Gas Laws: Pressure, Volume, and Hot Air

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Gas Laws Pressure, Volume, and Hot Air
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Introduction

• This interactive lesson will introduce three ways
  of predicting the behaviour of gases Boyles
  Law, Charles Law, and the Ideal Gas Law.

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Navigation

• Throughout this lesson, you will use buttons at
  the bottom right corner of the page to navigate.

Takes you to the next page
Takes you to the previous page
Takes you to the Main Menu
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Main Menu
Basic Terminology
Lesson 1
Lesson 3
Charles Law
Lesson 2
Lesson 4
Boyles Law
Ideal Gas Law
Review
Review of all four lessons
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Lesson 1 Basic Terminology

• This lesson reviews terms used to describe the
  properties and behavior of gases.

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Opening thoughts

• Have you ever

Seen a hot air balloon?
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Opening thoughts

• Have you ever

Seen a hot air balloon?
Had a soda bottle spray all over you?
Baked (or eaten) a nice, fluffy cake?
These are all examples of gases at work!
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Properties of Gases

• You can predict the behavior of gases based on
  the following properties

Pressure
Volume
Amount (moles)
Temperature
Lets review each of these briefly
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• You can predict the behavior of gases based on
  the following properties

Pressure
Volume
Amount (moles)
Temperature
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Pressure
Pressure is defined as the force the gas exerts
on a given area of the container in which it is
contained. The SI unit for pressure is the
Pascal, Pa.

• If youve ever inflated a tire, youve probably
  made a pressure measurement in pounds (force) per
  square inch (area).

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• You can predict the behavior of gases based on
  the following properties

Pressure
Volume
Amount (moles)
Temperature
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Volume
Volume is the three-dimensional space inside the
container holding the gas. The SI unit for
volume is the cubic meter, m3. A more common and
convenient unit is the liter, l.
Think of a 2-liter bottle of soda to get an idea
of how big a liter is. (OK, how big two of them
are)
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• You can predict the behavior of gases based on
  the following properties

Pressure
Volume
Amount (moles)
Temperature
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Amount (moles)
Amount of substance is tricky. As weve already
learned, the SI unit for amount of substance is
the mole, mol. Since we cant count molecules,
we can convert measured mass (in kg) to the
number of moles, n, using the molecular or
formula weight of the gas.
By definition, one mole of a substance contains
approximately 6.022 x 1023 particles of the
substance. You can understand why we use mass
and moles!
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• You can predict the behavior of gases based on
  the following properties

Pressure
Volume
Amount (moles)
Temperature
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Temperature
Temperature is the measurement with which youre
probably most familiar (and the most complex to
describe completely). For these lessons, we will
be using temperature measurements in Kelvin, K.
The Kelvin scale starts at Absolute 0, which is
-273.15C. To convert Celsius to Kelvin, add
273.15.
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How do they all relate?

• Some relationships of gases may be easy to
  predict. Some are more subtle.Now that we
  understand the factors that affect the behavior
  of gases, we will study how those factors
  interact.

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How do they all relate?

• Some relationships of gases may be easy to
  predict. Some are more subtle.Now that we
  understand the factors that affect the behavior
  of gases, we will study how those factors
  interact.

Lets go!
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Lesson 2 Boyles Law

• This lesson introduces Boyles Law, which
  describes the relationship between pressure and
  volume of gases.

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Boyles Law

• This law is named for Charles Boyle, who studied
  the relationship between pressure, p, and volume,
  V, in the mid-1600s.
• Boyle determined that for the same amount of a
  gas at constant temperature,
• p V constant
• This defines an inverse relationshipwhen one
  goes up, the other comes down.

pressure
volume
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Boyles Law

• This law is named for Charles Boyle, who studied
  the relationship between pressure, p, and volume,
  V, in the mid-1600s.
• He determined that for the same amount of a gas
  at constant temperature,
• p V constant
• This defines an inverse relationshipwhen one
  goes up, the othercomes down.

pressure
volume
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What does Boyles Law mean?

• p V constant

Suppose you have a cylinder with a piston in the
top so you can change the volume. The cylinder
has a gauge to measure pressure, is contained so
the amount of gas is constant, and can be
maintained at a constant temperature. A decrease
in volume will result in increased pressure. Hard
to picture? Lets fix that!
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Boyles Law at Work
Doubling the pressure reduces the volume by half.
Conversely, when the volume doubles, the
pressure decreases by half.
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Application of Boyles Law

• Boyles Law can be used to predict the
  interaction of pressure and volume.
• If you know the initial pressure and volume, and
  have a target value for one of those variables,
  you can predict what the other will be for the
  same amount of gas under constant temperature.
• Lets try it!

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Application of Boyles Law

• p1 V1 p2 V2
• p1 initial pressure
• V1 initial volume
• p2 final pressure
• V2 final volume
• If you know three of the four, you can calculate
  the fourth.

