*Gas Laws*
Objectives:
1. Identify the physical
characteristics of gasses
2. Be familiar with gas laws
3. Apply the gas laws to solve
problems involving gasses
Physical Characteristics of Gases
Physical Characteristics
Typical Units
Volume, V
liters (L)
Pressure, P
Temperature, T
atmosphere
(1 atm = 1.015x105 N/m2)
Kelvin (K)
Number of atoms or
molecules, n
mole (1 mol = 6.022x1023
atoms or molecules)
Boyle’s Law
 Pressure and volume are
inversely related at
constant temperature.
 PV = K
 As one goes up, the
other goes down.
 P1V1 = P2V2
“Father of Modern Chemistry”
ROBERT BOYLE
Chemist & Natural Philosopher
Listmore, Ireland
January 25, 1627 – December 30, 1690
Gas Pressure
• Just as a ball exerts a force when it
bounces against a wall, a gaseous
atom or molecule exerts a force
when it collides with a surface.
• The result of many of these
molecular collisions is pressure.
• Pressure is the force exerted per
unit area by gas molecules as they
strike the surfaces around them.
Boyle’s Law: P1V1 = P2V2
Boyle’s Law: P1V1 = P2V2
Charles’ Law
 Volume of a gas varies
directly with the absolute
temperature at constant
pressure.
 V = KT
 V1 / T1 = V2 / T2
Jacques-Alexandre Charles
Mathematician, Physicist, Inventor
Beaugency, France
November 12, 1746 – April 7, 1823
Charles’ Law: V1/T1 = V2/T2
Charles’ Law: V1/T1 = V2/T2
Avogadro’s Law
At constant temperature
and pressure, the volume of
a gas is directly related to
the number of moles.
V = K n
V1 / n1 = V2 / n2
Amedeo Avogadro
Physicist
Turin, Italy
August 9, 1776 – July 9, 1856
Avogadro’s Law: V1/n1=V2/n2
Gay-Lussac Law
 At constant volume,
pressure and absolute
temperature are
directly related.
P=kT
 P1 / T1 = P2 / T2
Joseph-Louis Gay-Lussac
Experimentalist
Limoges, France
December 6, 1778 – May 9, 1850
Dalton’s Law
The total pressure in a container
is the sum of the pressure each
gas would exert if it were alone
in the container.
The total pressure is the sum of
the partial pressures.
PTotal = P1 + P2 + P3 + P4 + P5 ...
(For each gas P = nRT/V)
John Dalton
Chemist & Physicist
Eaglesfield, Cumberland, England
September 6, 1766 – July 27, 1844
Dalton’s Law
Vapor Pressure
Water evaporates!
When that water evaporates, the vapor has a
pressure.
Gases are often collected over water so the vapor
pressure of water must be subtracted from the
total pressure.
Differences Between Ideal and Real Gases
Ideal Gas
Real Gas
Always
Only at very low
P and high T
Molecular volume
Zero
Small but
nonzero
Molecular attractions
Zero
Small
Molecular repulsions
Zero
Small
Obey PV=nRT
Real Gases
Real molecules do take up space and do interact
with each other (especially polar molecules).
Need to add correction factors to the ideal gas
law to account for these.
Ideally, the VOLUME of the molecules was neglected:
Ar gas, ~to scale, in a box 3nm x 3nm x3nm
at 1 Atmosphere Pressure
at 10 Atmospheres Pressure
at 30 Atmospheres Pressure
BOYLE'S LAW
Boyle's Law states that volume of a
given amount of gas held at a
constant temperature varies
inversely the with pressure. The
relationship between pressure and
volume of Boyle's Law is expressed
in mathematical terms as
P1V1= P2V2
BOYLE'S LAW
Example:
At 1.70 atm, a sample of gas
takes up 4.25L. If the pressure
in the gas is increased to 2.40
atm, what will the new
volume be?
CHARLE'S LAW
Charles' Law states that the volume
of a given mass of a gas is directly
proportional to its Kelvin
temperature at constant pressure.
In mathematical terms, the
relationship between temperature
and volume is expressed as
V1/T1=V2/T2
CHARLE'S LAW
Example:
A balloon takes up 625L at 0°C. If
it is heated to 80°C, what will its
new volume be?
GAY-LUSSAC’S LAW
Gay-Lussac's Law states that the
pressure of a given mass of gas
varies directly with the Kelvin
temperature when the volume
remains constant. Gay-Lussac's Law
is expressed in a formula form as
P1/T1 = P2/T2
GAY-LUSSAC’S LAW
Example:
If the pressure in a car tire is 1.88
atm at 25°C, what will be the
pressure if the temperature warms
to 37°C?
P1/T1 = P2/T2
25oC + 273 = 298K
37oC + 273 = 310K
1.88 atm = X
298K
310K
= 1.96atm
COMBINED GAS LAW
The Combined Gas Law combines
Charles' Law, Boyle's Law and Gay
Lussac's Law. The Combined Gas
Law states that a gas' (pressure ×
volume)/temperature = constant.
