CHEMISTRY FOR TEACHERS
MODULE VIII
SCI
211
GASES
CHEMISTRY FOR TEACHERS
Prepared by: KENNETH B. BLAS
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
MODULE VIII. GASES
Hello! How are you? You are now about to begin your journey
in understanding the concept of Gases. This module was being
developed as a final requirement in SCI 211 which is the Chemistry
for Teachers during my journey in graduate school taking up
Masters of Science Teaching in General Science as required by
Professor Maridith Pedrosa as she handles this course subject at the
Davao Oriental State College of Science and Technology which
was offered for the first semester. Have an enjoyable and
meaningful experience as you are going to explore all the
concepts provided in this module. It introduces you the concept
properties of gases and the use of ideal gas laws and other related
gas laws.
Gases
Upon completion of this module, you are expected to be able to:
To state properties of gases.
Solve stoichiometry problems involving gas laws
To state the value of knowing the different gases and
appreciate their value to real world.
To ensure the achievement of the learning outcomes, this module
is organized into three lessons listed as follows:
LESSON 1. Relating to the Properties for Gases: The Ideal Gas
Law
LESSON 2. Combined Gas Law
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
LESSON 1. Relating to the Properties of Gases: The Ideal
Gas Law
Learning Outcomes:
Having successfully completed this lesson, you will be able to:
Define gas
Identify the properties of gases
Identify the mathematical relationships between the various
properties of gases
Use the ideal gas law, and related gas laws, to compute the
values of various gas properties under specified conditions
Introduction
This module deals with the concept properties of gases and
the use of ideal gas laws and other related gas laws. This module
will help everyone to be guided on the several concepts of the
content. It aims to provide everyone the complete and organize
flow of the discussion, since the topic is so much interesting. This will
also develop the critical thinking and problem-solving skills of the
students.
Gases
Properties
Pressure
Mass
Temperature
Volume
Gas Laws
Boyle’s Law
Charle’s Law
Ideal Gas Law
Avogadro’s Law
Gay-Lussacs Law
Combined Gas Law
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CHEMISTRY FOR TEACHERS
Let’s Explore (Discussion)
GASES
GASES
 a state of matter that has no fixed shape and no fixed volume.
 have a lower density than other states of matter, such as
solids and liquids.
Physical properties of gases
Gases are physical properties of mark sensitivity of volume
change with the change of temperature and pressure. Thus
the gases are generally concerned with the relations among
four
properties,
temperature.
The
namely
mass,
relationship
pressure,
between
volume,
these
and
physical
properties of gases describes by Boyles, Charles, and Avogadro
gas laws. Gas molecules move very large speeds because of
the forces of attraction between them very low. Thus the gas
molecules do not possess fixed volume, they move partially
independent of one another.
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CHEMISTRY FOR TEACHERS
GAS LAWS
Boyle’s Law
Boyle’s law of gases
Boyle’s law states as, at a constant
temperature, the volume of a
definite mass of a gas is inversely
proportional to its pressure. Thus the
volume of a given quantity of gas,
at constant temperature decreases
with the increase of pressure of
gases. At constant temperature
and 1 atm pressure, a cylinder
contains 10 ml of methane gas. If
the pressure increases to 2 atm then according to this law
volume decreases to 5 ml.
Mathematical derivation of Boyle’s law
According to the mathematical definition of Boyle’s law at a
constant temperature
Therefore, PV = K = constant for a gas. Here the value of gas
constant depends on the nature and mass of the gases.
Graphical representation of Boyle’s law
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CHEMISTRY FOR TEACHERS
The relation between pressure and volume of gas can be
represented by an arm of a rectangular hyperbola given
below.
Image source: Online learning chemistry
1. The value of gas constant changes with temperature. Thus
there will be a separate curve for each fixed temperature.
These curves plotted at different fixed temperatures are
called isotherms.
2. At constant temperature, a given mass of gas is the product
of pressure and volume. If the product of pressure and
volume represents in Y-axis and pressure represents X-axis a
straight line curve obtained parallel to X-axis.
The relation between pressure and density of gas
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CHEMISTRY FOR TEACHERS
Thus at a constant temperature, the density of a definite mass
of a gas proportional to its pressure.
