Using the Gas
Laws
A Directed Learning Activity
for Hartnell College
Chemistry 1
Funded by a Title V STEM Grant from
Hartnell College
For information contact ataketomo@hartnell.edu
Start
Student Learning Objectives
This tutorial will help you to:
1. Manipulate the ideal gas laws to
calculate pressure, volume, temperature
and amount of gas present &
2. Use balanced equations and the ideal
gas laws to predict the amounts of
reagents and/or products for gaseous
reactions
Next
Getting Started



This set of Power Point slides will lead you through a
series of short lessons and quizzes on the topics
covered by this Directed Learning Activity tutorial.
Move through the slideshow at your own pace.
There are several hyperlinks you can click on to
take you to additional information, take quizzes,
get answers to quizzes, and to skip to other lessons.
You can end this slide show at any time by hitting
the “ESC” key on your computer keyboard.
Next
Table of Topics









What You Should Already Know
Boyle’s Law
Charles Law
Gay-Lussac’s Law
Combined Gas Law
Avogadro’s Law
Ideal Gas Law
Putting it All Together (Gas Stoichiometry)
Dalton’s Law of Partial Pressures
Next
What You Should Already
Know





How to manipulate algebraic equations
Conversions between different measurement
units
The basics of the Kinetic Molecular Theory of
ideal gases
Understand the “mole”
Write balanced chemical equations for
reactions
If you are uncertain about these skills, please
refer to your lecture text for help.
Next
Boyle’s Law
At constant temperature (T), the volume (V) of a fixed
mass of gas is inversely proportional to the Pressure (P).
1
𝑃 ∝
𝑉
If we have two sets of conditions (1 and 2) for the
same gas, we can then write this equation, which is
known as Boyle’s Law:
𝑃1𝑉1 = 𝑃2𝑉2
which is true when moles of gas and T are constant.
Next
Example 1 for Boyle’s Law
1. A sample of an ideal gas occupies 2.00 L at 760 torr.
What volume will this amount of gas occupy if the
temperature remains constant but the pressure
changes to 1.25 atm? Remember that 1 atm = 760 torr.
Solution: use Boyle’s law and substitute in the values
for conditions 1 and 2.
Property
1
2
P
760 torr =
1 atm
1.25 atm
V
2.00 L
?
Next
Example 1 for Boyle’s Law (cont’d)
Next
Example 2 for Boyle’s Law
A 1.00 L sample of an ideal gas at 760 torr is
compressed to 0.800 L at constant temperature.
Calculate the final pressure of the gas.
Solution: use Boyle’s law and substitute in the
values for conditions 1 and 2.
Property
1
2
P
760 torr =
1 atm
?
V
1.00 L
0.800 L
Next
Example 2 for Boyle’s Law (cont’d)
Next
Quiz Question 1
A mass of oxygen occupies 7.00 L under a
pressure of 740 torr. Determine the volume
of the same mass of gas at the standard
pressure of 760 torr, the temperature
remaining constant.
Click to review
Check answer
Answer to Quiz Question 1
Click to review
Next question
Quiz Question 2
Ten (10.0) liters of hydrogen under 7.0 atm
pressure is slowly compressed until it
occupies only 4.0 L of volume. Assume that
the temperature of the gas remains
constant. What pressure is needed for the
gas to remain compressed?
Click to review
Check answer
Solution to Quiz Question 2
Click to review
Next lesson
Charles’ Law
At constant pressure the volume (V) of a fixed
mass of an ideal gas is directly proportional to
the Kelvin temperature (T).
𝑉 ∝𝑇
If we have two sets of conditions (1 and 2) for
the same gas, we can then write this equation,
which is known as Charles’ Law:
𝑉1 𝑉2
=
𝑇1 𝑇2
which is true when moles and P are constant.
Next
Example for Charles’ Law
A given mass of chlorine gas occupies 25.0 L at
20 °C. What is the new volume at 45 °C,
assuming that the pressure remains constant?
Remember that T must be in Kelvin.
Solution: Use Charles’ Law and substitute the
values for conditions 1 and 2. Remember
temperature must be in Kelvin.
Property
1
2
V
25.0 L
?
T
20 °C + 273 K
45 °C + 273 K
Next
Example for Charles’ Law (cont’d)
Next
Quiz Question 3
A sample of gaseous argon is maintained at
a constant pressure. The sample has an
initial volume of 10.5 L at 25 °C. What will be
volume be if the same sample is kept at the
same pressure, but heated to 250 °C?
Click to review
Check answer
Answer to Quiz Question 3
Click to review
Next question
Quiz Question 4
A certain amount of gas occupies of volume
of 100. mL at a temperature of 20 °C. What
will the new volume be at 10 °C, if the
pressure remains constant?
Click to review
Check answer
Answer to Quiz Question 4
Click to reivew
Next lesson
Gay-Lussac’s Law
The pressure (P)of a fixed mass of an ideal gas,
at constant volume, is directly proportional to
the Kelvin temperature.
𝑃 ∝𝑇
If we have two sets of conditions (1 and 2) for
the same gas, we can then write this equation,
which is known as Gay-Lussac’s Law:
𝑃1 𝑃2
=
𝑇1 𝑇2
which is true when moles and V are constant.
Next
Example for Gay-Lussac’s Law
The air in a cylindrical tank has a pressure of 640
torr at 23 °C. When the tank was placed in the
sun, the temperature rose to 48 °C. What was
the final pressure in the tank if the mass and
volume of the gas does not change?
Solution : Use Gay-Lussac’s Law. Remember
