Unit 9: Gas Laws
Name:
Class Period:
Test Date:
1
Chemistry Calendar
Monday
Tuesday
Wednesday
Thursday
Friday
February 6th
7th
8th
9th
10th
6 week assessment
Kinetic theory
Combined Gas Law
Boyle’s Law
Ideal Gas Law
Charles’ Law
Dalton’s Law of
Partial Pressure
Behavior of Gases
13th
14th
15th
16th
17th
Review
Gas Law TEST
Lab
Flautus Chemistry
article with
accompanying
questions.
Student Holiday
Early Dismissal
18th
Student Holiday
2
The Behavior of Gases
DAY 1: _______________________________
REVIEW: Kinetic Theory
Kinetic refers to motion
The energy of an object has because of its motion is called
kinetic energy .
The Kinetic theory states that the tiny particles in all forms of matter are in constant motion.
Watch the video segment (Kinetic Molecular Theory – Standard Deviants School Chemistry:
Molecular Geometry) and fill in the missing information:
Basic assumptions of the kinetic theory as it applies to gases are:
1. A gas is composed of particles, usually molecules or atoms that are far apart from one
another in comparison with their own dimensions. Particles are relatively far apart from
one another and between them is empty space.
2. Gas molecules are in constant random motion. They travel in straight paths (unless
they collide with a wall of a container) and move independently of each other.
3. The molecules exert no force on each other or on the container until they collide with
each other or with the walls of the container.
4. The average kinetic energy of the molecules of a gas is proportional to the temperature.
5. Every time a molecule collides with the wall, it exerts a
force on it.
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Applying this knowledge we know…
Gases fill their containers regardless of the shape and volume of the containers.
Because there is so much space between particles, gases are easily
compressible. Because gases are compressible, they are used in
automobile airbags and other safety devices designed to absorb
the energy of an impact.
All collisions are perfectly elastic. This means that during
collisions kinetic energy is transferred without loss from one
particle to another, and total kinetic energy remains
constant.
The average speed of oxygen molecules in air at 20oC is 1700 km/h. At these high
speeds, the odor molecules from a hot pizza in Washington, D.C., should reach Mexico
City in about 106 minutes. Whey doesn’t this actually happen? Molecules are
constantly striking molecules of air and rebounding in other directions. Their path of
uninterrupted travel in a straight line is short.
Questions:
A. What happens when a closed container is inflated?
Pressure is increased by the addition of more gas particle. The pressure exerted by an
enclosed gas is caused by collisions of gas particles with the walls of the container. If
the number of gas particles is changed by any factor, the pressure changes by that
same factor; until the container ruptures.
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B. A gas inside a bicycle tire exerts a pressure of 35 pounds per square inch (psi). How
much air must be pumped into the tire to produce a pressure of 70 psi?
** The relationship between amount of gas and pressure is proportional, assuming the
volume & temperature stay the same.
C. What happens to pressure when a closed container is deflated?
The pressure of the gas is decreased because there are fewer gas particles and less collisions.
If the number of gas particles decreases by half, the pressure decreases by half.
(Note: Gas particles move from region of higher pressure to lower pressure until equilibrium
is reached.)
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Day 2:___________________________
COMBINED GAS LAW
The Combined Gas Law helps us explain what happens to gases as the pressure, temperature,
and volume changes.
P1 V1
P2 V2
__________
=
n1T1
__________
n2T2
Letter
or
Variable Name
Unit
Number
P
Pressure
atm (atmosphere)
mmHg (millimeters of
mercury)
torr (named after scientist E.
Torricelli)
kPa (kiloPascals)
V
Volume
L (Liters)
mL (milliliters)
cm3 (centimeter cubed)
m3 (meter cubed)
n*
T
1
2
Moles
Temperature
Initial variable
Final variable
Moles
K (Kelvin)
Conversions
1 atm = 760 mmHg =
760 torr = 101.3 kPa
1 L = 1000 mL
1 mL = 1 cm3
K = oC + 273
*NOTE: If “n” is not given in a problem, assume it to be 1 mole.
STP
=
Standard Temperature (273 K)
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and Pressure (1 atm)
Guided Practice:
1. The volume of a gas is 27.5 mL at 22.0 oC and 0.974 atm. What will the
volume be at 15 oC and 0.993 atm?