Boyle’s Law leads to the mathematical expression: *Assuming
temperature is constant
P1V1=P2V2
Where P1 represents the initial pressure
V1 represents the initial volume,
And P2 represents the final pressure
V2 represents the final volume
Exercise number 1:
Directions: Solve the given problem following the Boyle’s Law
Equation.
Problem: Atmospheric pressure on the peak of Kilimanjaro can
be as low as 0.20 atm. If the volume of an oxygen tank is 10.0L,
at what pressure must the tank be filled so the gas inside would
occupy a volume of 1.2 x 103L at this pressure?
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CHEMISTRY FOR TEACHERS
Charles’s Law
Relationship between pressure and volume
At constant pressure a given mass
of gas, volume increases with the
increasing temperature. Thus, the
volume of a given mass of gas at
constant
pressure
proportional
to
is
directly
its
kelvin
temperature.
Charles law formula for ideal gases
Let V0 = volume at ⁰C, then ¹⁰C rise of temperature the volume
of the gas rise V0/273.5 ml.
1⁰C rise of temperature the volume
Thus at t⁰C temperature the volume
It is convenient to use the absolute temperature scale on which
temperature is measured in Kelvin. Thus the reading on this
scale obtained by adding 273 to the celsius value.
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CHEMISTRY FOR TEACHERS
Since V0 = initial volume = constant at a given pressure, thus the
above relation expressed as the volume of a given mass of
gases is directly proportional to its kelvin temperature.
Graphical representation of Charles law
A typical variation of volume of gas with a
change in its kelvin temperature a straight line
plot is obtained. These plots are known as
V
isobars. Thus the general term isobar, which
means at constant pressure assigned to these
plots.
T
Absolute zero temperature gases
Since volume is directly proportional to its kelvin temperature.
Thus the volume is theoretically zero at zero kelvin or — 273 0C.
This is hypothetical because the gases from liquid and
then solid before this low temperature reached. In reality, no
substance exists as gases at the temperature near kelvin zero.
Temperature density relationship
Thus at constant pressure, the density of a given mass of gases
inversely proportional to its temperature.
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CHEMISTRY FOR TEACHERS
Derivation of combined gas laws equation
Charles law, V ∝ 1/P when T constant and Boyle’s law, V ∝ T
when P constant. Thus when all the variables are taken into
account the variation rule states as, V ∝ T/P; or, PV/T = constant.
Thus this ideal gas law states the physical properties as the
product of the pressure and volume of a given mass of gases
are proportional to its kelvin temperature.
Charles’ Law leads to the mathematical
expression:
*Assuming pressure remains constant
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CHEMISTRY FOR TEACHERS
Exercise number 2:
Directions: Solve the given problem following the Charle’s Law
Equation.
Problem: A beach ball is inflated to a volume of 25L of air at
15oC. During the afternoon, the volume increases by 1L.
What is the new temperature outside?
Gay-Lussac’s Law
Gay-Lussac’s law is a gas law which
states that the pressure exerted by a gas
(of a given mass and kept at a constant
volume) varies directly with the absolute
temperature of the gas. In other words,
the pressure exerted by a gas is
proportional to the temperature of the
gas when the mass is fixed and the
volume is constant.
This law was formulated by the French
chemist Joseph Gay-Lussac in the year
1808. The mathematical expression of Gay-Lussac’s law can be
written as follows:
P ∝ T ; P/T = k
Where:
•
•
•
P is the pressure exerted by the gas
T is the absolute temperature of the gas
k is a constant.
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CHEMISTRY FOR TEACHERS
The pressure and absolute temperature (K) of a gas are directly
proportional (as temperature rises, so does pressure) at constant
mass & volume.
The relationship between the pressure and absolute temperature
of a given mass of gas (at constant volume) can be illustrated
graphically as follows.
P
T
From the graph, it can be understood that the pressure of a gas
(kept at constant volume) reduces constantly as it is cooled until
the gas eventually undergoes condensation and becomes a
liquid.
Formula and Derivation
Gay-Lussac’s law implies that the ratio of the initial pressure and
temperature is equal to the ratio of the final pressure and
temperature for a gas of a fixed mass kept at a constant volume.
