Gas Laws
Chapter 12
Boyle’s Law:
The Pressure-Volume Relationship
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The Anglo-Irish chemist, Robert Boyle (16271691), was the first person to do systematic
studies of pressure and volume concerning
gases.
In 1662 he proposed a law to describe this
relationship. If pressure increases, volume
decreases. If pressure decreases, volume
increases. This is assuming that the number
of molecules and the temperature remain
constant.
P1V1 = P2V2
P1V1 = P2V2
This relationship is an inverse
relationship.
 Pressure is inversely proportional to
volume.
 With an inverse proportion, the product
will always be equal to a constant.

A proof for an inverse
proportion…
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In the pressure-volume
lab, an inverse
proportion graph was
generated.
By making the x-axis
the reciprocal of the
volume (1/V), a new
graph can be generated
that will be a direct
proportion and linear.
Boyle’s Law Practice Problem
A high altitude balloon contains 30.0 L
of helium gas at 103 kPa. What is the
volume when the balloon rises to an
altitude where the pressure is only 25.0
kPa? (assume temperature remains constant)
 124 L

Charles’ Law:
Temperature-Volume Relationship
In 1787, French physicist (and balloonist)
Jacque Charles investigated the effect of
temperature on the volume of a gas at
constant pressure.
 Charles’ Law: the volume of a fixed mass
of gas is directly proportional to its Kelvin
temperature if the pressure is kept
constant.
 V1
V2
 T1
T2

A proof for a direct
proportion…


Graphing a direct
proportionality will
give a linear graph.
For Charles’ Law, as
the temperature of a
gas increases, the
volume will increase.
Charles’ Law Practice Problem
A balloon inflated at 24°C has a volume
of 4.00 L. The balloon is then heated
to a temperature of 58°C. What is the
new volume if the pressure remains
constant?
 4.46 L

Guy-Lussac’s Law:
The Temperature-Pressure Relationship
Joseph Guy-Lussac (1778-1850) a
French chemist discovered in 1802 (at 24
years old) that temperature and pressure
are directly proportional.
 G-L Law: the pressure of a gas is
directly proportional to the Kelvin
temperature if the volume remains
constant

Guy-Lussac’s Formula
P1
 T1

P2
T2
G-L Practice Problem

A gas has a pressure of 6.58 kPa at 539
K. What will be the pressure at 211 K if
the volume does not change?

2.58 kPa
The Combined Gas Law
P1V1 = P2V2
T1
T2
 Problems using the combined gas law
typically take advantage of the
knowledge of conditions at STP to save
space…
Combined Gas Law practice
problem:
The volume of a gas-filled balloon is
30.0 L at 40.0°C and 153 kPa pressure.
What volume will the balloon have at
standard temperature and pressure
(STP=0°C and 101.3kPa)?
 39.5 L
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The Ideal Gas Law

P1V1
T1n1
P2V2
T2n2
R
• Using standard conditions for all
variables, a value for “R” can be
calculated.
•R = 8.31 (kPa*L)/(K*mol)
Ideal Gas Law rewritten…

Rearrange the variables and “R” so that
there are no numbers in the
denominator:

PV=nRT
Ideal Gas Law

Worksheet…
Gas Molecules:
Mixtures and Movements
Section
12.5
Avogadro’s Hypothesis
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Compare chlorine gas to hydrogen gas. Look
at structure and molar mass.
Cl2 and H2; 70.9 g/mol and 2 g/mol,
respectively.
If you have a collection of equal numbers of
molecules of both chlorine and hydrogen at
the same temperature, will they take up the
same volume or will one take up more and
the other less?
A.H. continued…
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
Avogadro’s Hypothesis stated that equal
volumes of gases at the same temperature
and pressure contain equal numbers of
particles.
This is possible because gas particles are
incredibly small and very far apart. Therefore
the spaces between particles is so great, the
size difference between gas molecules is
insignificant at normal pressures.
Calculations…
What is the volume occupied by 0.250
mol of a gas at STP?
 5.60 L
 What volume is occupied by 4.02 x 1022
molecules of helium gas at STP?
 1.50 L He
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Dalton’s Law
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Gas mixtures (with nonreacting gases) at the
same temperature have the same average
kinetic energy.
Pressure is determined by the number of gas
particles… each particle makes the same
contribution.
If you know the pressure exerted by each gas
in a mixture, you add the individual pressures
to get the total pressure.
Dalton’s Law
Ptotal = P1 + P2 + P3 …
 Dalton’s Law of Partial Pressures: At
constant volume and temperature, the
total pressure exerted by a mixture of
gases is equal to the sum of the partial
pressures of the component gases.

Dalton’s Law Problem
Determine the total pressure of a gas
mixture that contains oxygen, nitrogen, and
helium if the partial pressures of the gases
are as follows: PO = 20.0 kPa, PN = 46.7
kPa, and PHe = 26.7 kPa?
 93.4 kPa
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2
2
Graham’s Law
Terms

Diffusion: the tendency of molecules to move
toward areas of lower concentration until the
concentration is uniform throughout.

Effusion: the process in which a gas escapes
through a tiny hole in its container.
Graham’s Law
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Thomas Graham (1805-1869)a Scottish
chemist who noticed that gases of lower
molar mass effuse faster than gases of higher
molar mass.
Graham’s Law: the rate of effusion of a gas is
inversely proportional to the square root of
the gas’s molar mass. (This is also true for a
gas’s rate of diffusion)
Rate = .
1
.
molar mass