The Combined Gas Law - Waterford Public Schools

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All About Gases
Advanced Chemistry
Demonstration #1
Inflating a Balloon
Inflating a Balloon
Demonstration #2
Imploding Soda Can
Demonstration #3
Eggs in a Flask
Five Characteristics of Gases
Gases expand to fill their containers
• Gases are fluid – they flow
• Gases have low density
•
• 1/1000 the density of the equivalent liquid or solid
Gases are compressible
• Gases effuse and diffuse
•
Ideal Gases
•
Ideal gases are imaginary gases that perfectly fit all of
the assumptions of the kinetic molecular theory (KMT)
• Gases consist of tiny particles that are far apart relative to
their size.
• Gas particles are in constant, rapid motion.
• They therefore possess kinetic energy, the energy of motion
• There are no forces of attraction between gas particles
• The average kinetic energy of gas particles depends on
temperature, not on the identity of the particle.
PRESSURE
Pressure is the force created by the collisions of molecules with
the walls of a container
Unit
Symbol
Definition/Relationship
Pascal
Pa
SI pressure unit
1 Pa = 1 newton/meter2
Millimeter of
mercury
mm Hg
Pressure that supports a 1
mm column of mercury in a
barometer
Atmosphere
atm
Average atmospheric
pressure at sea level and 0 C
Torr
torr
1 torr = 1 mm Hg
An Early Barometer
Pressure is measured with
a barometer
 The normal pressure due
to the atmosphere at sea
level can support a
column of mercury that is
760 mm high

Common Units for Pressure
•
1 standard atmosphere (atm)
= 101.3 kPa (kilopascals)
= 14.7 lbs/in2
= 760 mm Hg (millimeters of mercury)
= 760 torr
Standard Temperature and Pressure
(STP)
• Often the volume of a gas is needed at
“standard conditions”
• For scientists, this means “STP”
• Standard temperature is 273 K
• Standard pressure is 1atm
101.3 kPa = 1 atmosphere (atm) = 760 mm Hg =
29.92 inches Hg = 14.7 lbs/in2 (psi)
Gas Conversions Factors
•
At STP conditions (0°C, 1 atm):
•
•
1 mole of any gas occupies 22.4 liters of space. Here are the
conversion factors:
23
6.02
x
10
22.4 (at STP)
1 mole= __________ particles= _____L
At SLC, standard lab conditions, (25°C, 1 atm):
•
1 mole of any gas occupies 24.5 L/mol. Here are the conversion
factors:
23
6.02
x
10
24.5 (at SLC)
1 mole= __________ particles= _____L
Gas Volume to Mole Sample
Problem

Convert 3 moles of helium to liters (at
STP)
Gas Laws
Robert Boyle
Jacques Charles
Amadeo Avogadro
Joseph Louis Gay-Lussac
The Gas Laws

When we make changes in a property of
a gas, other properties change in a
predictable way
◦ Led to the creation of the Gas Laws
•
•
•
Avogadro’s Hypothesis
Avogadro’s hypothesis states that ________
equal volumes of gases
(under the same temp. and pressure conditions) contain _______
equal
number of particles.
If containers have the same ____,
T ____,
P and ___,
V then they will
# of particles regardless of the _________
have the same ____
of the
size
gas particle.
You might think that a small gas molecule would take up ______
less
doesn’t
space than a large gas molecule, but it ___________
at the same
temperature
pressure
_________________
and ______________!!
Avogadro’s Law
Volume and Moles
 As the # of gas particles increase, the volume of a
flexible container will increase if the temperature
and pressure of the container remain constant
◦ DIRECT relationship
 Example
◦ Blowing more air into a balloon makes it larger
# particles ___,V ___
Gas Laws
• Here is the qualitative relationship between the pressure,
temperature, and volume of a constant # of gas particles in a container:
(1) ___________
Boyle’s
Law: At a constant temperature, as the volume of a
container __________
decreases the pressure of the container will ___________.
increase
↓ P ___
↑
V___,
*Example: Compressing the gas in a flexible container will
decrease its volume.
_________
Pressure
Volume
Boyle’s Law
Pressure is inversely proportional to volume
when temperature is held constant.
P1V1  P2V2
Gas Laws (continued)
(2) Guy-Lussac’s
____________ Law: At a constant volume, as the temperature of a
container __________
increases the pressure of the container will ___________.
increase
↑ P ___
↑
T___,
*Example: Heating a rigid container causes the gas inside
faster which causes _________
more pressure.
to move __________
Be careful! Too much heat will make it explode!
Pressure
Temperature (K)
Gay Lussac’s Law
The pressure and temperature of a gas are directly
related, provided that the volume remains constant.
P1 P2

T1 T2
Temperature MUST be in KELVINS!
Gas Laws (continued)
(3) ____________
Charles’s Law: At a constant pressure, as the temperature of a
container __________
increases the volume of the container will ___________.
increase
↑ V ___
↑
T___,
inflate
*Examples: Heating a balloon will cause it to ___________.
Taking a balloon outside on a cold winter day will cause
shrink
it to _____________.
• If you could keep a gas from condensing,
you could cool it off to absolute zero and the
zero
volume of the gas would be _________!
Volume
Temperature (K)
Charles’s Law
The volume of a gas is directly proportional to
temperature, and extrapolates to zero at zero Kelvin.
(P = constant)
V1 V2

T1 T2
Temperature MUST be in KELVINS!
The Combined Gas Law
• This equation combines all of the previous three laws into one
convenient form.
Boyles Law:
PxV = constant
Guy-Lussac’s Law:
P .= constant
T
Charles’s Law:
V = constant
T
= constant
• Using the Combined Gas Law
P1 x V 1
P2 x V2
=
T1
T2
K
K
(initial conditions) = (final conditions)
requires you to have the
temperature in _____________
Kelvin
units. The pressure and volume
units can be anything as long as
the initial and final units are
the __________.
same
______
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
Combined Gas Law Sample Problem

A balloon at a pressure of 4.5
atmospheres, 300 K, and a volume of 35.0
liters is changed to STP conditions. What
will the new volume of the balloon
become?
•
•
The Ideal Gas Law
An equation used to calculate the __________
amount of gas in a container
(in units of _________.)
moles
PV=nRT
Kelvin V = _________,
Liters n = # of moles
The units for T= __________,
R = Ideal Gas Constant
•
The value of R changes depending on the unit of ____________
pressure
used in the equation:
R = 62.4 (mm Hg)(L)/(mole)(K)
R = 8.31 (kPa)(L)/(mole)(K)
R = 0.0821 (atm.)(L)/(mole)(K)
R = 2.45 (in. Hg)(L)/(mole)(K)
The Ideal Gas Law
Practice Problems:
1) 6.5 moles of a gas has a pressure of 1.30 atmospheres and it has a
temperature of 20˚Celsius. What is the volume of the gas?
( 1.30 ) ( V ) = ( 6.5 ) (0.0821) ( 293 K)
V = 120 L
2) How many moles of gas are there in a 7.3 liter balloon with a
pressure of 1.11 atm and temperature of 395 K?
( 1.11 ) ( 7.3 ) = (
n ) ( .0821 ) ( 395 K)
n = 0.25 moles
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