This formula can be expressed as follows:
(P1/T1) = (P2/T2)
Where:
P1 is the initial pressure
• T1 is the initial temperature
• P2 is the final pressure
• T2 is the final temperature
This expression can be derived from the pressure-temperature
proportionality for gas. Since P ∝ T for gases of fixed mass kept at
constant volume:
•
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
P1/T1 = k (initial pressure/ initial temperature = constant)
P2/T2 = k (final pressure/ final temperature = constant)
Therefore, P1/T1 = P2/T2 = k
Or, P1T2 = P2T1
Gay-Lussac’s Law leads to the mathematical expression:
*Assuming volume remains constant
Exercise number 3:
Directions: Solve the given problem following the Gay-Lussac’s Law
Equation.
Problem: The pressure of a gas in a sealed canister is 350.0kPa at a
room temperature of 15oC. The canister is placed in a refrigerator
that drops the temperature of the gas by 20K. What is the new
pressure in the canister?
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
The Ideal Gas Law
To this point, four separate laws have been discussed that relate
pressure, volume, temperature, and the number of moles of the
gas:
•
•
•
•
Boyle’s law: PV = constant at constant T and n
Amontons’s law: P/T = constant at constant V and n
Charles’s law: V/T = constant at constant P and n
Avogadro’s law: V/n = constant at constant P and T
Combining these four laws yields the ideal gas law, a relation
between the pressure, volume, temperature, and number of moles
of a gas:
PV=nRT
where P is the pressure of a gas, V is its volume, n is the number of
moles of the gas, T is its temperature on the kelvin scale, and R is a
constant called the ideal gas constant or the universal gas
constant. The units used to express pressure, volume, and
temperature will determine the proper form of the gas constant as
required by dimensional analysis, the most commonly encountered
values being 0.08206 L atm mol–1 K–1 and 8.314 kPa L mol–1 K–1.
Gases whose properties of P, V, and T are accurately described by
the ideal gas law (or the other gas laws) are said to exhibit ideal
behavior or to approximate the traits of an ideal gas. An ideal gas
is a hypothetical construct that may be used along with kinetic
molecular theory to effectively explain the gas laws as will be
described in a later module of this chapter. Although all the
calculations presented in this module assume ideal behavior, this
assumption is only reasonable for gases under conditions of
relatively low pressure and high temperature. In the final module of
this chapter, a modified gas law will be introduced that accounts
for the non-ideal behavior observed for many gases at relatively
high pressures and low temperatures.
The ideal gas equation contains five terms, the gas constant R and
the variable properties P, V, n, and T. Specifying any four of these
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
terms will permit use of the ideal gas law to calculate the fifth term
as demonstrated in the following example exercises.
Exercise number 4:
Directions: Solve the given problem following the Ideal Gas Law
Law Equation.
Problem: Calculate the pressure in bar of 2520 moles of hydrogen
gas stored at 27 °C in the 180-L storage tank of a modern hydrogenpowered car.
If the number of moles of an ideal gas are kept constant under two
different sets of conditions, a useful mathematical relationship
called the combined gas law is obtained:
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
using units of atm, L, and K. Both sets of conditions are equal to the
product of n × R (where n = the number of moles of the gas and R is
the ideal gas law constant).
Let’s Do It (Assessment)
Problem Solving:
Directions: Solve the given problem following the various gas
properties formula.
1. If 22.5 L of nitrogen at 748 mm Hg are compressed to 725 mm Hg
at constant temperature. What is the new volume?
2. A container containing 5.00 L of a gas is collected at 100 K and
then allowed to expand to 20.0 L. What must the new temperature
be in order to maintain the same pressure (as required by Charles'
Law)?
3. The pressure of a gas in a cylinder when it is heated to a
temperature of 250K is 1.5 atm. What was the initial temperature of
the gas if its initial pressure was 1 atm?
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
LESSON 2. Combined Gas Law
Learning Outcomes
Having successfully completed this lesson, you will be able to:
Understand the concept of combined gas laws.
Performing Calculation applying the formula of Combined
Gas Law
Introduction
Let’s Explore (Discussion)
The combined gas law combines is a law that combines the three
gas laws. Moreover, these three laws are Boyle’s Law, Charles Law,
and Gay-Lussac’s Law. So this law is an amalgamation of these three
laws that were previously discovered.
