The Combined Gas Law
1
Curriculum

Big Idea: Changes in matter are
accompanied by changes in energy.

Competency: Apply the gas laws to
problems involving pressure, temperature,
volume, and amount of a gas.

PA Standard: 3.2.C.A3: Describe the three
normal states of matter in terms of energy,
particle motion, and phase transitions.
2
Today’s Agenda
Opener:
1. What is the relationship between temperature
and volume? What is the name of this law?
2. What is the relationship between pressure and
volume? What is the name of this law?
3. What is the relationship between pressure and
temperature? What is the name of this law?
 Review Charles’ Law
 Review Boyle’s Law
 Review Gay Lussac’s Law
 Powerpoint on the gas laws chapter with practice
 Closure: Solve a combined gas laws problem
Take Home Assignment: 14.3 Section Assessment
on page 429

3
 Kinetic
Molecular Theory : gases
typically behave in a way that allows
us to make
assumptions in order to simplify
their behavior and conclude basic
mathematical relationships
4
Assumptions for ideal gases:
•
•
•
•
•
gas particles do not attract or repel each
other
gas particles are much smaller than the
distances between them
gas particles are in constant, random
motion
no kinetic energy is lost when gas
particles collide with each other or with
the walls of their container (elastic
collisions)
All gases have the same average kinetic
energy at a given temperature
5
Variables that affect gases:
Volume – (V) the amount of space the gas
takes up
 Pressure – (P) a measure of the number of
collisions the gas particles have with the
container holding it. Standard pressures: 1atm

=760mmHg= 760Torr = 101.3kPa

Temperature – (T) a measure of the average
kinetic energy of the gas particles Standard
temperature: 0oC or 273K

Moles – (n) the amount of gas held in the
container
6
Boyle’s Law:
 Defined
by Robert Boyle (1627-1691)
while studying the relatedness of the
volume and pressure of gases
 States that: “the volume and
pressure of a gas are inversely
proportional when the temperature
and amount of gas are held
constant”
7
Boyle’s Law
 As
one goes up the other goes down
 Easier to use P1 x V1=P2 x V2
 Constant = T and n
 the 1’s and 2’s are indicated starting
vs. ending conditions
If the volume of a gas is
constrained to a smaller
container, how much force
does it exert?
P ~ 1/V
P
Boyle’s Law:
P1V1 = P2V2
V
The effect of adding gas.
 When
we blow up a balloon we are
adding gas molecules.
 Doubling the number of gas particles
doubles the pressure.
(of the same volume at the same
temperature).
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 in.
 If
you double the number of
molecules
1 atm
 If
you double the number of
molecules
 You double the pressure.
2 atm
4 atm
 As
you remove
molecules from a
container
2 atm
 As
you remove
molecules from a
container the pressure
decreases
1 atm
 As
you remove
molecules from a
container the pressure
decreases
 Until the pressure inside
equals the pressure
outside
 Molecules naturally
move from high to low
pressure
Examples
A
balloon is filled with 25 L of air at
1.0 atm pressure. If the pressure is
change to 1.5 atm what is the new
volume?
 A balloon is filled with 73 L of air at
1.3 atm pressure. What pressure is
needed to change to volume to 43
L?
Charles’s Law:
Defined by Jacques Charles (1746-1823)
while studying the relatedness of the
volume and temperature of gases
 States that: “the volume and temperature
of a gas are directly proportional when the
pressure and amount of gas are held
constant”
 V1/T1= V2/T2
 Constant = P and n
 the 1’s and 2’s are indicated starting vs.
ending conditions

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Scale – a temperature scale
with no negative values; allows for
calculations with temperature

K = 273 + C
 All temperatures must be converted
to Kelvin when using Charles’s Law,
even if they are already positive.
Otherwise the formula becomes
invalid.
 Kelvin
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If the temperature of gas is
increased, how will its
volume respond (if the
pressure is kept constant)?
V
Charle’s Law:
T
V1/T1 = V2 / T2
Temperature
 Raising
the temperature of a gas
increases the pressure if the
volume is held constant.
 The molecules hit the walls
harder.
 The only way to increase the
temperature at constant pressure
is to increase the volume.
300 K
 If
you start with 1 liter of gas at 1
atm pressure and 300 K
 and heat it to 600 K one of 2 things
happens
600 K
300 K
 Either
the volume will
increase to 2 liters at 1
atm
300 K
•Or
the pressure will increase
to 2 atm.
•Or someplace in between
600 K
Examples
 What
is the temperature of a gas that
is expanded from 2.5 L at 25ºC to
4.1L at constant pressure.
 What is the final volume of a gas that
starts at 8.3 L and 17ºC and is heated
to 96ºC?
Gay-Lussac’s Law:






Defined by Joseph Gay-Lussac while studying
the relatedness of the pressure and temperature
of gases
States that: “the pressure and temperature of a
gas are directly proportional when the volume
and amount of gas are held constant”
Mathematically stated: P1/T1= P2/T2
Constant = V and n
the 1’s and 2’s are indicated starting vs. ending
conditions
All temperatures must be converted to Kelvin
when using Gay-Lussac’s Law, even if they are
already positive. Otherwise the formula becomes
invalid.
26
P
T
Examples
 What
is the pressure inside a 0.250 L
can of deodorant that starts at 25ºC
and 1.2 atm if the temperature is
raised to 100ºC?
 At what temperature will the can
above have a pressure of 2.2 atm?
Putting the pieces together
 The
Combined Gas Law Deals with
the situation where only the number
of molecules stays constant.
 a synthesis of the 3 basic laws into
one mathematical
 expression where the amount of gas
is held constant
 (P1 x V1)/T1= (P2 x V2)/T2
The Combined Gas Law and Avogadro’s Principle:

Avogadro’s Principle – equal volume of gases at
the same temperature and pressure contain equal
numbers of particles

Molar volume – the volume of one mole of ANY
gas at zero degrees Celsius and 1 atmosphere of
pressure

STP – standard temperature and pressure; zero
degrees Celsius and 1 atmosphere of pressure

Conversion Factors:
1 mole = 22.4L (of gas @STP) = 6.02x1023
particles

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The Gas Laws
 Describe
HOW gases behave.
 Can be predicted by the theory.
 Amount of change can be calculated
with mathematical equations.
 The
combined gas law contains
all the other gas laws!
 If the temperature remains
constant.
P 1 x V1
=
T1Boyle’s Law
P2 x V2
T2
 The
combined gas law contains
all the other gas laws!
 If the pressure remains constant.
P 1 x V1
T1
=
P2 x V2
Charles’ Law
T2
 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 Law
The Fourth Part
 Avagadro’s
Hypothesis
 V is proportional to number of
molecules at constant T and P.
 V is proportional to moles.
 V = n ( n is the number of moles.
 Gets put into the combined gas Law
Closure: Combined Gas Law Example
A
15 L cylinder of gas at 4.8 atm
pressure at 25ºC is heated to 75ºC
and compressed to 17 atm. What is
the new volume?