It’s a Gas
GAS LAWS
Mr. Trotts
2/14/2011
Lesson Objectives
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You will be able to:
Name and describe 5 characteristics of gases
Identify three differences between ideal gases and real
gases.
Define the term “STP”
List 4 units for pressure measurement
Explain and describe the relationship between
temperature and pressure of gases, according to
Charles’ Law.
Explain and describe the relationship between volume
and pressure of gases, according to Boyle’s Law.
Explain how temperature, pressure, and volume of gases
are all related according to the combined gas law.
Solve mathematic problems about Charles’ Law, Boyle’s
Law, and the combined gas law.
Vocabulary: Journal
Pressure
Volume
Temperature Kelvin
Boyle’s Law Charle’s Law
Ideal Gas Law
STP
Combined Gas Law
Test questions: journal
1. Describe the 5
characteristics of gases
2. Compare the 3 real and
ideal characteristics of
gases
What are Characteristics
of a GAS?
: Gas Laws
In the REAL WORLD:
Gases are fat.
(they have mass)
Gases hog the sofa.
(they have volume)
Gases are pushy and
have an attitude
toward other gases.
(they exert forces
on each other)
Image Source: mtv.com
In an IDEAL WORLD:
Gases are skinny.
(they have no mass)
Gases make
themselves invisible.
(they have no volume)
Gases are not
confrontational.
(they do not
interact… elastic
collisions)
IT’S A GAS…
Daily grade:
1. name those 5 characteristics given 2
slide ago.
2. What were the 3 differences between
a real gas (what is really happening)
and an ideal gas (assumptions used to
make gas laws work)
IT’S A GAS…
3. List the physical
characteristics of gases
4. Describe the kinetic
molecular theory (KMT)
5. List the 3 assumption of
the KMT
The Nature of Gases
Gases have some interesting
characteristics that have
fascinated scientists for 300 years.
The first gas to be studied was air
& it was a long time before it was
discovered that air was actually a
mixture of particles rather than a
single gas.
The Nature of Gases
But this realization did not make the
study of gas behavior more difficult.
Although air is a mixture of several
different gases, it behaves much the
same as any single gas.
Regardless of their chemical
identity, gases tend to exhibit similar
physical behaviors
The Nature of Gases
Gas particles can be monatomic (Ne),
diatomic (N2), or polyatomic (CH4) –
but they all have these
characteristics in common:
1) Gases have mass.
2) Gases are compressible.
3) Gases fill their containers.
4) Gases diffuse
5) Gases exert pressure.
6) Pressure is dependent on Temp.
Kinetic Molecular Theory
There is a theory that modern day
chemist’s use to explain the
behaviors and characteristics of
gases - the Kinetic Molecular
Theory of Matter.
• The word kinetic refers to
motion.
• The word molecular refers to
molecules
Kinetic Molecular Theory
The theory states that the tiny
particles in all forms of matter in
all forms of matter are in
constant motion.
This theory is used to explain the
behaviors common among gases
There are 3 basic assumptions of
the KMT as it applies to gases.
KMT Assumption #1
A gas is composed of small hard
particles.
The particles have an insignificant
volume and are relatively far apart
from one another.
There is empty space between
particles.
No attractive or repulsive forces
between particles.
KMT Assumption #2
The particles in a gas move in
constant random motion.
Particles move in straight paths
and are completely independent
of each of other
Particles path is only changed by
colliding with another particle or
the sides of its container.
KMT Assumption #3
All collisions a gas particle
undergoes are perfectly elastic.
No energy is lost from one
particle to another, and the total
kinetic energy remains constant.
6. Compare the density of
several gases at STP
7. Describe why gases are
compressible
8. Describe the expansion
of gases
Gases have mass.
• Gases seem to be weightless, but
they are classified as matter, which
means they have mass.
• The density of a gas – the mass per
unit of volume – is much
less than the density of a
liquid or solid, however.
Gases have mass.
It’s this very low density that allows
us to be able to walk through the
room without concerning ourselves
with air resistance.
Since it is so easy to “swim” across
the room we don’t put much
thought into the mass of a gas.
Really it is only noticeable if we have
a large collection of gas in a
container.
The Kinetic-Molecular theory
explanation of it is that we
assume that gases are composed
of a collection of particles.
You can’t see these particles
directly, so they are very tiny, and
to notice any mass you must weigh
a collection of the particles.
