Chapter 13 “Gases”
What are the properties of
gases?
Tuesday 4/8/14
Learning Target
13-1 Student must be able to relate the behavior of
gases to the Kinetic Molecular Theory (KMT)
Learning Outcomes
 Students must know and understand the postulates
(parts) of the KMT.
 Students must be able to use the KMT to explain
what causes pressure in a sample of gas.
How do we explain gas behavior?
 Gas properties are explained by a model that describes
the behavior of the tiny particles of a gas.




Gases have mass.
It is easy to compress a gas.
Gases fill their containers completely.
Gases exert pressure.
How do we explain gas behavior?
Gas properties are explained by a model
that describes the observed behavior of
tiny gas particles.
This is known as “The Kinetic Molecular
Theory” or the “K-M” Theory.
The Kinetic-Molecular (K-M) Theory
5 Postulates:
• Gas particles have no volume, but are spaced widely,
with lots of empty space between them.
 Gas particles don’t repel or attract each other.
 Gas particles move in constant, rapid, random motion
(straight lines).
 No kinetic energy is lost when particles collide with each
other or wall (perfectly elastic).
 The average kinetic energy of the molecules of a gas is
proportional to the temperature of the gas (measured in
Kelvin).
http://www.chm.davidson.edu/chemistryap
plets/KineticMolecularTheory/BasicConcepts.ht
ml
13-2 Measuring Gases
To completely describe a gas sample and
to make predictions about its behavior
under new conditions, we must deal with
four variables:
Amount of gas (n, in moles)
n = mass/molar mass = m(g)/M(g/mol)
Volume of gas (V, in liters)
1 L = 1000mL = 1000 cm3
Temperature (T, in kelvins)
T(K) = T(°C) + 273
Pressure (P, in atm, torr, kPa, etc.)
Thursday 4/10/14
Learning Goals for “Gas Variables” Whole
Class Discussion:
1. Understand the relationships between the 4 gas
variables (n, P, V, and T) in how gases behave.
2. Understand the gas variable relationships with respect
to the Kinetic Molecular Theory.
Using the Kinetic Molecular Theory explain
the behavior of the gas particles in
Experiment B.
Give a molecular level explanation of the
increased volume in Experiment C.
How does this differ or is similar to
Experiment D?
Explain what is occurring at the molecular
level for the increased volume in
Experiment E.
If scientists wanted to know the
relationship between all of the variables in
the gas laws (P,V, T, n), why do they set 1
(or more) as controls to study these
relationships?
How does this relate to the scientific
method?
Explain other phenomena that exists in the
world around us related to gas behavior
and explain it in terms of the KMT.
What are some practical uses of gas laws
in the real world?
Oil Tanker
Record what you think occurred and talk to
your partner.
Why did the oil tanker implode after steam
cleaning?
Explain in terms of the Kinetic Molecular
Theory.
Which gas law is demonstrated here?
Friday 4/11/14
Learning Target:
Be able to convert pressure values between common
pressure units.
Learning Outcome:
Complete pressure conversion problems and manometer
problems.
How to Measure Pressure
 Pressure = Force/Area (newtons/meter2 =
pascals)
 Atmospheric pressure results from the mass of
the air being attracted by Earth’s gravity.
The mass of the air attracted by gravity produces a
force.
 Conversions:
1 atmosphere (atm) = 101.325 kPa
1 atmosphere = 760 mm Hg (same as torr)
1 atmosphere = 14.70 lb/in2
Tools for Measuring Pressure
 Barometer
Atmospheric pressure for predicting weather changes
Water vapor is lighter than nitrogen and oxygen.
 High water vapor content = Low barometric pressure
 Low water vapor content = High barometric pressure
 Pressure gauge
Tire pressure gauges or gas regulators
Manometers
PROBLEMS
The pressure in a certain tire is 109 kPa.
What is the pressure of the air in the tire in
atmospheres?
Tools for Measuring Pressure
 Manometer
 Laboratory tool for working with gases
 Examples: How to use manometers.
 http://www.ce.utexas.edu/prof/kinnas/319lab/applets/Manometer
1.html
Manometer Measurements
In an open-tube manometer:
If the gas pressure (Pgas) is greater than the
atmospheric pressure (Patm), then
Pgas = Patm + height difference
If the gas pressure is less than the atmospheric
pressure, then Pgas = Patm – height difference
In a closed-tube manometer:
The Pgas = the difference in Hg levels
Manometer Problem
A gas container is fitted with a
manometer. The level of the mercury is
15 mm lower on the open side. Using a
laboratory barometer, you find that the
atmospheric pressure is 750 mmHg. What
is the pressure in atmospheres of the gas
in the container? In kPa?
Exploring Gas Behavior (Class
Activity)
• http://www.chm.davidson.edu/chemistryapple
ts/KineticMolecularTheory/BasicConcepts.ht
ml
• Then go to “Maxwell Distribution,” followed
by “Pressure” and “Pressure-Volume
Relation.”
