10

SCIENCE
QUARTER 4– MODULE 1
WEEK 1-2

Gas Laws
 What I Need to Know
Gases are the least compact and the most mobile of the three states of matter.
Gas molecules move with very high velocities and thus have high kinetic energy.
Gases behave in different conditions which can be explained through the
assumptions in the Kinetic Molecular Theory. The characteristics of gases are
described fully in terms of parameters such as volume, temperature, pressure, and
the number of moles. Moreover, the relationships between volume, temperature, and
pressure can be analyzed using established gas laws. You will learn all of these by
taking up the three lessons in this module
There are problem- solving activities in this learning module. Solve each
problem patiently to facilitate mastery on the volume-pressure and volume-
temperature relationships. Try to perform the activities included in this learning
module with diligence, and you will be fascinated with what you will observe and
learn.
After going through the activities and discussions in this learning module, you
are expected to:
1. investigate the relationship between: (S10MT-Iva-b-21)
a. volume and pressure at constant temperature of a gas
b. volume and temperature at constant pressure of a gas
c. explain these relationships using the Kinetic Molecular Theory
2. recognize by citing some applications of Boyle’s and Charles’ gas laws in
daily occurrences.

What I Know

Directions: Carefully read each item. Choose the letter of the best answer for each
question and write your answer on a separate sheet of paper.

1. If the amount and temperature of a gas are kept constant, the pressure and
volume of the gas are ______________.
A. also unchanging C. inversely proportional
B. directly proportional D. independent of one another

2
2.You have given for flasks below which are of the same size and are the same
temperature. Which one contains the greatest volume?

A. flask 1 C. flask 3
B. flask 2 D. flask 4
3.To use Boyle's Law, which of the following needs to remain constant?
A. Temperature and volume
B. Temperature and pressure
C. Pressure and number of moles of a gas
D. Temperature and number of moles of a gas
4. A sample of hydrogen has a volume of 25 L under a pressure of 5 atm. What will
the pressure of this gas be if the volume were decreased to 5 L?
A. 25 atm B. 15 atm C. 10 atm D. 5 atm
5.A certain amount of gas at 25 C occupies a container with an adjustable volume.
It currently has a volume of 10.5 L., with a pressure of 1.5atm. What would its
volume be if the pressure were adjusted to 1.2 atm?
A. 13.1 L B. 12.1 L C. 10.2 L D. 7.31 L
6. The characteristics (variables) of gases needed to describe a gas completely include
all of the following except
A.. density B. pressure C. temperature D. volume
7. An instrument used to measure the pressure exerted by a gas is the
A. anemometer B. climometer C. manometer D. pressometer
8. Which of the following is NOT one of the postulates of the Kinetic Molecular Theory
for ideal gases?
A. The collisions between particles are elastic.
B. The particles are in constant random motion.
C. The particles attract and then repel each other.
D. The particle size is very small compared to the space between the particles.
9. A sample of gas is contained in a closed container under 2 atm of pressure.
According to kinetic molecular theory, what causes this pressure?
A. The gas particles are chemically reacting with each other releasing energy.
B. The gas molecules are colliding with each other, exerting a force on each other.
C. The gas molecules are attaching to the walls of the container, pulling it inward.
D. The gas molecules are colliding with the walls of the container, exerting a force
on the container.
10. Which of the following is NOT a property of gases?
A. gases can be compressed
B. gases exert pressure on their containers
C. gases diffuse quickly through other gases
D. gases are weightless near the surface of the Earth
11.If the pressure on a gas is constant and the temperature is decreased, the volume
will_______________
A. decrease. B. increase. C. stay the same. D. randomly change.