It is usually necessary to have a
mole or more of gas particles to
have significant a significant
change in mass.
nd
2 –
Gases “R” squeezable
If you squeeze a
gas, its volume can
be reduced
considerably
A gases low density
allows for there to
a lot of empty
space between gas
molecules.
Gas particles have a high velocity,
relative to their masses.
This gives them a lot of energy and
movement.
The movement causes the gases to
spread out, which leaves a lot of
space between molecules.
That empty space can be
compressed by pressure allowing
gas particles less room to move
around thus decreasing the
volume.
This empty space can be
compressed simply by adding
pressure.
We can use this ability of a gas to
do work for us.
Think of a shocks on a car.
You really are riding on a
pillow of air.
A bump in the road
compresses the gas in the
shocks until the bump’s
energy is absorbed.
rd
3
– Gases fill their containers
Gases expand until they take up as
much room as they possibly can.
Gases spread out to fill containers
until the concentration of gases is
uniform throughout the entire
space.
This is why that nowhere around
you is there an absence of air.
The Kinetic-Molecular theory alludes
to this by the fact that these
particles are in constant random
motion.
Gases move in a straight line until it
they collide with other particles or
the sides of the container, which
causes them to change directions
until they collide with something else.
This bouncing off of everything
around them spread the particles out
until they are uniform throughout
the entire container.
If I opened up a bag of popcorn in
front of the class you would soon
be able to smell it in the back.
The popcorn smell is a high energy
molecule or group of molecules
that is in the gas state.
There are really two properties
going on here:
- This property of gases spreading
out until they have filled the
room
- And the property of diffusion
Explain why when adding air
to a balloon it will stop at
a certain volume, and
then when adding more
air gets bigger and stops
at a new volume
9. What is meant by gases
diffuse?
10. Explain how gases exert
pressure
th
4
– Gases diffuse
Gases can move through each other
rapidly.
The movement of one substance
through another is called diffusion.
Because of all of the empty space
between gas molecules, another gas
molecule can pass between them
until each gas is spread out over the
entire container.
The same logic from the
observation that gases spread out
applies here.
If the gases are in constant random
motion the fact that they are
moving and colliding with
everything around them then they
will mix with other gases uniformly.
This doesn’t happen at the same
speeds for all gases though.
Some gases diffuse more rapidly
then other gases based on their size
and their energy.
Diffusion explains why gases are
able to spread out to fill their
containers.
It’s why we can all breath oxygen
anywhere in the room.
It also helps us avoid
potential odoriferous
problems.
th
5
– Gases exert pressure
Gas particles exert pressure by
colliding with objects in their
path.
The sum of all
of the
collisions
makes up the
pressure the
gas exerts.
The Kinetic-Molecular theory alludes
to this by the fact that these
particles are colliding with anything
in their path.
Imagine a gas in a container as a
room of hard rubber balls.
The collisions of the balls bouncing
around exert a force on the object
that with which they collide.
The definition of a pressure is a
force per unit area – so the total of
all of the tiny collisions makes up the
pressure exerted by the gas.
The gases push against the walls of
their containers with a force.
The pressure of gases is what keeps
our tires inflated, makes our
basketballs bounce, makes hairspray
come out of the can, etc.
11. Desribe what happens to
the gases in a fixed
volume container as the
temperature is increased
12. Give examples
th
6
– Pressure depends on Temp
The higher the temperature of a gas
-the higher the pressure that the gas
exerts
The reverse of that is true as well,
a the temperature of a gas decreases
– the pressure decreases.
Think about the pressure of a set of
tires on a car
Today’s Temp: 35°F
Pressure
Gauge
Today’s Temp: 85°F
Pressure
Gauge
th
6
– Pressure depends on Temp
The reverse of that is true as well,
a the temperature of a gas
decreases – the pressure
decreases.
Think about the pressure of a set
of tires on a car
Do you recall the definition of
temperature?
- the average kinetic energy of the
particles that make up an object
The higher the temperature the
more the energy
The more the energy the more
impacts the gases administer
The more the impacts or collisions
the more the pressure exerted.
The pressure increases when
temperature increases because the
molecules are moving with greater
speed and colliding against the sides
of their containers more often.
Therefore, the pressure inside that
container is greater, because there
are more collisions.
13. What variables effect
the characteristics of
gases?
14. Describe these variables
15. What is STP?
Measuring Gases
The conditions under which a gas is
studied is very important to its
behavior.