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Application of Boyles Law

• p1 V1 p2 V2
• p1 1 KPa
• V1 4 liters
• p2 2 KPa
• V2 ?
• Solving for V2, the final volume equals 2 liters.
• So, to increase the pressure of 4 liters of gas
  from 1 KPa to 2 KPa, the volume must be reduced
  to 2 liters.

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Boyles Law Summary

• Pressure Volume Constant
• p1 V1 p2 V2
• With constant temperature and amount of gas, you
  can use these relationships to predict changes in
  pressure and volume.

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Lesson 2 Complete!

• This concludes Lesson 2 on Boyles Law!

Click the Main Menu button below, then select
Lesson 3 to learn about how temperature fits in.
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Lesson 3 Charles Law

• This lesson introduces Charles Law, which
  describes the relationship between volume and
  temperature of gases.

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Charles Law

• This law is named for Jacques Charles, who
  studied the relationship volume, V, and
  temperature, T, around the turn of the 19th
  century.
• He determined that for the same amount of a gas
  at constant pressure,
• V / T constant
• This defines a direct relationship an increase
  in one results in an increase in the other.

volume
temperature
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What does Charles Law mean?

• V / T constant

Suppose you have that same cylinder with a piston
in the top allowing volume to change, and a
heating/cooling element allowing for changing
temperature. The force on the piston head is
constant to maintain pressure, and the cylinder
is contained so the amount of gas is constant. An
increase in temperature results in increased
volume. Hard to picture? Lets fix it (again)!
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Charles Law at Work
As the temperature increases, the volume
increases. Conversely, when the temperature
decreases, volume decreases.
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Application of Charles Law

• Charles Law can be used to predict the
  interaction of temperature and volume.
• If you know the initial temperature and volume,
  and have a target value for one of those
  variables, you can predict what the other will be
  for the same amount of gas under constant
  pressure.
• Lets try it!

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Application of Charles Law

• V1 / T1 V2 / T2
• V1 initial volume
• T1 initial temperature
• V2 final volume
• T2 final temperature
• If you know three of the four, you can calculate
  the fourth.

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Application of Charles Law

• V1 / T1 V2 / T2
• V1 2.5 liters
• T1 250 K
• V2 4.5 liters
• T2 ?
• Solving for T2, the final temperature equals 450
  K.
• So, increasing the volume of a gas at constant
  pressure from 2.5 to 4.5 liters results in a
  temperature increase of 200 K.

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Charles Law Summary

• Volume / Temperature Constant
• V1 / T1 V2 / T2
• With constant pressure and amount of gas, you can
  use these relationships to predict changes in
  temperature and volume.

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Lesson 3 Complete!

• This concludes Lesson 3 on Charles Law!

Click the Main Menu button below, then select
Lesson 4 to put all the pieces together with the
Ideal Gas Law.
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Lesson 4 Ideal Gas Law

• This lesson combines all the properties of gases
  into a single equation.

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Ideal Gas Law

• Combining Boyles and Charles laws allows for
  developing a single equation

PV nRT
P pressure V volume n number of moles R
universal gas constant (well get to that in a
minute) T temperature
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Ideal Gas Law
PV nRT
This is one of the few equations in chemistry
that you should commit to memory! By remembering
this single equation, you can predict how any two
variables will behave when the others are held
constant.
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Gas Constant

• The Ideal Gas Law as presented includes use of
  the Universal Gas Constant.
• The value of the constant depends on the units
  used to define the other variables.
• For the purposes of this lesson, we will use the
  equation only to predict gas behavior
  qualitatively. Specific calculations and units
  will be part of our classroom work.

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Putting pVnRT to Work

• After using Boyles and Charles law for
  predicting gas behavior, use of the Ideal Gas Law
  should be relatively straightforward.
• Use NASAs Animated Gas Lab to explore the
  interaction of these variables on gas behavior.
• Follow the directions on the page for changing
  values for the variables.
• When youre finished, click the Back button on
  your browser to return to this lesson.
• Link to site Animated Gas Lab

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Ideal Gas Law Summary

• PV nRT
• Learn it!
• Use it!
• This single equation can be used to predict how
  any two variables will behave when the others are
  held constant.

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Lesson 4 Complete!

• This concludes Lesson 4 on the Ideal Gas Law!

Click the Main Menu button below, then select
Review to try some questions based on these
lessons.
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Review

• This review contains multiple choice questions on
  the material covered by Lessons 1 4. Select an
  answer by clicking the corresponding letter.
• If you choose an incorrect answer, you will be
  given feedback and a chance to try again. If you
  want to return to a lesson to review the
  material, click on the Main Menu button, then
  select the lesson. When youre ready to complete
  the review again, go back to the Main Menu and
  click the Review button.