3
12. Which two variables are compared in Charles’s Law?
A. pressure & volume C. temperature & pressure
B. volume & temperature D. volume & moles (amount of gas)
13.Tina wants his balloon back to normal size so she decides to put it on a heating
vent. If the balloon initially has a volume of 0.6 L and a temperature of 293 K, what
will the volume of the balloon be when heated to a temperature of 176°C?
A. 0.39 L B. 0.78 L C. 0.92 L D. 2.92 L
14. Four hundred twenty (420) mL of a gas at 25.0°C is compressed to 210 mL.
What is the temperature of the gas after compression?
A. 12.5 0C B. 149K C. 273K D. 25.7 0C
15. Julian and Jimmy are playing basketball outside under a 52°C weather
temperature. If they leave the ball outside and temperature drops down to 43°C,
what will happen to the volume of the gas in the ball if the pressure remains
constant? The volume will _______________
A. decrease C. double in size
B. increase D. remain the same

Lesson
Boyle’s Law:
1 Pressure-Volume Relationship

What’s In
Getting Started With Gases
Gases are important aspects in sustaining life here on Earth. Oxygen for
instance is essential to animals to be utilized in different biological processes
such as cellular respiration. Carbon Dioxide is used by plants through the process
of photosynthesis. It is not surprising that the study of gases has a very long
history in Science, but how do these gases behave? What are their properties that
make them interesting topic to learn?
The properties of gases can be described fully with the following terms:
volume, pressure, mass, and temperature.

A. Identify the different properties of gases in the situations below. Use a

separate sheet of paper for your answers.
________1. You are experiencing the heat trapped by the greenhouse gases.
_______ 2. The inflated ball is filled with air, it bounces while you are dribbling it.
_______ 3. Opening a can or bottle of softdrinks and it fizzes because of the
escaping dissolved carbon dioxide.
_______ 4. Inflated balloon is heavier than deflated balloon.
_______ 5. You can feel the wind blows.

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 Now that you have known that gases have properties like mass, volume,
pressure, and temperature. How are these properties being measured? or what
units are used to express them?

B. Below is a table of the properties of gases, identify the units of measure by

choosing from the list given in the box with their corresponding symbols.

Pascal (Pa) cubic centimeter (cm3) degrees Fahrenheit (oF)

cubic meter (m3) liter (L) centimeters of mercury
Torr quart (qt) (cmHg)
Kelvin (K), Pascal (Pa) millimeter of mercury
lb/in2 (psi) atmosphere (atm) (mmHg)
degrees Celsius (oC) gallon (gal)
cubic decimeter (dm3) milliliter (mL)

Table 1: Units of Measure of Properties of Gases

VOLUME PRESSURE TEMPERATURE

You will encounter most of these units as we go along.

What’s New

Picture Analysis
Directions: Study each picture carefully and answer the following questions to
derive Boyle’s law. Use a separate sheet of paper for your answers.
Picture A

Q1. At constant temperature, what happens to

the volume of a gas when the

a. pressure increases? ___________________

b. pressure decreases? ___________________

Q2. At constant temperature, what happens to the

pressure of a gas when the
a. volume increases? ___________________
b. volume decreases? ___________________

source: https://byjus.com/chemistry/boyles-law/

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Picture B

Q3. Complete the statements below as shown in Picture B.

At a constant temperature, if the pressure on a fixed amount of
gas is doubled, the volume is ___________________.
and if the pressure is halved, the volume is _________________.

source: https://byjus.com/chemistry/boyles-law/

Picture C

Q4. Using Picture C, state the relationship between the

pressure exerted on a quantity of gas and its volume if the
temperature is held constant.
____________________________
Q5. If you want to decrease the volume of nitrogen gas inside
a cylinder, what will you do with the pressure?
_____________________________
source: https://byjus.com/chemistry/boyles-law/

What is It

In 1662, Robert Boyle first observed the relationship between the pressure(P)
and volume(V) of a gas at constant temperature. He performed an experiment
wherein he trapped a fixed amount of air in the J-tube, he changed the pressure and
controlled the temperature and then, he observed its effect to the volume of the air
inside the J-tube. He found out that as the pressure is increased, the volume
decreases. He finally concluded that the volume of a fixed amount of gas is inversely
proportional to its pressure at constant temperature.
𝟏
Mathematically, Boyle’s law can be expressed as: 𝑷 ∝
𝑽
Where, P ➜ Pressure V➜ Volume ∝ ➜ Proportionality sign to
equal sign, then:
𝟏
𝑷 = 𝒌𝟏
𝑽
Where k is proportionality constant. Furthermore,
𝒌𝟏
𝑷=
𝑽
𝒌𝟏 = 𝑷𝑽
For a given sample of gas under two different sets of condition, at constant
temperature,
𝑷𝟏 𝑽𝟏 = 𝒌𝟏 = 𝑷𝟐 𝑽𝟐 or
𝑷𝟏 𝑽𝟏 = 𝑷𝟐 𝑽𝟐 (Boyle’s Law) Equation 1