Experimental work in chemistry
requires the measurement of such
quantities as volume, temperature,
pressure, and the amount of sample.
These quantities are called variables
and if they are not accounted for then
the results of the experiment might be
jeopardized.
Gas variables
In order to describe a gas sample
completely and then make
predictions about its behavior under
changed conditions, it is important
to deal with the values of:
1) amount of gas
2) volume
3) temperature
4) pressure
Amount (n)
The quantity of gas in a given sample
expressed in terms of moles of gas.
This of course is in terms of
6.02 x 1023 molecules of the gas.
Don’t forget to convert mass to
moles you just divide by the molar
mass of the gas.
Volume (V)
The volume of the gas is simply the
volume of the container it is
contained in.
The metric unit of volume is the
liter (L)
There might also be problems that
use cubic meters as the unit for
volume.
- 1 L = 1 dm3
Temperature (T)
The temperature of a gas is generally
measured with a thermometer in
Celsius.
All calculations involving gases
should be made after converting the
Celsius to Kelvin temperature.
Kelvin = C° + 273
Pressure (P)
The pressure of a gas is the force
exerted on the wall of the container
a gas is trapped in.
There are several units for pressure
depending on the instrument used
to measure it including:
1) atmospheres (atm)
2) Millimeters of Mercury (mmHg)
3) Kilopascal (kPa)
STP
The behavior of a gas depends very
strongly on the temperature and the
pressure at which the gas is held.
To make it easier to discuss the
behavior of a gas, it is convenient to
designate standard conditions, called
STP.
- Temperature = 0°C or 273K
- Pressure = 1atm or 760mmHg or 101.3kPa
16. What causes
atmospheric pressure to
vary?
17. 1 atmosphere of pressure
= how many mmHg,
pascals, torres?
Atmospheric Pressure
The gases in the air are exerting a
pressure called atmospheric pressure
Atmospheric pressure is a result of
the fact that air has mass is and is
attracted by gravity producing a force.
Knowing this atmospheric pressure
and predicting changes in the
atmospheric pressure is how
forecasters predict the weather.
Atmospheric Pressure
Atmospheric pressure varies with
altitude
- the lower the altitude, the longer
and heavier is the column of air
above an area of the earth.
Look on the back of a box of cake
mix for the difference in baking times
based on the atmospheric pressure in
your region.
1 atm = 760mmHg
= 760 torr =
101.3kPa
Atmospheric Pressure
Low pressure or dropping pressure
indicates a change of weather from
fair to rain.
High pressure is an
indication of clear
skies and sun.
It all has to do with
the amount of air
pressing down on us.
Boyle’s Law
Boyle’s Law:
18. Variables = ?
19. Constant = ?
20. Formula = ?
21. Examples of system
Gas Laws
Studies of the behavior of gases
played a major role in the
development of physical sciences in
the 7th and 8th centuries.
The Kinetic Molecular theory marked
a significant achievement in
understanding the behavior of gases.
Observations have become
mathematical laws which we can use
to predict quantitative outcomes.
Boyle’s Law
Robert Boyle was among the first to
note the relationship between
pressure and volume of a gas.
He measured the volume of air at
different pressures, and observed a
pattern of behavior which led to his
mathematical law.
During his experiments Temperature
and amount of gas weren’t allowed to
change
As the pressure
increases
Volume
decreases
22. How does Pressure and Volume
of gases relate graphically?
Volume
PV = k
Temperature,
# of particles
remain constant
Pressure
Boyle’s Mathematical Law:
What if we had a change in conditions?
since PV = k
P1V1 = P2V2
Eg: A gas has a volume of 3.0 L at
2 atm. What is its volume at 4 atm?
1) determine which variables you
have:
 P1 = 2 atm
 V1 = 3.0 L
 P2 = 4 atm
 V2 = ?
2) determine which law is being
represented:
P and V = Boyle’s Law
3) Rearrange the equation for
the variable you don’t know
P1 V1 = V 2
P2
4) Plug in the variables and
chug it on a calculator:
(2.0 atm)(3.0L) = V2
(4atm)
V2 = 1.5L
Complete practice sheet on
Boyle’s Law
Charle’s Law
Charle’s Law
23. Variable’s = ?
24. Constant = ?
25. Formula = ?
26. Example of system
Charles’s Law
Jacques Charles determined the
relationship between temperature
and volume of a gas.