Furthermore, this law states that the ratio of the product of volume
and pressure and the gas’s absolute temperature is equal to a
constant. Most noteworthy, when the addition of Avogadro’s law
happens to combined gas law, the ideal gas law results. There is no
official discoverer of combined gas law.
Prepared by: KENNETH B. BLAS MST GS 1
CHEMISTRY FOR TEACHERS
Combine gas law is simply a combination of the other gas laws.
Moreover, this law works when everything with the exception of
volume, pressure, and temperature are held constant. This law
makes use of relationships shared by temperature, pressure, and
volume.
Understanding the Combined Gas Law
In order to understand the combined gas law properly, imagine that
there is a diver and his lungs are full of air when he begins the dive.
Furthermore, as he goes deeper underwater, the pressure in the lungs
escalates.
When this pressure escalates, the air inside the lungs gets squished.
Consequently, the volume decreases. This is where Boyle’s law is in
action, which states that the higher the pressure consequently
means lower the volume.
Another example can be that of a balloon in the refrigerator. As the
temperature of the balloon in the refrigerator decreases, then
consequently the gas volume inside the balloon also decreases.
Also, the balloon reverts to the original size once it is out. Similarly,
when temperature increases then consequently there is an increase
in volume as well. This shows Charles law in action.
Take a third example in which a driver is driving down the road.
Gradually, the temperature inside the tire increases. So, as the air
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CHEMISTRY FOR TEACHERS
expands inside the tire then consequently the pressure also increases.
This example represents the Gay-Lussac’s law.
After combining the above three laws, one gets the combined gas
law, which shows that:
•
Pressure happens to be inversely proportional to the volume
•
Pressure happens to be directly proportional to temperature
Volume is directly proportional to the measure of temperature
Derivation of the Combined Gas Law
•
The combined gas law is an amalgamation of the three previously
known laws which are- Boyle’s law PV = K, Charles law V/T = K, and
Gay-Lussac’s law P/T = K. Therefore, the formula of combined gas law
is PV/T = K,
Where P = pressure, T = temperature, V = volume, K is constant.
One can adjust the formula for the combined gas law so as to
compare two sets of conditions in one substance. In the equation,
the figures for temperature (T), pressure (P), and volume (V) with
subscripts of one are representative of the initial condition. Also, those
with the subscripts of two are representative of the final condition.
P1V1/T1 = P2V2/T2
An important point to note is that the temperature should always be
in kelvin for the purpose of calculation. So, if the units are available in
the Celsius scale, then one must convert them to kelvin. Furthermore,
the conversion to kelvin can easily be done by adding 273 to the
particular unit.
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CHEMISTRY FOR TEACHERS
Exercise number 1:
Figure
1.
Scuba
divers
use
compressed air to breathe while
underwater. (credit: modification of
work by Mark Goodchild)
Problem: When filled with air, a typical scuba tank with a volume of
13.2 L has a pressure of 153 atm (Figure 1). If the water temperature
is 27 °C, how many liters of air will such a tank provide to a diver’s
lungs at a depth of approximately 70 feet in the ocean where the
pressure is 3.13 atm?
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CHEMISTRY FOR TEACHERS
Let’s Do It (Assessment)
Problem Solving:
Directions: Solve the given problem following the combined gas law
formula.
1. The initial volume of a gas is 6L and its final volume is 3L. Find
out the final pressure of the gas such that the initial
temperature is 273 K while the final temperature is 200K.
Moreover, 25K Pa is the initial pressure.
References
https://pandakajal42.medium.com/physical-properties-of-gases2beabaf00cb8
https://www.priyamstudycentre.com
https://byjus.com/chemistry/gay-lussacslaw/#:~:text=The%20pressure%20of%20a%20gas%20is%20directly%
20proportional%20to%20its,Gay%2DLussac%20's%20law.
https://www.toppr.com/guides/chemistry-formulas/combinedgas-lawformula/#:~:text=Therefore%2C%20the%20formula%20of%20combi
ned,%3D%20volume%2C%20K%20is%20constant.
https://hdqwalls.com/fluid-gas-8k-wallpaper
https://www.npsd.k12.nj.us/cms/lib/NJ01001216/Centricity/Domai
n/472/Gas%20Laws%20Worksheet%20answer%20key.pdf
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