COMBINED GAS LAW
Example:
A gas at 110kPa at 30.0°C fills a
flexible container with an initial
volume of 2.00L. If the
temperature is raised to 80,0°C and
the pressure increases to 440Kpa,
what is the new volume?
Real Gases Do Not Behave Ideally
CH4
N2
2.0
H2
PV
nRT
CO2
Ideal
gas
1.0
0
0
200
400
600
P (atm)
800
1000
CHARACTERISTICS OF GASES
• There is a lot of “free” space in a gas
– Expand to fill their container
– They can be expanded infinitely
• Can be compressed
• Are fluids (like liquids) because they
can be made to flow, or move.
• Have very low densities
• Diffuse and mix rapidly
Physical Characteristics of Gases
Physical Characteristics
Typical Units
Volume, V
liters (L)
Pressure, P
Temperature, T
atmosphere
(1 atm = 1.015x105 N/m2)
Kelvin (K)
Number of atoms or
molecules, n
mole (1 mol = 6.022x1023
atoms or molecules)
VOLUME
VOLUME
Conversion factors needed:
1 cm3 = 1 mL
100 cm = 1 m
1000 mL = 1 L
100 cm = 1 m
(100 cm)3 = (1 m)3
1,000,000 cm3 = 1 m3
since 1 cm3 = 1 mL
1 m3 = 1,000,000 mL
PRESSURE
Pressure Buildup in a Bottle of
Champagne
Gas Pressure
• The total pressure exerted by a gas depends on
several factors, including the concentration of gas
molecules in the sample.
The higher the concentration, the greater the pressure.
• As volume increases, concentration of gas
molecules decreases (number of molecules does
not change, but since the volume increases, the
concentration goes down).
This in turn results in fewer molecular collisions, which
results in lower pressure.
Atmospheric Pressure Effects
• Variation in pressure in Earth’s
atmosphere creates wind, and
changes in pressure help us to
predict weather.
 The H’s in this map indicate regions of
high pressure, usually associated with
clear weather.
 The L’s indicate regions of low
pressure, usually associated with
unstable weather.
 The number of gas particles in a
given volume decreases with
increasing altitude.
 Hence, pressure decreases with
increasing altitude.
• Pressure exerted by a gas is
dependent on the number of
gas particles in a given volume.
• The fewer the gas particles, the
lower the force per unit area
and the lower the pressure.
 A low density of gas particles
results in low pressure. A high
density of gas particles results in
high pressure.
Pressure Imbalance in the Ear
• If there is a difference
in pressure across the
eardrum membrane,
the membrane will be
pushed out—what we
commonly call a
“popped eardrum.”
The Manometer
• The pressure of a gas trapped in a container can be
measured with an instrument called a manometer.
• Manometers are U-shaped tubes partially filled with a
liquid that are connected to the gas sample on one
side and open to the air on
the other.
• A competition is established between the pressures of
the atmosphere and the gas.
• The difference in the liquid levels is a measure
of the difference in pressure between the gas and the
atmosphere.
The Manometer
For this sample the gas
pressure is greater than
atmospheric pressure,
the mercury level on the
left side of the tube is
higher than the level on
the right.
Blood Pressure
• Blood pressure is the force
within arteries that drives the
circulation of blood throughout
the body.
• Blood pressure is measured
with an instrument called a
sphygmomanometer—an
inflatable cuff equipped with a
pressure gauge and a
stethoscope.
Blood Pressure
Ideal gas law the functional
relationship between the
pressure, volume, temperature
and moles of a gas. PV = nRT;
all gases are ideal at low
pressure. V =nRT. Each of the
individual laws is contained in
this equation.
Ideal Gases
An “ideal” gas exhibits certain
theoretical properties. Specifically, an
ideal gas …
• Obeys all of the gas laws under all
conditions.
• Does not condense into a liquid when
cooled.
Ideal Gases
• Shows perfectly straight lines when
its V and T & P and T relationships are
plotted on a graph.
In reality, there are no gases that fit this
definition perfectly. We assume that
gases are ideal to simplify our
calculations.
The Ideal Gas Law
PV = nRT
P = Pressure (in kPa)
V = Volume (in L)
T = Temperature (in K) n = moles
R = 8.31 kPa • L
K • mol
R is constant. If we are given three of P, V, n,
or T, we can solve for the unknown value.
From Boyle’s Law:
PiVi = PfVf or PV = constant
From combined gas law:
PiVi/Ti = PfVf/Tf or PV/T = constant
Sample problems
How many moles of H2 is in a 3.1 L sample of
H2 measured at 300 kPa and 20°C?
PV = nRT P = 300 kPa, V = 3.1 L, T = 293 K
(300 kPa)(3.1 L) = n (8.31 kPa•L/K•mol)(293 K)
(300 kPa)(3.1 L)
= n = 0.38 mol
(8.31 kPa•L/K•mol)(293 K)
Ideal Gas Law Questions
1. How many moles of CO2(g) is in a 5.6 L sample
of CO2 measured at STP?
Greetings from Aiah Nikole