Mind Catalyst
Stick It!
O With a partner, use the following scenarios as a guide
to come up with the relationships of the gas
properties. For each scenario, write the two
properties and their relationship on a sticky note and
place it on the front board!
O Bicycle tires seem more flat in the winter than in
summer
O A can of soda explodes if left in the hot sun
O You blow air into a balloon and it gets bigger
The Kinetic
Molecular
Theory and
its Relation
to the Gas
Laws
Robert Boyle
Jacques Charles
Amadeo Avogadro
Joseph Louis Gay-Lussac
The Kinetic Molecular Theory
of Gases
O In the simulation, you personally observed the
behavior of an ideal gas but not why they behave as
they do
O Why does a gas expand when heated at constant
pressure?
O Why does the pressure increase when a gas is
compressed at constant temperature?
O To understand the physical properties of gases, we
need a model that helps us picture what happens to
gas particles when conditions such as pressure or
temperature change
O This model is known as the kinetic-molecular theory
of gases
Gases and the Kinetic
Molecular Theory Model
O All particles are in constant, random motion
O All collisions between particles are perfectly
elastic
O The volume of the particles in a gas is
negligible
O The average kinetic energy of the molecules
is in its Kelvin temperature
Why do We Care?
O Assumptions of the KMT successfully account for the
observed behavior of an ideal gas
O In reality, real gases have a finite volume and exhibit
attractive forces between other gas molecules
O But now, we must ask the question:
“How do these assumptions explain your observations?”
The KMT and the Relationship
between Pressure and Volume
O You observed that as the volume of the
container decreased, the pressure of the
gas increased (at constant temperature and
amount of gas)
O This is due to the gas particles hitting the
wall more often
O As a result, the force exerted on the walls of
the container increases
O This inverse relationship is referred to as
Boyle’s Law
Introducing Boyle’s Law
P
Volume
(mL)
Pressure
(torr)
P·V
(mL·torr)
10.0
20.0
30.0
40.0
760.0
379.6
253.2
191.0
7.60 x 103
7.59 x 103
7.60 x 103
7.64 x 103
PV = k
V
The KMT and the Relationship
between Volume and Temperature
O You observed as heat was
applied to the gas particles (at
constant pressure and amount
of gas), the temperature
increased and volume of the
container increased
O This is because the speed of
the gas particles increased and
thus, hit the walls more often
and with more force
O Only way to keep pressure
constant is to INCREASE the
VOLUME of the container!
O This direct relationship is
referred to as Charles’ Law
Introducing Charles’ Law
V
T
Volume
(mL)
Temperature
(K)
V/T
(mL/K)
40.0
44.0
47.7
51.3
273.2
298.2
323.2
348.2
0.146
0.148
0.148
0.147
V
k
T
The KMT and the Relationship
between Pressure and Temperature
O You observed that when the temperature of a gas
increases, the speeds of its particles increase
O The particles are hitting the wall with greater force
and greater frequency
O Since the volume remains the same, this would
result in INCREASED gas pressure
O This direct relationship is referred to Amonton’s
Law
Introducing Amonton’s Law
P
k
T
The KMT and the Relationship Between
Volume and the Amount of a Gas
O You observed that an increase in the number of particles at the
same temperature would cause the pressure to increase if the
volume were held constant
O The only way to keep constant pressure is to vary the volume the
same way!
O This direct relationship is referred to as Avogadro’s Law
O Another way to express this relationship is that equal volume of all
ideal gases at the same temperature and pressure contain the
same number of molecules
O This relationship is important because you may think a small gas
molecule would take up less space than a large gas molecule
O But , it doesn’t at the same temperature and pressure!
Introducing Avogadro’s Law
Gas
O2
N2
CO2
Volume
(mL)
100.0
100.0
100.0
Mass
(g)
0.122
0.110
0.176
Moles, n
3.81  10-3
3.93  10-3
4.00  10-3
V/n
(L/mol)
26.2
25.5
25.0
V
k
n
V
n
Illustration of Avogadro’s Law
A Summary of the Four Gas Laws
O Boyle’s law
PV = k
(at constant T and n)
O Charles’ law
O Amonton’s law
O Avogadro’s law
V
=k
T
(at constant P and n)
P
=k
T
(at constant V and n)
V
=k
n
(at constant T and P)
The Ideal Gas Law
Who’s got time to remember all four of those relationships? NOT ME!