He measured the volume of air at
different temperatures, and
observed a pattern of behavior which
led to his mathematical law.
During his experiments pressure of
the system and amount of gas were
held constant.
Volume of balloon
at room
temperature
Volume of balloon
at 5°C
27. How does Temperature and
Volume of gases relate graphically?
Volume
V/T = k
Pressure,
# of particles
remain constant
Temp
Charles’s Mathematical Law:
What if we had a change in conditions?
since V/T = k
V1 V2
=
T1 T2
Eg: A gas has a volume of 3.0 L at
127°C. What is its volume at 227 °C?
1) determine which variables you
have:
 T1 = 127°C + 273 = 400K
 V1 = 3.0 L
 T2 = 227°C + 273 = 5ooK
 V2 = ?
2) determine which law is being
represented:
T and V = Charles’s Law
4) Plug in the variables:
3.0L
V2
=
400K
500K
5) Cross multiply and chug
(500K)(3.0L) = V2 (400K)
V2 = 3.8L
Complete practice sheet on
Charle’s Law
Gay-Lussac’s Law
Gay –Lussac’s Law:
28. Variables = ?
29. Constant = ?
30. Formula = ?
31. Example of system
Gay Lussac’s Law
Old man Lussac determined the
relationship between temperature
and pressure of a gas.
He measured the temperature of air
at different pressures, and observed
a pattern of behavior which led to his
mathematical law.
During his experiments volume of the
system and amount of gas were held
constant.
Think of a tire...
Car before a trip
Let’s get on
the road
Dude!
Pressure
Gauge
Think of a tire...
Car after a long trip
WHEW!
Pressure
Gauge
32. How does Pressure and
Temperature of gases relate
graphically?
Pressure
P/T = k
Volume,
# of particles
remain constant
Temp
Lussac’s Mathematical Law:
What if we had a change in conditions?
since P/T = k
P1 P2
=
T1 T2
Eg: A gas has a pressure of 3.0 atm at
127º C. What is its pressure at 227º C?
1) determine which variables you
have:
 T1 = 127°C + 273 = 400K
 P1 = 3.0 atm
 T2 = 227°C + 273 = 500K
 P2 = ?
2) determine which law is
being represented:
T and P = Gay-Lussac’s Law
4) Plug in the variables:
3.0atm
P2
=
400K
500K
5) Cross multiply and chug
(500K)(3.0atm) = P2 (400K)
P2 = 3.8atm
Complete practice sheet on
Gay-Lussac’s Law
LAW
RELATIONSHIP
LAW
CONSTANT
Boyle’s
P V
P 1 V1 = P 2 V 2
T, n
Charles’ V T V1/T1 = V2/T2
P, n
GayP T P1/T1 = P2/T2
Lussac’s
V, n
Combined Gas Law
Combined Gas Law:
33.Variables
34.Constant
35.Formula
…THEREFORE:
Temperature, Volume,
and Pressure
are
all
=
related!
P1 V1
T1
P 2 V2
T2
Practice
1. 100.0 cm3 oxygen at 10.50 kPa changes to
9.91 kPa. What is the new volume of the
gas?
P1 V1
P2 V2
=
T1
T2
P1 V1
=
P2 V2
Boyle’s Law!
(10.50 kPa) x (100.0 cm3
= (9.91 kPa) x (V2)
O2)
V2 = (10.50 kPa) x (100.0 cm3
= 106 cm3
O2)
O2
(9.91 kPa)
Practice
2. 150.0 mL sulfur dioxide at 748 mmHg changes
to a new volume of 140.6 mL. What is the new
pressure of the gas?
P1 V1
P2 V2
=
T1
T2
P1 V1
=
P2 V2
(748
x (150.0 mL SO2) = (P2) x (140.6 mL SO2)
mmHg)
(150.0 mL SO2) = 798 mmHg
P2 = (748
mmHg)
(140.6 mL SO2)
Complete practice sheet on
Combined Gas Law
The Ideal Gas Law &
Co.
Mr.
Trotts
Feb
2011
A Reminder…
We
that we live in an
world where:
Gas particles have no mass
Gas particles have no volume
Gas particles have elastic collisions
These assumptions are used when trying to
calculate the AMOUNT of a gas we have!
Why are these
assumptions important?