• Conclude with “Pressure-Temperature
Relation.”
• Complete the exercise by working on the
Boyle & Charles.
• QUESTION: What did you learn about gas
behavior?
Monday 4/14/14
Learning Target:
 Know the variables in Boyle’s Law and how those
variables are related.
Learning Outcome:
 Be able to use the KM Theory to explain Boyle’s Law.
 Be able to perform Boyle’s Law problems.
13-3 The Gas Laws (1)
 Do you remember STP?
 STP = Standard Temperature & Pressure
 STP = 273 K (0°C) & 1 atm (760 mmHg, etc.)
 STP is important for measuring gas properties.
What happens when you put pressure on a gas?
o Examples: Small balloon being squeezed, books
piled on a small cylinder.
• Robert Boyle (Ireland -1600s) studied the effect of
pressure (P) on the volume (V) of a gas.
Boyle’s Law
The pressure and volume of a sample of gas are
inversely proportional to each other at constant
temperature.
P1V1 = P2V2
Robert Boyle
Boyle’s Law
Pressure (inches Hg)
Sam ple Data for Boyle's Law
60
50
40
30
20
10
0
0
50
100
Volum e (cubic inches)
150
The Kinetic-Molecular (K-M) Theory
5 Postulates:
• Gas particles have no volume, but are spaced widely,
with lots of empty space between them.
 Gas particles don’t repel or attract each other.
 Gas particles move in constant, rapid, random motion
(straight lines).
 No kinetic energy is lost when particles collide with each
other or wall (perfectly elastic).
 The average kinetic energy of the molecules of a gas is
proportional to the temperature of the gas (measured in
Kelvin).
http://www.chm.davidson.edu/chemistryap
plets/KineticMolecularTheory/BasicConcepts.ht
ml
Boyles Law Problem
A gas occupies a volume of 458 mL at a
pressure of 1.01 kPa and a temperature of
295 K. When the pressure is changed, the
volume becomes 477 mL. If there is no
change in temperature what is the new
pressure?
A gas occupies a volume of 458 mL at a pressure
of 1.01kPa and a temperature of 295K. When the
pressure is changed, the volume becomes 477
mL. If there is no change in temperature what is
the new pressure?
A sample of Ne gas occupies 0.220 L at 0.860
atm. What is the its volume at 29.2kPa?
Tuesday 4/15/14
Learning Target:
 Know the variables in Charles’ Law and how those
variables are related.
Learning Outcome:
 Be able to use the KM Theory to explain Charles’ Law.
 Be able to perform Charles’ Law problems.
Boyle’s Law and Manometer
1. A gas container is fitted with a manometer. The level of
the mercury is 15mm lower on the open side. Using a
barometer, you find that the atmospheric pressure is
750mmHg. What is the pressure of the gas in the
container in kPa?
2. 1.50 L of a gas at standard temperature and pressure is
compressed to 473 mL. What is the new pressure of
the gas?
13-3 The Gas Laws (2)
 What happens when you change the temperature of a
gas?
Examples: Hot air balloon inflating, automobile
tires in very cold weather.
 Jacques Charles (1700s) studied the effect of
temperature (T) on the volume (V) of a gas.
 Charles’ Law: The volume of a sample of gas is
directly proportional to the Kelvin temperature at
constant pressure.
V1 T2 = V2 T1
or
Charles’ Law
Volume (liters)
Data for Charles' Law
6
5
4
3
2
1
0
0
200
400
600
Tem perature (kelvins)
800
CHARLES’ LAW PROBLEM
 A gas sample at 83ºC occupies a volume of 1400 m3. At
what temperature will it occupy 1200 m3.
 A gas can be used as a thermometer. If it is known that a
sample of gas has a volume of 1.00 L at 235 K, what is
the temperature if the volume of the gas is changed to
0.45 L at a constant pressure?
Monday 4/21/14
Learning Target:
 Know the variables in Combined Gas Law Equation and
how those variables are related.
Learning Outcome:
 Be able to use the KM Theory to explain Combined Gas
Law Equation.
 Be able to perform Combined Gas Law problems.
13-3 The Gas Laws (3)
What happens to the pressure of a fixed
volume of gas if you change the
temperature?
Example: “Empty” aerosol can thrown into an
incinerator. (Read the warning on the label!)
Gay-Lussac (1700s-France) studied the
effect of pressure (P) and temperature (T)
on a fixed volume (V) of gas.
Gay-Lussac’s Law: The pressure and
temperature of a fixed volume of gas are
directly proportional to each other.