Where,
P1 ➜ initial pressure P2 ➜ final pressure
V1 ➜ initial volume V2 ➜ final volume

6
 Boyle’s Law states that the pressure and volume are inversely proportional to
each other at a constant temperature. Let us apply the equation you learned about
Boyle’s law.
Sample Problem
A fixed amount of gas occupies a syringe with a volume of 6.0L. The pressure
at 250C is 1.00atm. What will be the new pressure if the volume becomes 3.0L at
the same temperature?
Given:P1 = 1.0 atm V1 = 6.0 L
P2 = ? V2 = 3.0 L
Analysis: Based on the given, we expect the new pressure, P2 to increase since
the volume decreased from 6.0L to 3.0L. Also, we will use the derived formula below
to solve for P2.
𝑷𝟏 𝑽𝟏 𝑷𝟐 𝑽𝟐 𝑷𝟏 𝑽𝟏
Formula: = therefore, 𝑷𝟐 =
𝑽𝟐 𝑽𝟐 𝑽𝟐
Solution:
(1 𝑎𝑡𝑚)(6.0 𝐿) (1 𝑎𝑡𝑚)(6.0 𝐿)
𝑃2 = 𝑃2 =
(3.0 𝐿) (3.0 𝐿)

(1atm)(6.0)
𝑃2 =
(3.0)
𝑃2 = 2 𝑎𝑡𝑚
Interpretation: Based on the given, it is expected that the pressure should
increase due to the decreasing amount of volume since pressure and volume are
inversely proportional to each other.

What’s More

Problem Solving
You are now equipped with the fundamental knowledge to cope with the
problem-solving activities related to Boyle’s law. Let us try to solve the following
Boyle’s Law problems to facilitate mastery of concepts on the pressure-volume
relationship.
1.My grandmother was hospitalized at the Community Hospital due to difficulty in
breathing. The nurse supported her breathing with the aid of oxygen gas. The
nurse noted that the tank of oxygen gas has a volume of 14.0L and a pressure of 1
atm. Find the volume of the oxygen when its pressure is changed to 1.2 atm while
the temperature is held constant.
Given: V1=14.0 L, P1= 1.0 atm, P2= 1.2 atm

2. The owner of Molina’s Toy Balloon at Public Market has a 200.0 L Helium gas at
a temperature of 280C and a pressure of 760 mmHg and transferred to a tank with
a volume of 68.0 L. What is the internal pressure in atm of the tank if the temperature
is maintained?
Formula: P1 V1= P2V2 therefore, P2= P1V1
V2 V2 V2

3. A balloon contains 14.0 L of air at a pressure of 760 torr. What will the volume of
the air be when the balloon is taken to a depth of 10 ft in a swimming pool where the
pressure is 981 torr? The temperature of the air does not change.

7
 What I Have Learned
Directions: Fill in each blank with the correct word from the pool of words inside the
box. You can use some words more than once. Use a separate sheet of paper for your
answers.

Robert Boyle increased decreased inversely final volume

Volume pressure temperature initial pressure

P1V1=P2V2

Using a J-shaped piece of glass tubing that was sealed on one end that
1.__________ employed, he was able to establish the relationship between 2.
_____________ and 3. ___________ .He noticed that when 4. __________ is held
constant, the 5. ________ of a given amount of gas decreases as the pressure is
6. ____________. On the contrary , if the pressure that is applied is
7. ___________ the gas 8. _____________ becomes larger.
Boyle’s experiment proved that the 9. _________ is 10. _____________
proportional to the volume of gas at constant 11. _____________, that is the
volume decreases with the increasing 12. ___________and vice-versa.
Mathematically, Boyle’s law can be expressed as, 13. ___________ where
P1 is the 14. ______________ and V2 is the 15.______________ of a given gas.

Lesson
Charles’ Law: Volume -
2 Temperature Relationship

What’s In

From the previous lesson, you have learned that Boyle’s Law depends
on two factors- pressure and volume at constant temperature. But what if the
temperature changes? How will the pressure and volume be affected when the
temperature changes?