Givens and Unknowns:
Equation:
P1 = 0.974 atm
V1 = 27.5 mL
n1 = 1 mole
T1 = 22.0 oC + 273 = 295K
P2 = 0.993 atm
V2 = unknown
n2 = 1 mole
T2 = 15 oC + 273 = 288 K
P1 V1
__________
P2 V2
=
n1 T 1
__________
n2T2
Substitute & Solve:
(0.974 atm) (27.5 mL)
(1 mole) (295 K)
=
(0.993 atm) (V2)
(1 mole) (288 K)
0.09079661 atm*mL = 0.003447917 atm (V2)
(mole) (K)
(mole) (K)
0.09079661 atm*mL(mole) (K) = (V2)
0.003447917 atm(mole) (K)
26.32419104 mL = V2
Use 3 sig figs
26.3 mL = V2
2. A 700.0 mL gas sample at STP is compressed to a volume of 200.0 mL, and
the temperature is increased to 30.0 oC. What is the new pressure of gas in
kilopascals (kPa)?
Givens and Unknowns:
Equation:
P1 V1
P2 V2
P1 =
__________
=
__________
V1 =
n1 T 1
n2T2
n1 =
T1 =
Substitute & Solve:
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P2 =
V2 =
n2 =
T2 =
8
Boyle’s Law and Charles’ Law
Day 3: ______________________
The combined gas law equation is:
P1 V1
P2 V2
__________
=
n1 T 1
__________
n2T2
The Effect of Changing Size of Container
WHAT IF…temperature and moles do not change and we just look at the
relationship between pressure and volume. Our equation would look like this:
P1 V1
=
Boyle’s Law
P2 V2
Boyle’s Law states that at a constant temperature, the volume of a gas is
inversely proportional to the pressure exerted by that gas.
P
∆
∆
V
Think of two kids (Paul Pressure and
Victor Volume) on a see-saw. If Paul
goes up, Victor goes down. If Victor
goes up, Paul goes down.
∆
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Examples:
a. If a gas is compressed from 2L to 1L, the pressure will increase by a factor of
2.
b. If a gas is expanded from 1L to 3L, the pressure will decrease by a factor of 3.
c. Gases cool when they expand and heat when they compress. Why?
If the volume of a container is decreased in size, the pressure of gas
particles in the container is increased.
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The Effect of Temperature
changes on Volume
As the gas inside a balloon cools, the average KE of molecules decreases. With fewer and less
collisions, the gas molecules move closer together and occupy a smaller volume than they
previously did.
The volume decreases, assuming no change in the amount of gas and
pressure.
V1
____
=
T1
V2
____
Charles’ Law
T2
Charles law states: At a constant pressure, the volume of a gas is directly proportional to
the temperature in Kelvin.
Mr Charles
Mr. Charles is the elevator
operator. Thelma Temperature
and Violet Volume enter the
elevator. When one goes up the
other does too!
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GUIDED PRACTICE:
1. The pressure on 2.5L of anesthetic gas is changed from 760 mmHg to 304
mmHg. What is the new volume if temp is constant? (Boyle’s Law)
Givens and Unknowns:
P1 =
V1 =
Equation:
P1 V1 =
P2 V2
(Boyle’s Law)
Substitute & Solve:
P2 =
V2 =
2. A gas occupies 6.45 L at 0.860 atm. What is the pressure, in atm, if the
volume becomes 15.0 L.
Givens and Unknowns:
P1 =
V1 =
Equation:
P1 V1 =
P2 V2
Substitute & Solve:
P2 =
V2 =
12
(Boyle’s Law)
3. A sample of gas occupies a volume of 80 mL at a temperature of 0oC. What
is the new temperature if the volume is decreased to 32 mL? Assume no
change in pressure.
Givens and Unknowns:
Equation:
V1
V2
Charles’ Law
____
=
____
V1 =
T1
T2
T1 =
Substitute & Solve:
V2 =
T2 =
4. A volume of 3.0L of air is warmed from 50oC to 100oC. What is the new
volume if the pressure remains constant?
Givens and Unknowns:
V1 =
T1 =
Equation:
V1
V2
Charles’ Law
____
=
____
T1
T2
Substitute & Solve:
V2 =
T2 =
13
Ideal Gas Law
DAY 4: ___________________________
Charles’ Law
V1
____
T1
Boyle’s Law
V2
=
P1 V1
____
T2
=
P2 V 2
Combined Gas Law
P2 V 1
__________
P2 V2
=
n1T1
__________
n2T2
An ideal gas is one that follows the gas laws at all conditions of pressure and
temperature.
Such a gas would have to conform precisely to the assumptions of kinetic
theory.
As you probably suspect, there is __ no gas __ for which this is true. An ideal
gas ____ does not ______ exist. Nevertheless, at many conditions of temperature
and pressure, __ real gases ___ behave very much like an ideal gas.
An important behavior of real gases that differs from that of a hypothetical
ideal gas is that real gases can be __ liquefied ________________ and sometimes __
solidified _____________ by cooling and by applying pressure. Ideal gasses
cannot be. For example, when water vapor is cooled below 100oC at
standard atmospheric pressure, it condenses to a liquid. The behavior of
other real gases is similar, although lower temperature and greater
pressures may be required.