that temperature must be in Kelvin.
Property
1
2
P
640 torr
?
T
23 °C + 273 K
48 °C + 273 K
Next
Example for Gay-Lussac’s Law
(cont’d)
Next
Quiz Question 5
A sealed glass bulb contains a sample of He
gas at a pressure of 750 torr and 27 °C. The
bulb was cooled down to -73 °C. What was
the new gas pressure inside the bulb?
Click to review
Check answer
Answer to Quiz Question 5
Click to review
Next question
Quiz Question 6
A steel tank contains carbon dioxide gas at
27 °C and at a pressure of 11.0 atm.
Determine the internal pressure when the
gas and its contents are heated to 100 °C.
Assume that the amount of carbon dioxide
and the volume of the tank are constant.
Click to review
Check answer
Answer to Quiz Question 6
Click to review
Next lesson
The Combined Gas Law
Next
Example for the Combined Gas Law
What would be the new pressure for a 2.00 L
sample of gas at 1.00 atm and -20 °C that is
compressed to a new volume of 0.500 L at 40
°C?
Solution: Use the combined gas law.
Temperatures must be converted to Kelvin.
1
2
P
1.00 atm
?
V
2.00 L
-20 °C + 273 K
T
0.500 L
40 °C + 273 K
Next
Example for the Combined Gas Law
(cont’d)
Next
Quiz Question 7
A 2.50 L sample of gas is at 0 °C and 1.00
atm pressure. What will the temperature of
the gas be if it is placed in a 2.00 L
container at 1.50 atm pressure?
Click to review
Check answer
Answer to Quiz Question 7
Click to review
Next lesson
Avogadro’s Gas Law
Under Standard Temperature and Pressure
(STP) conditions, the volume of one mole of
an ideal gas will occupy 22.414 Liters.
1 mole ideal gas = 22.414 L, at STP
STP conditions are 273K and 1 atmosphere
(760 mm Hg) of pressure.
Next lesson
The Ideal Gas Law
To adequately describe an ideal gas under
a particular set of physical conditions, you
need to know:
the temperature, pressure and volume of
the gas; and
the amount of gas.
This is summarized in the following equation:
Next
The Ideal Gas Law cont’d
Next
Example for the Ideal Gas Law
What is the pressure in atmospheres of
3.4x10-3 moles of argon gas in a 75-mL glass
bulb at 20 °C?
Solution: The problem gives three out of the
four properties of an ideal gas (moles,
volume, and temperature) and asks for the
fourth (pressure). Use the Ideal Gas Law.
Next
Example for Ideal Gas Law
cont’d
Next
Quiz Question 8
An incandescent light bulb contains 0.0421
g of Ar in a 23.0-mL volume. The pressure
inside the light bulb under these conditions
is 952 torr. What is the temperature of the
Ar gas under these conditions?
Click to review
Check answer
Answer to Quiz Question 8
Click to review
Next lesson
Putting it All Together – Gas
Stoichiometry
If we are given a chemical reaction where one or
more of the reactants is a gas, we can use the
balanced chemical equation to determine the
volume of gas that is obtained if we know the
amounts of the reagents. If we know the
experimental conditions of temperature and
pressure, we can use the Ideal Gas Law. Often
problems like this are written to be solved under STP
conditions, so the results of Avogadro’s Law can
also be used. This kind of problem is sometimes
called gas stoichiometry. Let’s look at an example.
Next
Example Problem
How many liters of carbon dioxide at STP will be formed from
the complete combustion of 82.60 g of ethanol, C2H5OH(l)?
What would this volume be if we then changed the conditions
of the gas to 23 °C and 0.95 atm to expand the gas after
formation?
Solution:
First we need to write the balanced equation for the reaction.
C2H5OH(l) + 3 O2(g) → 2 CO2(g) + 2 H2O(l)
Next, we need to know how many moles of ethanol we have
as starting material. This will allow us to use this procedure:
g C2H5OH → mol C2H5OH → mol CO2 → L CO2 @ STP
For the last step, since the conditions are at STP, we know that
each mole of CO2 = 22.414 L. If the conditions are different
than STP, we have to use the Ideal Gas Law to determine the
volume.
Next
Example Problem cont’d
Next
Quiz Question 9
Calculate the volume of O2 that can be
prepared at 60 C and 760 torr by the
decomposition of 20.0 g H2O2 to H2O and
O2. The reaction is:
2 H 2 O2 → 2 H 2 O + O2 .
Click to review
Check answer
Answer to Quiz Question 9
Next
Answer to Quiz Question 9
cont’d
Click to review
Next lesson
Dalton’s Law of Partial
Pressures
Next
Example Using Dalton’s Law
Next
Quiz Question 10
Exactly 100 mL of oxygen gas is collected
over water at 23 °C and 800 torr. Calculate
the standard volume of the dry oxygen if
the vapor pressure of water at 23 °C is 21.1
torr.
Click to review
Check answer
Answer to Quiz Question 10
Next
Solution to Quiz Question 10
cont’d
You must then use the combined gas law
to determine the volume of the oxygen at
STP. Here is what you know.
1
2
P
779 torr
760 torr
V
100. mL
?
T
23 + 273
273
Next
Solution to Quiz Question 10
cont’d
Click to review
Next
Congratulations!
You have successfully completed this
Directed Learning Activity tutorial. We
hope that this has helped you to better
understand this topic.
Click here to end.
Click here to repeat this activity.
Information
This document has been prepared in
compliance with US & International
Copyright Laws
© 2011 Hartnell College
Hit the ESC key to end this slide show