You may now proceed to the different activities of this learning module
and find out if there is a relationship between volume and temperature at
constant pressure.

8
 What’s New

Activity 1: Blow Me Up...

What you need: Rubber balloon,100mL cold water,100 mL hot water,bowl, tape
measure
What you will do: (Please take precautionary measures in performing the activity)
1.Fill the bowl with 100mL cold water and another bowl with 100mL hot water.
2.Inflate a balloon.
3.Measure the circumference of the balloon using a tape measure,
4.Put the balloon in hot water for 2 minutes, then measure again its circumference.
5.Put the balloon in cold water for 2 minutes,then measure again its circumference.
Answer the questions in a separate sheet of paper.
What happens to the size of the inflated balloon when it was placed on top of the
bowl filled with hot water? _______________________________
What happens to the size of the inflated balloon when it was placed on top of the
bowl filled with cold water? _______________________________
How does the change in temperature relate to the volume of gas in the balloon?
___________________________________

Activity 2: Analyze and Describe Me

The table below shows temperature and volume data for a given amount of gas at a
constant pressure.
Temperature Volume Data
Temperature (K) Volume mL)
50 20
100 40
150 60
200 80
300 120
500 200
1000 400
The graphic presentation of the result of the data is shown in figure 1 below.

Figure 1. Graph of temperature versus volume of a gas

Answer the following questions in a separate sheet of paper.
1. Describe the graph formed. ______________________________________
2. Based on the graph, how does the change in the temperature relate to the
volume of gas at constant pressure? _______________________________________

9
 What is It

French physicist Jacques Charles in full Jacques-Alexandre-César Charles,

(1746-1823) studied the effect of temperature on the volume of a gas at constant
pressure.
In his experiment, Jacques Charles trapped a sample of gas in a cylinder with
a movable piston in water bath at different temperatures. He found out that different
gases decreased their volume by factors 1/273 per °C of cooling. With this rate of
reduction, if gas will be cooled up to -273°C, it will have zero volume, or referred to
as the absolute zero, and is theoretically lowest attainable temperature. This
temperature is the zero point or the Kelvin (absolute) temperature scale.
To convert °C to K, use this formula K= °C + 273.15
Charles’ Law states that at constant pressure, the volume of a fixed amount
of gas is directly proportional to its absolute temperature. Mathematically, the direct
relationship of Charles's Law can be represented by the following equations:
𝑽
V = kT or =k
𝑻
Where k is the constant for a fixed mass of gas. Since the volume-to-
temperature ratio is constant for a given mass of a gas at the same pressure,
𝑽𝟏 𝑽
= 𝟐 or V1T1 = V2T2
𝑻𝟏 𝑻𝟐
Where: V1 = initial volume V2 = final volume
T1 = initial temperature T2 = final temperature
Note that the temperatures should be expressed in Kelvin.

Sample Problem: Study the sample problem on Charles’ Law.

Three liters of hydrogen at -20°C is allowed to warm to 27 °C. What is the volume at
this temperature if the pressure remains constant?
Answer:
Given: V1 = 3L
T1=-20°C +273=253 K T2=27°C +273K =300K
Unknown: 𝑽𝟐
𝑽 𝑽 𝑽 𝑻
Formula: 𝟏 = 𝟐 𝑽𝟐 = 𝟏 𝟐
𝑻𝟏 𝑻𝟐 𝑻𝟏
(𝟑.𝟎𝟎𝑳)(𝟑𝟎𝟎𝑲)
Solution: 𝑽𝟐 =
𝟐𝟓𝟑𝑲
Final answer: 𝑽𝟐 = 3.56L

What’s More

A. Problem Solving:
Directions: Answer the following Charles’ Law in a separate sheet of paper.
1. A hot air balloon has a volume of 2800 m 3 at 990C. What is the volume if the air
cools to 800C.
Given: V1 = 2800m3
T1=99°C+273K = 372 K T2 =80°C +273K =353K
Unknown: V2
Formula:
Solution:
Final answer:

