volume to liters
T=
19800 mL =
Plug and Chug
PV = nRT
so
P =
P =
P =
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Sample Problem #2-Finding Volume
What volume would be occupied by
a temperature of
and a pressure of
of helium at
First convert Temp to Kelvin. Pressure to atm and grams to moles
Plug and Chug
Sample Problem #3-Finding Moles
How many grams of nitrogen gas can be contained in a
flask at a temperature of
and a pressure of
liter
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Sample Problem #4 – Finding Temp.
What temperature in degrees Celsius is
occupies a volume of
of fluorine if it
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