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****Gases behave ideally at ______ high temperatures and low pressure
____________________________________________.
If we look at one side of the Combined Gas Law:
P = Pressure
V = Volume
PV
nT
n = moles
T = Temperature
and solve it for one mole at STP, you would get a “constant” (symbolized as R).
(101.3 kPa)(22.4 L) = 8.31 (L . kPa)/(K . mol)
(1 mole)(273 K)
We call this the ideal gas constant (R):
If pressure is measured in: The ideal gas constant (R) is:
kPa
atm
8.31 (L . kPa)/(K . mol)
0.0821 (L . atm)/(K . mol)
mmHg
62.4 (L . mmHg)/(K . mol)
62.4 (L . torr)/(K . mol)
torr
P = Pressure
SO…
PV
nT
=R
V = Volume (must be in
liters)
n = moles
T = Temperature (must
be in Kelvin)
OR
R = Ideal gas constant
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PV = nRT
THIS IS THE IDEAL GAS LAW
GUIDED PRACTICE:
1. Calculate the number of moles of oxygen in a 12.5 L tank containing 250 atm, measured
at 22oC.
Givens and Unknowns:
P=
Equation:
PV = nRT
Substitute & Solve:
V=
n=
R =
T=
2. If 4.5 g methane gas (CH4) is introduced into an evacuated 2.00 L container at 35oC,
what is the pressure in the container, in atm?
Givens and Unknowns:
P=
Equation:
PV = nRT
Substitute & Solve:
V=
n=
R =
T=
3.
At STP 150.0 mL of an unknown gas has a mass of 0.250 grams. Calculate its molar mass.
Givens and Unknowns:
P=
Equation:
PV = nRT
Substitute & Solve:
V=
n=
R =
16
T=
Molar mass = ???
Dalton’s Law of
Partial Pressures
Partial pressure of a gas in a mixture of gases is the pressure which that gas
would exert if it were the only gas present in the container.
Dalton's Law of Partial Pressures states that the total pressure in a gas mixture is
the sum of the partial pressures of each individual gas.
Ptotal = Pgas a + Pgas b + Pgas c + etc
Dalton's Law of Partial Pressures assumes each gas in the mixture is behaving like
an ideal gas.
Ptotal
=
Pgas a
=
+
+
17
Pgas b
Dalton’s Gas Law of Partial Pressures Problems
For each problem, calculate the pressure using correct units.
Box final answer. SHOW ALL WORK!!
1) Three of the primary components of air are nitrogen, oxygen, and carbon dioxide. In a sample containing a
mixture of only these gases at exactly one atm pressure (total), the partial pressures are P CO2 = 0.285 torr
and PN2 = 593.525 torr. What is the partial pressure of oxygen?
P1 =
Ptotal =
P2 =
P3 =
2) Oxygen gas from the decomposition of potassium chlorate, KClO3, was collected by water displacement.
2 KClO3  2 KCl + 3 O2
What is the partial pressure of oxygen collected if the barometric pressure (total) was 731.0 torr and the
vapor pressure of water at 20.0C was 17.5 torr?
P1 =
Ptotal =
P2 =
3) A sample of nitrogen gas was collected over water at a temperature of 23.0C. What is the partial
pressure of nitrogen if the atmospheric pressure (total) was 785 mmHg and the vapor pressure of water
was 21.1 mmHg?
P1 =
P2 =
Ptotal =
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Day 5
REVIEW
1. Define Boyle’s Law and Charles’ Law.
2. A sample of gas occupies a volume of 95.2 mL at a pressure of 710 torr and a
temperature of 30°C. What will be its volume at a standard pressure and 30°C?
3. The volume of a gas is 17.4 liters, measured at standard pressure. Calculate the
pressure of the gas if the volume is changed to 19.4 liters and the temperature
remains constant.
4. A gas measures 150 mL at 1.00 atmosphere and 27°C. Calculate its volume at 0°C
and 1.00 atmosphere.
5. A gas occupies a volume of 4.50 liters at 27°C. At what temperature in °C would the
volume be 6.00 liters (the pressure is constant).
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6. The temperature of 1 liter of gas originally at STP is changed to 200°C at constant
volume. Calculate the final pressure of the gas in torr.
7. What are the formulas for the Combined Gas Law and the Ideal Gas Law?
8. A gas occupies 500 ml at 760 torr and 0°C. What volume will it occupy at 10.0 atm
and 100°C?
8. A gas occupied 20.0 L at 50°C and 780 torr. Under what pressure in torr would this
gas occupy 75.0 liters at 0°C?
9. Calculate the number of moles of oxygen in a 2.5 liter tank containing 25 atm,
measured at 23°C.
11. If 2 grams of CH4 (methane gas) is introduced into a 2.0 liter container at 27°C, what
is the pressure in the container in mmHg?
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