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I - Chapter 12 Gases Revisited
“Ideal gas” An ideal gas
is one that
behaves like
our mental
picture
predicts.
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Section 1
Gases Revisited
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What are the characteristics of an “Ideal” Gas?
1) How big are gas molecules?
Gas molecules are tiny and
insignificant compared to the
space between them.
Because of this different
gases will usually behave the
same.
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What are the characteristics of an “Ideal” Gas?
1) How big are gas molecules?
The volume that a sample of gas
occupies depends on how many
molecules are in the sample.
…not on how big the molecules are.
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What are the characteristics of an “Ideal” Gas?
2) How do the molecules move?
Molecules move in a straight line
until they run into one another
where they can transfer kinetic
energy to one another.
We don’t notice this since
they’re not colliding with us.
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What are the characteristics of an “Ideal” Gas?
2) How do the molecules move?
Collisions are “elastic”
Elastic means that no energy
is lost during the collision.
So molecules can exchange energy
with each other, but the temperature
should remain the same.
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What are the characteristics of an “Ideal” Gas?
2) How do the molecules move?
Their motion and collisions create
pressure to hold up the gas.
The more molecules or
faster they move should
make pressure get higher?
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What are the characteristics of an “Ideal” Gas?
2) How do the molecules move?
Their motion and collisions create
pressure to hold up the gas.
The volume the gas takes
up will depend on the
number of molecules in the
sample and their speed.
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What are the characteristics of an “Ideal” Gas?
3) Are there intermolecular sticky
forces like in liquids and solids?
Gases appear to have little
or no sticky forces holding
molecules together.
They might if we could get
them close together.
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What are the characteristics of an “Ideal” Gas?
3) Are there intermolecular sticky
forces like in liquids and solids?
For this reason gases made of large
“sticky” molecules act just like gases
made from little molecules (CO2 vs. H2 )
Because of this different gases
will usually behave the same.
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What are the characteristics of an “Ideal” Gas?
4) How are gases with small
molecules different from gases with
big molecules?
Recall that at the same temperature, two
different samples will have molecules with
the same “average kinetic energy”?
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What are the characteristics of an “Ideal” Gas?
4) How are gases with small
molecules different from gases with
big molecules?
(KE = ½ mv2)
Energy is a function of speed
(velocity - V) and mass – m
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What are the characteristics of an “Ideal” Gas?
4) How are gases with small
molecules different from gases with
big molecules?
…so small molecules have to move
faster to make up for their lower mass.
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What are the characteristics of an “Ideal” Gas?
4) How are gases with small
molecules different from gases with
big molecules?
Large molecules move slow so their
kinetic energy will be the same as
that of the smaller molecules
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Here’s an example to illustrate this:
Effusion – Escape of a gas through a pin hole
Why does a
helium
balloon
deflate faster
than an air
balloon?
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Here’s an example to illustrate this:
Effusion – Escape of a gas through a pin hole
Which
molecules
will find the
hole the
quickest?
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Here’s an example to illustrate this:
Effusion – Escape of a gas through a pin hole
Helium
molecules
move faster,
will find the
hole sooner.
Test Your Understanding
He (4g)
NH3 (17g)
O2 (32g)
The following are trick questions:
1. If each sample above contained 1 mole
of molecules, which sample should
occupy the largest volume?
All have the same volume, Why?
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Test Your Understanding
He (4g)
NH3 (17g)
O2 (32g)
The following are trick questions:
2. As molecules collide over time,
what should happen to the pressure
inside each balloon?
It would stay the same, Why?
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Test Your Understanding
He (4g)
NH3 (17g)
O2 (32g)
The following are trick questions:
3. Which sample will have the strongest
IM sticky forces?
None, Why?
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Try these regents questions:
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Try these regents questions:
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Try these regents questions:
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Section 2A
The gas laws
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Section II - THE GAS LAWS:
Math relationships between Pressure,
volume and temperature for ideal gases
Click here to try this online simulation
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Pressure vs. Volume (Boyle’s law)
More pressure
Smaller volume
The Volume of a gas is inversely proportional to its
pressure, If temperature is kept constant… (the same)
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This means that when one increases, the other
decreases by a proportional quantity.