Gay-Lussac’s Law
Pressure (mm Hg)
Data for Gay-Lussac's Law
6
4
2
0
0
200
400
600
Tem perature (kelvins)
800
13-3 The Gas Laws (Combined)
These Gas Laws seem complicated, but fortunately we
can simplify things by combining the relationships into two
simple expressions, the one first being:
P1V1
T1
=
P2V2
T2
This equation is used to solve “Combined Gas Law” problems, by simply
“plugging in” the numbers!
Just remember two things:
“Go Kelvin!” (Convert temperature to kelvins.)
Be sure all units are consistent for P and V.
PRACTICE PROBLEM
 The initial temperature of a 1.00 liter sample
of argon is 20.° C. The pressure is decreased
from 720 mm Hg to 360 mm Hg and the
volume increases to 2.14 liters. What was the
change in temperature of the argon?
Warm-Up
 A gas that has a volume of 28 L, a temperature
of 45°C, and an unknown pressure has its
volume increased to 34 L and its temperature
decreased to 35°C. If I measure the pressure
after the chance to be 2.0 atm, what was the
original pressure of the gas?
Tuesday 4/22/14
Learning Target:
 Know the formula for the Ideal Gas Law and be able to
use it to solve for P, V, n or T.
Learning Outcome:
 Know the difference between Ideal and Real Gases.
 Be able to perform Ideal Gas Law problems.
13-3 The Gas Laws (4)
 How is the number of gas particles related to its
volume under constant conditions?
Examples: Two balloons of different size.
 Amedeo Avogadro (1800s) studied different
gases to determine the relationship between the
number of gas particles and the volume at a
given pressure (P) and temperature (T).
 Avogadro’s Law: Equal volumes of gases at
the same pressure and temperature contain an
equal number of particles.
But what is an “Ideal Gas”?
Ideal Gas: one that is described by the
postulates of the Kinetic-Molecular Theory.
The gases we encounter are “real” – not
“ideal”!
However, most gases behave like ideal
gases under ordinary conditions of
temperature and pressure.
At low temperature and high pressure real gases
behave in non-ideal ways. (Remember BoseEinstein Condensate)
13-4 The “Ideal Gas Law”
 The second equation that may be derived from
the various gas laws is the “Ideal Gas
Equation”:
PV = nRT
 This describes the relationship among the four
variables (P,V,n,T) of an ideal gas, where R is
the gas constant.
R = 0.0821 atm-L/mol-K
R = 8.314 Pa-m3/mol-K
R = 8.314 J/mol-K
 Problems may be solved by simple substitution,
but be careful to use consistent units.
Deviations from Ideal Gas Behavior
Occur Because:
 Kinetic-Molecular Theory makes two simplifying,
but WRONG, assumptions:
Gas particles have no volume of their own.
Gas particles have no attraction for each other.
 But, as pressure increases…
…gas particles get closer together.
At very high pressure, the volume of the gas particles
themselves become a significant part of the total
volume, contrary to K-M Theory.
 As temperature decreases…
…gas particles slow down.
At very low temperature, attractive forces between gas
particles become significant, contrary to K-M Theory, so
gases liquefy.
13-3 The Gas Laws (5)
• Another relationship about gases was proposed by John
Dalton. (Remember him? Why?)
• He proposed that gas particles in a mixture of gases act
independently to exert pressure on the container.
o
o
Each gas in the mixture exerts the same pressure that it
would if it was alone in the container.
This proposal was made before the Kinetic Molecular
Theory was developed, so he didn’t really have its ideas to
help him.
• Dalton’s Law of Partial Pressure: the sum of the
partial pressures of all components of a gas mixture is
equal to the total pressure of the gas mixture, or...
• PT = P1 + P2 + P3 + .….
• See sample problems.
Dalton’s Law of Partial Pressures
Problem
A flask contains a mixture of hydrogen and
oxygen. The pressure being exerted by
these gases is 7785 mmHg. If the partial
pressure of the hydrogen in the mixture is
395 mmHg, what is the partial pressure of
oxygen?
PT = PH2 + PO2
785mmHg = 395 mm Hg + PO2
PO2 = 390mmHg
Nevertheless…
K-M Theory is valid for studying gas
behavior under ordinary conditions.
We are safe to use the Ideal Gas Equation
(PV = nRT) to solve problems for real
gases, except at low temperature and high
pressure conditions where gases start to
behave in a non-ideal manner.
13-5 How Gases Work: Lift
Lifting Power
This is the result of low density of a gas, but the
density must be lower than that of the air.
Low molar mass gases (H2, He, NH3, CH4) may
be used to gain lift.
Or the gas, usually air, may be heated.
Higher mass gases (CO2, Kr) are too dense, so
they sink in air.
Can have disastrous effects.
13-5 How Gases Work: Effusion
Effusion
Related to ‘diffusion’ (one gas moving through
another).
Effusion is the gas movement through a tiny hole
one particle at a time.
Small, light gases have greater speeds than
large, heavy gases at a given temperature, so
they effuse faster.
Graham’s Law of Effusion relates effusion to
mass.