Chapter 14
“The Behavior of Gases”
Pre-AP Chemistry
By Stephen L. Cotton
Section 14.1
The Properties of Gases
 OBJECTIVES:
Explain
why gases are easier
to compress than solids or
liquids are.
Section 14.1
The Properties of Gases
 OBJECTIVES:
Describe
the three factors
that affect gas pressure.
Compressibility
 Gases
can expand to fill its
container, unlike solids or liquids
 The reverse is also true:
 They
are easily compressed, or
squeezed into a smaller volume
 Compressibility
is a measure of
how much the volume matter
decreases under pressure
Compressibility
 This
is the idea behind placing “air
bags” in automobiles
 In
an accident, the air compresses
more than the steering wheel or dash
when you strike it
 The impact forces the gas particles
closer together, because there is a lot
of empty space between them
Compressibility
 At
room temperature, the
distance between particles is
about 10x the diameter of the
particle
 Fig.
 How
14.2, page 414
does the volume of the
particles in a gas compare to the
overall volume of the gas?
Variables that describe a Gas
 The
four variables and their
common units:
1. pressure (P) in kilopascals
2. volume (V) in Liters
3. temperature (T) in Kelvin
4. amount (n) in moles
• The amount of gas, volume, and
temperature are factors that
affect gas pressure.
1. Amount of Gas
 When we inflate a balloon, we are
adding gas molecules.
 Increasing the number of gas
particles increases the number of
collisions
thus, the pressure increases
 If temperature is constantdoubling the number of particles
doubles the pressure
Pressure and the number of
molecules are directly related
 More
molecules means more
collisions.
 Fewer molecules means fewer
collisions.
 Gases naturally move from areas of
high pressure to low pressure
because there is empty space to
move into – a spray can is example.
Common use?
 Aerosol (spray) cans
gas moves from higher pressure
to lower pressure
a propellant forces the product
out
whipped cream, hair spray, paint
 Fig. 14.5, page 416
 Is the can really ever “empty”?
2. Volume of Gas
 In a smaller container, the
molecules have less room to
move.
 The
particles hit the sides of
the container more often.
 As volume decreases, pressure
increases. (think of a syringe)
3. Temperature of Gas
Raising the temperature of a gas
increases the pressure, if the volume is
held constant.
 The molecules hit the walls harder, and
more frequently!
 Fig. 14.7, page 417
 Should you throw an aerosol can into a
fire? What could happen?
 When should your automobile tire
pressure be checked?

Section 14.2
The Gas Laws

OBJECTIVES:
Describe
the relationships
among the temperature,
pressure, and volume of a
gas.
Section 14.2
The Gas Laws

OBJECTIVES:
Use
the combined gas law
to solve problems.
The Gas Laws
 These will describe HOW gases
behave.
 Gas
behavior can be predicted by
the theory.
 The
amount of change can be
calculated with mathematical
equations.
 You need to know both of these:
the theory, and the math
Robert Boyle
(1627-1691)
• Boyle was born into an
aristocratic Irish family
• Became interested in
medicine and the new
science of Galileo and
studied chemistry.
• A founder and an
influential fellow of the
Royal Society of London
• Wrote extensively on
science, philosophy, and
theology.
#1. Boyle’s Law - 1662
Gas pressure is inversely proportional to the
volume, when temperature is held constant.
Pressure x Volume = a constant
Equation: P1V1 = P2V2 (T = constant)
Graph of Boyle’s Law – page 418
Jacques Charles (1746-1823)
French Physicist
• Part of a scientific
balloon flight on Dec. 1,
1783 – was one of
three passengers in the
second balloon
ascension that carried
humans
• This is how his interest
in gases started
• It was a hydrogen filled
balloon – good thing
they were careful!
•
#2. Charles’s Law - 1787
The volume of a fixed mass of gas is
directly proportional to the Kelvin
temperature, when pressure is held
constant.
This extrapolates to zero volume at a
temperature of zero Kelvin.
V1
V2

T1
T2
( P  constant)
Converting Celsius to Kelvin
•Gas law problems involving
temperature will always require that
the temperature be in Kelvin.
(Remember that no degree sign is
shown with the kelvin scale.)
•Reason? There will never be a
zero volume, since we have never
reached absolute zero.
Kelvin = C + 273
and
°C = Kelvin - 273
Joseph Louis Gay-Lussac (1778 – 1850)
French chemist and
physicist
 Known for his studies on
the physical properties of
gases.
 In 1804 he made balloon
ascensions to study
magnetic forces and to
observe the composition
and temperature of the air
at different altitudes.