10
 2. If 15.0 L Neon at 60 0C is heated at constant pressure, what temperature will it
have if it occupies a volume of 4.50 L?
Given: V1= 15.0L V2 = 4.50 L
T1 = 60 0C Convert 60 0C + 273 K = 333 K
Unknown: T2
𝑽 𝑻
Formula: 𝑻𝟐 = 𝟐 𝟏
𝑽𝟏
Solution:
Final answer

B. Assessment
Directions: Read each item carefully. Write the letter of the correct answer in a
separate sheet of paper.
1.Which of the following phenomena best illustrates Charles Law
A. carbon dioxide being dissolved in water
B. breathing apparatus being used by a patient
C. leavening agent causing the fluffiness of cake products
D. expansion of the balloon as it is being submerged in hot water
2. Last summer vacation, the Cruz family decided to go to Dasol, Pangasinan to have
a beach party. On their way, all of them were surprised when the tire suddenly
exploded. What the probable explanation for the blown-out tire during a long
summer drive?
A. The mass of gas inside the tire increases
B. The amount of gas inside the tire is increased.
C. High temperature causes a decrease in volume.
D. The volume of gas increases as the temperature increases.
3. At constant pressure, the volume of gas decreases as its temperature _________
A. approaches 1000C B. decreases C. increases D. stays the same
4. The temperature of nitrogen gas contained in hot rigid vessel is reduced from
100°C to 5.0°C? Which of the following describes the resulting behavior of nitrogen
gas molecules?
I. The average kinetic energy suddenly increases, thus the pressure increases.
II. The average kinetic energy suddenly decreases, thus the pressure decreases.
III. The volume occupied by the gas molecules suddenly increases, thus the
container expand.
IV. The volume occupied by the gas molecules suddenly decreases, thus the
container also decreases.
A. I & III B. II & IV C. I & IV D. II &III
5. A balloon with a volume of 200 mL at 30°C is submerged in hot water to obtain
a temperature of 50°C. Find out what will happen to the volume of the balloon, when
the pressure remains the same.
A. the volume of the balloon will become higher than 200 mL
B. the volume of the balloon will become lower than 200 mL
C. the volume of the balloon will stay the same
D. there is no enough data

11
 What I Have Learned

Directions: Fill in each blank with the correct word from the pool of words inside
the box. You can use some words more than once.
Jacques Charles increases double decreases directly
final temperature initial volume Volume pressure
temperature Kelvin Celsius V1T1 = V2T2
Charles's Law states that the volume of a given mass of gas varies
1. _____________with the absolute 2. _____________ of the gas when 3. _____________is
kept constant. The absolute temperature is measured with the 4. _____________scale.
Charles experiment proved that the 5. _____________ is 6. _____________ proportional
to the absolute 7. _____________of gas at constant 8. _____________ that is the volume
9. _____________with the increasing 10. ____________and vice-versa. So if the absolute
temperature Is doubled, the volume will also 11. ___________ This means that at
constant 12. ____________the same gas will have a different volume when temperature
is changed.
Mathematically, Charles’ law can be expressed as, 13. _____________where V1 is the
14. _____________and T2 is the 15.____________ of a given gas.

Lesson
Kinetic Molecular Theory
3 (KMT)

What’s In

A. Study the illustrations below:

www.siyavula.com

Particles of solid, liquid and gas

12
 Among the three states of matter, which has the most kinetic energy?
What phase of matter is separated by a large distance? Which among the three
particles is the most compressible? Why?
B. Can you still recall what are the properties of gases? Identify property of
gases based on the descriptions below
_______________ 1. The force applied per unit area.
_______________ 2. The amount of space a substance occupies.
________________3. The degree of hotness or coldness of an object.
________________4. A measure of the amount of material in a substance.
The Kinetic Molecular Theory (KMT) explains the properties of gases and
describes the behavior of gases. You can understand more about Kinetic
Molecular Theory as you move on to the next activities.

What’s New

Word Search
Let us familiarize with the Kinetic Molecular Theory by answering the activity
below.

Directions: Find all the hidden KMT words in the word search puzzle below. Words
can be spelled forward, backward, downward, and upward.