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Ex: If pressure is doubled, volume becomes one-half
Or If volume is doubled, pressure becomes one-half
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Lets use our Kinetic molecular theory to explain why:
(molecules confined to smaller space collide more,
and create more pressure)
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Pressure vs. Volume (Boyle’s law)
Ex: A sample of a gas is confined
to a closed container with a movable piston
Lets measure the volume as pressure increases
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Lets measure the volume as pressure increases
Notice as
pressure
increases,
volume
decreases
Trial 1
Trial 2
Trial 3
Press
50 kPa
100 kPa
150 kPa
Vol
6 liters
3 liters
2 liters
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Lets measure the volume as pressure increases
Notice:
P x V always = 300
Trial 1
Trial 2
Trial 3
Press
50 kPa
100 kPa
150 kPa
x
x
x
Vol
6 liters
3 liters
2 liters
k
= 300
= 300
= 300
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Lets measure the volume as pressure increases
P x V is a constant
The symbol for a
constant is “k”
Trial 1
Trial 2
Trial 3
Press
50 kPa
100 kPa
150 kPa
x
x
x
Vol
6 liters
3 liters
2 liters
k
= 300
= 300
= 300
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Lets measure the volume as pressure increases
Ex: If pressure is reduced to 25,
what is the new volume?
P x V = 300
25 x ? = 300
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Lets measure the volume as pressure increases
Since P x V is a constant then
P1 x V1 = P2 x V2 = P3 x V3
etc.
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So now we have a formula for
these types of problems:
P1 x V1 = P2 x V2
Lets use the initial values:
50 x 6 = P2 x V2
And our new value for Pressure:
50 x 6 = 25 x V2
And solve for the new volume:
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So now we have a formula for
these types of problems:
P1 x V1 = P2 x V2
50 x 6 = 25 x V2
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25
12 liter = V2
Pressure vs. Volume (Boyle’s law)
Ex: A sample of a gas is confined
to a closed container with a movable piston
Pressure
Volume k
1
50
6
300
2
100
3
300
3
150
2
etc.
Graph the values:
This an hyperbola:
It shows an
inverse
relationship
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Try one:
At a pressure of 240 kPa the gas above occupies a volume of 25
liters. Calculate the new volume when the pressure drops to 100 kPa.
P1= 240 kPa
V1 = 25 L
P2 = 100 kPa
Show work here:
P1V1 = P2V2
THE GAS LAWS:
Math relationships between Pressure, volume and
temperature for ideal gases
Volume vs. Temperature (Charles law)
The Volume of a gas
is directly proportional to
Kelvin temperature
(as long as pressure is kept the same!)
As temperature increases, volume increases
Why?
(Molecules move faster, push out
…and volume expands)
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THE GAS LAWS:
Math relationships between Pressure, volume and
temperature for ideal gases
Volume vs. Temperature (Charles law)
Volume / Temperature
k
200 mL
100 kelvins
600 mL
300 kelvins
2
100 mL
50 kelvins
2
2
Notice V ÷ T = 2
So V/T = k
Equation:
V1
T1
=
V2
T2
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THE GAS LAWS:
Math relationships between Pressure, volume and
temperature for ideal gases
V1
V
= 2
T1
T2
A different gas has a volume of 1.0 liter at 200
Kelvin's. If temperature is reduced to 50 K,
what is the new volume?
Substitute values and solve:
1.0 L =
200 K
V2
50 K
(1.0 L)(50 K) = (200 K )V2
(1.0 L)(50 K) = V2
(200 K)
V2 = 0.25 L
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THE GAS LAWS:
Math relationships between Pressure, volume and
temperature for ideal gases
Graphing:
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Where is absolute zero Kelvin?
Cool a gas until its
molecules stop
moving
Absolute zero is the
temperature at which
gas molecules would
stop moving.
-273.14oC
0
50
100
150
200
Kelvins
250
300
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Do these Practice problems
1. A 150. mL sample of a gas at standard pressure (1 atm) is
compressed to 125 mL. What is its new pressure?
Show work here:
P1V1 = P2V2
1.2 atm
2. A 150 ml sample of a gas at standard temp (00C) is heated to 250C.
What is its new volume?
Show work here:
V1 = V2
T1 T2
Don’t forget:
0 o C + 273 =
o
25 C + 273 =
163 ml
Pressure vs. Temperature (Gay-Lussac’s law) pressure is directly
proportional to Kelvin Temp. As Kelvin temp increases, pressure
increases
P/T=K
P1 =
T1
P2
T2
(KMT: faster molecules collide more, increase pressure)
Ex: an “empty” 0.5 liter aerosol can at 250C is heated to 8000C. What is the
final pressure inside the can?
P1 = 1 atm
P2 = ?
P1 = P2
T1 T2
P2 = 3.6 atm
T1 = 250C + 273 = 298 K
T2 = 800 + 273 = 1073 K
(1 atm) = P2
(298 K)
(1074 K)
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Combined laws (Three equations in one!)