PV = nRT
Image source:
PV = nRT
PRESSURE
V OLUME
n MOLES OF GAS
R GAS CONSTANT
TEMPERATURE
Image source:
The MysteRious R
• R is a constant (doesn’t change).
• Number value of R depends on other units.
• Units of R are a combination of many units.
62.4 mmHg · L
mol · K
8.31 kPa · L
mol · K
0.0821 atm · L
mol · K
Image source:
Ummm… What?
PV = nRT
Solve for R:
R =
Plug in
units:
R=
PV
nT
(atm)
(mm
(kPa)
Hg)
(L)atm)
L)
(mol) (K)
!
e
V1
T1
=
V2
T2
P1 x V1 = P2 x V2
P1 V1
P2 V2
=
T
T
1
2
P V = n RT
Used with only ONE SET OF CONDITIONS
When to Use PV = nRT
Calculating amount of gas in
moles
Calculating P, V, or T if moles
of gas are known.
IMPORTANT! We must have 3
out of 4 pieces of information:
P
V
n
T
Practice with the Ideal Gas Law
1. A gas sample occupies 2.62 L at 285ºC and 3.42
atm. How many moles are present in this sample?
PV = nRT
P
V
n =
RT
n =
(3.42 atm) (2.62
0.196 mol
=
L) (558 K)
0.0821 L · atm
mol · K
But Let’s Be
Practical…
We don’t usually measure in moles!
We usually measure quantities in GRAMS!
PV = nRT
PVM = gRT
PVM = gRT
PRESSUR
E
V OLUME
MOLAR MASS OF GAS (g/mol)
g RAMS OF GAS
R GAS CONSTANT
TEMPERATURE
Image source:
Practice with the Ideal Gas Law
A balloon is filled with 0.2494 g of helium to a pressure of 1.26 atm. If the
desired volume of the balloon is 1.250 L, what must the temperature be in
ºC?
PVM = gRT
T =
PV M
gR
(1.26 atm) (1.250 L) 4.00 g
mol
T =
0.0821 L · atm
mol · K
(0.2494 g)
=
308 K
- 273
35 ºC
PV=nRT vs. PVM=gRT
Use PV=nRT when:
You are given moles in the problem.
You are searching for moles as an
answer.
Use PVM=gRT when:
You are given grams in the problem.
You are searching for grams as an
answer.
What Else Happens Under Unchanging Conditions
?
At constant V and T, pressure is easy to
calculate!
“The sum of the individual pressures is equal to the total
pressure.”
Total Pressure = Pressure of gas 1 + Pressure of gas 2
+ Pressure of gas 3 + Pressure of gas 4 …
Ptotal = P1 + P2 + P3 +
…
Partial Pressures Practice
A sample of hydrogen gas is collected over water at
25ºC. The vapor pressure of water at 25ºC is 23.8
mmHg. If the total pressure is 523.8 mmHg, what is
the partial pressure of the hydrogen?
Ptotal = PH2 + PH2O
523.8 mm Hg
PH2
=
=
PH2 + 23.8 mm
Hg
500.0 mm Hg
Source: 2003 EOC Chemistry
What do Changing Conditions Affect
?
We have learned that we can change 3 variables:
Temperature, Volume, and Pressure.
If MASS remains
constant…
…But VOLUME changes…
Then DENSITY CHANGES!
D = M
V
Two Types of Density Problems:
At STP:
Not at STP:
• molar volume of any
gas at STP =
• Determine new volume (V2
) using Combined Gas Law
P1 V1
P2 V2
=
T
T
1
• Density at STP =
2
• Density at non-STP =
molar mass
molar mass
molar
volume
22.4LLiters
V2
Practice with Density
Problems:
Determine the density of
Determine the density of
ethane (C2H6) at STP:
molar
D (at STP)
mass
molar
=
volume
molar mass = 30.08 g
molar volume = 22.4 L
D =
30.08 g
22.4 L
= 1.34 g/L
C2H6 at 3.0 atm and 41ºC.
V1 8.6 L P2 V2
V2P1==
=
8.6 LT
T
D =
V1 2molar
= Pmass
1 V12 T2
V2 T1 P2
P1 = 1.0 atm
P2 = 3.0 atm
V2 D
= (1.0
atm) (22.4
(314
= 30.08
gg =L)3.5
g/L
L L V2 = ?
K)V1 = 22.48.6
(273 K) (3.0
T1 = 273atm)
K
T2 = 314 K
V2 = 8.6 L