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Question 1

• Based on Boyles Law (p V constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and temperature (T) are held constant,
  pressure and volume are

a. Inversely proportional if one goes up, the
other comes down. b. Directly proportional if
one goes up, the other goes up. c. Not related
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Question 1 is Correct!

• Based on Boyles Law (p V constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and temperature (T) are held constant,
  pressure and volume are

a. Inversely proportional if one goes up, the
other comes down.
Decreasing volume increases pressure. Increasing
volume decreases pressure.
pressure
volume
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Try Question 1 again

• Based on Boyles Law (p V constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and temperature (T) are held constant,
  pressure and volume are

a. Inversely proportional if one goes up, the
other comes down. b. Directly proportional if
one goes up, the other goes up. c. Not related
You selected b. While pressure and volume are
related, it is not a direct proportion. Try
again!
TRYAGAIN
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Try Question 1 again

• Based on Boyles Law (p V constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and temperature (T) are held constant,
  pressure and volume are

a. Inversely proportional if one goes up, the
other comes down. b. Directly proportional if
one goes up, the other goes up. c. Not related
You selected c. Pressure and volume are related.
Is the relationship inverse or direct?
TRYAGAIN
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Question 2

• Based on Charles Law (V / T constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and pressure (p) are held constant,
  volume and temperature are

a. Inversely proportional if one goes up, the
other comes down. b. Directly proportional if
one goes up, the other goes up. c. Not related
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Try Question 2 again

• Based on Charles Law (V / T constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and pressure (p) are held constant,
  volume and temperature are

a. Inversely proportional if one goes up, the
other comes down. b. Directly proportional if
one goes up, the other goes up. c. Not related
You selected a. While volume and temperature are
related, it is not an inverse proportion. Try
again!
TRYAGAIN
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Question 2 is Correct!

• Based on Charles Law (V / T constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and pressure (p) are held constant,
  volume and temperature are

b. Directly proportional if one goes up, the
other goes up.
volume
temperature
Increasing temperature increases volume.
Decreasing temperature decreases volume.
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Try Question 2 again

• Based on Boyles Law (p V constant) or the
  Ideal Gas Law (pVnRT), when the number of
  moles (n) and temperature (T) are held constant,
  pressure and volume are

a. Inversely proportional if one goes up, the
other comes down. b. Directly proportional if
one goes up, the other goes up. c. Not related
You selected c. Pressure and volume are related.
Is the relationship inverse or direct?
TRYAGAIN
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Question 3

• Lets put the Ideal Gas Law (pVnRT) to some
  practical use. To inflate a tire of fixed
  volume, what is the most effective way to
  increase the pressure in the tire?

a. Increase the force pressing on the outside of
the tire. b. Increase the temperature of the gas
(air) in the tire. c. Increase the amount (number
of moles) of gas in the tire.
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Try Question 3 again

• Lets put the Ideal Gas Law (pVnRT) to some
  practical use. To inflate a tire of fixed
  volume, what is the most effective way to
  increase the pressure in the tire?

a. Increase the force pressing on the outside of
the tire. b. Increase the temperature of the gas
(air) in the tire. c. Increase the amount (number
of moles) of gas in the tire.
While increasing the load in the car might
increase the force on the tires, it would prove
to be a difficult way to adjust tire pressure.
Try again!
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TRYAGAIN
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Try Question 3 again

• Lets put the Ideal Gas Law (pVnRT) to some
  practical use. To inflate a tire of fixed
  volume, what is the most effective way to
  increase the pressure in the tire?

a. Increase the force pressing on the outside of
the tire. b. Increase the temperature of the gas
(air) in the tire. c. Increase the amount (number
of moles) of gas in the tire.
Increasing the temperature of the air in the tire
would definitely increase pressure. That is why
manufacturers recommend checking air pressures
when the tires are cold (before driving). But
how would you increase temperature without
damaging the tire? Is there a more practical
solution?
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TRYAGAIN
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Question 3 is Correct!

• Lets put the Ideal Gas Law (pVnRT) to some
  practical use. To inflate a tire of fixed
  volume, what is the most effective way to
  increase the pressure in the tire?

a. Increase the force pressing on the outside of
the tire. b. Increase the temperature of the gas
(air) in the tire. c. Increase the amount (number
of moles) of gas in the tire.
When you inflate a tire with a pump, you are
adding air, or increasing the amount of air in
the tire. This will often result in a slight
increase in temperature because a tire is not a
controlled environment. Such deviations and
quirks will be discussed in class!
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Mission complete!

• You have completed the lessons and review.
  Congratulations!
• You should now have a better understanding of the
  properties of gases, how they interrelate, and
  how to use them to predict gas behavior.
• Please click on the button below to reset the
  lesson for the next student. Thanks!

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