P V and T
P1V1 = P2V2
T1 T2
Ex: 100 mL of a gas at STP has its temp increased to 546 K while its
pressure is increased to 2 atmospheres. What is the new volume?
(1 atm)(100 mL)
(273 K)
=
(1 atm)(100 mL) (546 K) =
(1 atm)(100 mL) (546 K) = V2
(273 K)(2 atm)
Why didn’t the volume change?
(2 atm) V2
(546 K)
(273 K)(2 atm) V2
100 mL =
V2
Three equations in one.
If variables are
Held constant:
P1V1 = P2V2
T1
T2
P1V1 = P2V2
Boyles law
P1V1 = P2V2
T1
T2
V1 = V2
T1 T2
Charles
P1V1 = P2V2
T1
T2
P1 = P2
T1 T2
etc.
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The PTV Card will help you check
PTV
Volume
increases
Keeping Temp
constant
If pressure
decreases
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PTV Card
PTV
Keeping pressure
constant
If pressure
Temperature
increases
Volume
increases
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PTV Card
PTV
Keeping volume
constant
pressure
decreases
If Temperature
decreases
Do these Practice problems:
PTV
3. A 200 mL aerosol can contains gas under pressure at room
temperature (270C). If its initial pressure is 500 kpa.
What pressure will the gas exert when its temperature is
increased to 627 0C?
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4) A 5.0 Liter He balloon is released and rises into the air.
The temperature decreases from 300 k to 250 k, while the
pressure decreases from 100 kpa to 50 kpa.
What is the final volume of the balloon?
PTV
Learning Check
1.
Describe the molecules in an ideal gas.
2.
In terms of the kinetic theory, explain why gas pressure increases while its volume
decreases?
3.
Why do aerosol containers contain the label “do not incinerate?
4.
For the graph below estimate the value of the k constant.
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Section 2B
Other stuff
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Are our Assumptions about ideal gases always true?:
Assumption 1
Molecules act like they have no volume
(far apart relative to their small size)
Assumption 2Molecules have no attraction for each other
(they move so fast, the weak forces are not noticeable)
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Are our Assumptions about ideal gases always true?:
Gases will act most ideal when the molecules are
Far apart ….. (at low pressure)
Moving fast …. (at high temperature)
Also, Small molecules like H2 and He are more ideal
(Must move faster to make up for their tiny size)
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Gases will begin to deviate when molecules are
Close together….. (as pressure increases)
Moving slow…. (as temperature decreases)
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Deviations- Gases will Deviate
(they won’t behave according
to the gas laws) when
molecules are…
The Deviant
Moving slowly
(at low temperature)
sticky forces attract molecules
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When molecules are Close together
(at high pressure)
larger molecules’ size interfere with
each other
Large molecules deviate
more than small ones.
Ex: CO2 (mass = 44) moves
slower,
and has stronger sticky
forces, than He or H2
The Deviant
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Where are deviations apparent?
Examples:
Air cools as it rises up
(its cold on mountain tops?)
Why?
Kilimanjaro
in Africa
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Where are deviations apparent?
As air rises, the pressure on it
decreases.
It expands
(As P decreases, V increases)
Sticky forces slow molecules down
as they move away from each other
so Temp decreases.
Kilimanjaro
in Africa
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Gas liquefaction:
Gases can be liquefied at Low
temperatures and high
pressures
Push Molecules close together,
and Cool them so they move
slow
…can now stick together and
liquefy
What state is
liquid
propane
gas?
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Questions
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Partial Pressures
In a mixture of gases, each gas produces its own
part of the total pressure (Each molecule own
pressure!)
Ex: 2 moles of O2 gas are mixed with 1 mole of H2
gas. If the total pressure is 100 kpa, how much
pressure does each gas exert?
Since
2/3rds of the molecules are O2
and
1/3rd are H2
The oxygen will produce 2/3rds of the pressure
2
x
(100 kpa)
3
and hydrogen 1/3 rd of the pressure:
1
x
(100 kpa)
3
=
67 kpa
=
33 kpa
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AVOGADRO’S HYPOTHESIS
Equal volumes of gases, at the same temperature and Pressure
Must have equal numbers of molecules
Or Two gas samples with equal number of molecules Under same
conditions of Temp and Press Will occupy equal volumes
1 liter
250C
1 atmosphere
H2
O2
Ex: Two balloons one with hydrogen, the other with oxygen both
occupy 1 liter at the same temp and pressure. If the hydrogen
balloon contains 0.25 moles of gas, how much oxygen gas is
contained in the other balloon?
0.25 moles Duh…
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