O So, the previous 4 relationships can be combined into one very important equation
called the ideal gas law:
O
PV = nRT
O
R is the combined proportionality constant called the universal gas constant
O Always use the value 0.0821
O
𝐿∙𝑎𝑡𝑚
for R
𝐾∙𝑚𝑜𝑙
The ideal gas law is an equation of state for a gas
O
State of a gas is its condition at a given time
O A particular state of a gas is described by its pressure, volume, temperature, and
number of moles
O
A gas that obeys this equation is said to behave ideally
Practice!
O A sample of hydrogen gas (H2) has a volume
of 8.56 L at a temperature of 0°C and a
pressure of 1.5 atm.
O Calculate the moles of H2 molecules present
in the sample.
The Molar Volume of a Gas at STP
O Use PV = nRT to solve for the volume of one
mole of gas at standard temperature
pressure (STP)
O Look familiar?
O It’s on your Mole Road Map!
O This is the molar volume of a gas at
standard temperature and pressure (STP)
O The volume that one mole of any gas takes
up at 0°C (273 K) and 1 atm
Practice!
O What is the volume of 3.0 mol of nitrous
oxide, NO2(g), at STP?
The Molar Volume of a Gas at
Standard Lab Conditions
O Use PV = nRT to solve for the volume of one
mole of gas at standard lab conditions (SLC)
O This is the molar volume of a gas at
standard lab conditions (SLC)
O The volume that one mole of any gas takes up at
25°C (298 K) and 1 atm
O Notice, the volume increased from that at
STP!
O Satisfies Charles’s Law
Practice!
O Suppose you have 44.8L of CH4 (methane)
gas at SLC
O How many moles of methane gas are
present?
O What is the mass of the gas in grams?
O How many molecules of the gas are present?
The Ideal Gas Law and Gas
Stoichiometry Problems
Gas Stoichiometry
O Use stoichiometry to solve gas problems
only if gas is at STP or SLC conditions
O Use the ideal gas law to convert quantities
that are NOT at STP
Practice!
O Quicklime (CaO) is produced by the thermal
decomposition of calcium carbonate
(CaCO3).
O Calculate the volume of CO2 at STP produced
from the decomposition of 152 g CaCO3 by
the reaction:
CaCO3 s → CaO s + CO2 (g)
Practice!
O A sample of methane gas (CH4) having a
volume of 2.80 L at 25°C and 1.65 atm was
mixed with a sample of oxygen gas having a
volume of 35.0 L at 31°C and 1.25 atm.
The mixture was then ignited to form carbon
dioxide and water.
O Calculate the volume of CO2 formed at a
pressure of 2.50 atm and a temperature of
125°C
“Numbered Heads Together”
Practice with the Ideal Gas Law
How to Play “Numbered Heads Together”
O Members of learning teams (composed of 4
individuals) count off 1, 2, 3 or 4.
O I present each learning team with an Ideal Gas Law
problem to solve.
O Learning teams discuss the question, and answer it
together
O Every group member must agree upon the answer
O I then call a specific team number and individual
number
O The team members originally designated that
number during the count off respond as the group
spokesperson
Let’s Begin…
O Calculate the volume in liters of 4.0 moles of
oxygen gas at a temperature of 40.0°C and
a pressure of 500.0 mm Hg
O 1.2 x 10
molecules of xenon gas occupy a
volume of 20.0 liters at a temperature of
60.0°C. Determine the pressure in atm.
24
O If 5.0 X 10
moles of neon gas have a
volume of 200.0 ml at a pressure of 50.0
torr, then calculate the centigrade
temperature
-2
O Calculate the number of molecules in a
nitrogen gas sample that occupies a volume
of 10.0 liters at a temperature of 60.0 °C
and a pressure of 5.0 atmospheres
Real-Life Applications of
the Ideal Gas Law
Gas Laws are Everywhere!
O As we have previously discussed, the behavior of
gases can be observed on a daily basis
O The science behind hot air balloons
O A tire or ball gets “flat” in the winter
O At higher elevations, potato chip bags and
marshmallow bags tend to over-inflate
O Packing lotion in a carry-on or in your luggage is a
big mistake as the pressure inside the container
is more than the pressure in the atmosphere
while flying. End result: a big mess
Another Great Example – Air Bags
O Have you stopped to wonder how exactly air
bags work and as a result, save lives?
O With a partner, come up with some ideas on
how you think air bags work
O Try to think about what has to happen at the
molecular level
O Also, think about what makes them actually
save lives? What is their purpose?
Time for Videos!
Car Airbags – Explained
The Chemistry Behind Air Bags
Follow-Up Discussion
O Based on what you observed in the videos,
what features of an airbag make it effective
in saving lives?
O Discuss with a partner and be prepared to
share with the class!