#3. Gay Lussac’s Law - 1802
•The pressure and Kelvin temperature of
a gas are directly proportional, provided
that the volume remains constant.
P1 P2

T1 T2
•How does a pressure cooker affect the time
needed to cook food?
•Sample Problem 14.3, page 423
#4. The Combined Gas Law
The combined gas law expresses the
relationship between pressure, volume
and temperature of a fixed amount of
gas.
P1V1 P2V2

T1
T2
Sample Problem 14.4, page 424
The combined gas law contains
all the other gas laws!
 If the temperature remains
constant...

P 1 x V1
T1
=
P2 x V2
T2
Boyle’s Law
The combined gas law contains
all the other gas laws!
 If the pressure remains
constant...

P 1 x V1
T1
=
P2 x V2
T2
Charles’s Law
The
combined gas law contains
all the other gas laws!
If the volume remains
constant...
P 1 x V1
T1
=
P2 x V2
T2
Gay-Lussac’s Law
Section 14.3
Ideal Gases

OBJECTIVES:
Compute
the value of an
unknown using the ideal gas
law.
Section 14.3
Ideal Gases

OBJECTIVES:
Compare
and contrast real
an ideal gases.
5. The Ideal Gas Law #1
Equation: P x V = n x R x T
 Pressure times Volume equals the
number of moles (n) times the Ideal Gas
Constant (R) times the temperature in
Kelvin.

R
= 8.31 (L x kPa) / (mol x K)
The other units must match the value of
the constant, in order to cancel out.
 The value of R could change, if other
units of measurement are used for the
other values (namely pressure changes)

The Ideal Gas Law

We now have a new way to count
moles (amount of matter), by
measuring T, P, and V. We aren’t
restricted to only STP conditions:
PxV
n=
RxT
Ideal Gases
We are going to assume the gases
behave “ideally”- in other words, they
obey the Gas Laws under all conditions
of temperature and pressure
 An ideal gas does not really exist, but it
makes the math easier and is a close
approximation.
 Particles have no volume? Wrong!
 No attractive forces? Wrong!

Ideal Gases
 There are no gases for which this
is true; however,
 Real gases behave this way at a)
high temperature, and b) low
pressure.
Because at these conditions, a
gas will stay a gas!
Sample Problem 14.5, page 427
#6. Ideal Gas Law 2

PxV=
mxRxT
M
 Allows LOTS of calculations, and
some new items are:
 m = mass, in grams
 M = molar mass, in g/mol

Molar mass = m R T
PV
Density

Density is mass divided by volume
D=
m
V
so,
m
D=
V
=
MP
RT
Ideal Gases don’t exist, because:
1. Molecules do take up space
2. There are attractive forces between
particles
- otherwise there would be no liquids formed
Real Gases behave like Ideal Gases...
When the molecules are
far apart.
 The molecules do not
take up as big a
percentage of the space

 We
can ignore the particle
volume.

This is at low pressure
Real Gases behave like Ideal Gases…
 When
molecules are moving fast
 This is at high temperature
 Collisions are harder and faster.
 Molecules are not next to each
other very long.
 Attractive forces can’t play a role.
Section 14.4
Gases: Mixtures and Movements

OBJECTIVES:
Relate
the total pressure of a
mixture of gases to the
partial pressures of the
component gases.
Section 14.4
Gases: Mixtures and Movements

OBJECTIVES:
Explain
how the molar mass
of a gas affects the rate at
which the gas diffuses and
effuses.
#7 Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P3 + . . .
represents the “partial pressure”
or the contribution by that gas.
•Dalton’s Law is particularly useful in
calculating the pressure of gases
collected over water.
•P1

If the first three containers are all put into the
fourth, we can find the pressure in that container
by adding up the pressure in the first 3:
2 atm
1
+ 1 atm
2
+ 3 atm
3
Sample Problem 14.6, page 434
= 6 atm
4
Diffusion is:
Molecules
moving from areas of high
concentration to low concentration.
Example:
perfume molecules spreading
across the room.

Effusion: Gas escaping through a tiny
hole in a container.
 Both
of these depend on the molar
mass of the particle, which
determines the speed.
•Diffusion:
describes the mixing
of gases. The rate of
diffusion is the rate
of gas mixing.
•Molecules move
from areas of high
concentration to low
concentration.
•Fig. 14.18, p. 435
Effusion: a gas escapes through a tiny
hole in its container
-Think of a nail in your car tire…
Diffusion
and effusion
are
explained
by the next
gas law:
Graham’s
8. Graham’s Law
RateA
RateB
=
 MassB
 MassA
The rate of effusion and diffusion is
inversely proportional to the square root
of the molar mass of the molecules.
 Derived from: Kinetic energy = 1/2 mv2
 m = the molar mass, and v = the
velocity.

Graham’s Law
Sample: compare rates of effusion of
Helium with Nitrogen – done on p. 436
 With effusion and diffusion, the type of
particle is important:



Gases of lower molar mass diffuse and
effuse faster than gases of higher molar
mass.
Helium effuses and diffuses faster than
nitrogen – thus, helium escapes from a
balloon quicker than many other gases!