A B E L B I G I L G E N C D E F G C H I S
J K L R A N D O M Q M O T I O N O O P Q E
R S V T S U V W X Y Z A B Y C D E L F G I
H M O L E C U L E S I M J R K L M L N O T
P Q L R S P H E R I C A L O B O D I E S R
S T U T N A T S N O C S U E V W I S L X E
Y Z M A B C D E F G H S I H J E M I A K P
P R E S S U R E L M N O P T Q N E O S R O
Q A T T R A C T I V E F O R C E N N T T R
T E M P E R A T U R E U V W X R S S I Y P
A V E R A G E K I N E T I C V G I A C B C
M O L E C U L A R D E F G H I Y O G K L M
R E P U L S I V E F O R C E O P N Q R S T
Word Bank
GASES ELASTIC PRESSURE
MOLECULES MASS COLLISION
VOLUME AVERAGE KINETIC TEMPERATURE
RANDOM MOTION ENERGY SPHERICAL BODIES

13
 What is It

Kinetic Molecular Theory (KMT) describes why gases behave the way they
do and explains the properties of gases. The Kinetic Molecular Theory of gases is
based on the following five postulates:

1. A gas is composed of a large number of particles called molecules and considered

as spherical bodies that are in constant, rapid, random and in a straight-line
motion.
2. The distance between gas molecules is much greater than the size of the
molecules, the volume and mass of the molecules are negligible.
3. There is a neither intermolecular interactions, whether repulsive nor attractive
force between or among gas molecules.
4. Gas molecules collide with one another and with the walls of the container, but
these collisions are perfectly elastic; that is, they do not change the average
kinetic energy of the molecules. None of the energy of a gas particle is lost when
it collides with another particle or with the walls of the container.
5. The average kinetic energy of the molecules of any gas is directly related to the
temperature of gas. At a given temperature, all gaseous molecules have exactly
the same average kinetic energy.

Source: https://chem.libretexts.org/
Fig. Visualizing molecular motion. Molecules of a gas are in constant motion and collide
with one another and with the container wall.
Kinetic Molecular Theory can be used to explain both Boyle’s and Charles’ Laws

Boyle’s law states that at constant temperature and amount of gas, pressure
is inversely proportional to volume. Boyle’s law is supported by the Kinetic Molecular
theory. When the volume of gas decreases, the rate at which gas molecules collide
increases, and the pressure shoots up. Conversely, when the volume increases, the
collision rate and the pressure drops.

Charles’ law states that, at constant pressure, volume is directly proportional

to temperature. Again, if you consider kinetic theory, this is a reasonable
relationship. It basically states an increase in temperature will increase the average
kinetic energy of the molecules. As the particles move faster, they will likely hit the
edge of the container more often. If the reaction is kept at constant pressure, they
must stay farther apart, and an increase in volume will compensate for the increase
in particle collision with the surface of the container.

14
 What’s More

Part I: Identification
Directions: Give the word the word/ group of words that best describe the
following statements. Write your answer on a separate sheet of paper.
1. It is the relationship between the average kinetic energy of the molecules and the
temperature of a gas.
2. It is the cause of more frequent collision and faster movement of the molecules.
4. It is the motion which is always constant in gas molecules.
5. It is a variable that affects the movement of gas molecules.

Part II. True or False

Directions: Read and analyze carefully the different postulates embodied in the
KMT. Write TRUE if the postulate is accurate and FALSE if the postulate is flawed.
Write your answer on a separate sheet of paper.
1.The kinetic molecular theory only applies to gases.
2.The collisions between air molecules use up energy and eventually make a room
cooler.
3.At 35 oC, on average nitrogen molecules will move faster than nitrogen molecules
at 12 oC.
4.According to KMT, gas particles have negligible mass but no volume.
5.Warming a gas results in an increase in the average kinetic energy of its particles.
6.The average kinetic energy of a collection of gas particles is assumed to be
directly proportional to the Kelvin temperature of the gas.
7.The molecules move in constant, rapid, random, circular motion.
8.The particles are so small compared with the distances between them that
the volume of the individual particles can be assumed to be zero.
9.The particles are assumed to exert no forces on each other; they are assumed
neither to attract nor to repel each other.
10.The energy of a gas particle is lost when it collides with another particle or
with the walls of the container.

Part III. Modified True or False

Directions: Write true if the statement is correct and if the statement is false
change the underlined word(s) to make the statement correct. Write your answer on
a separate sheet of paper.
1. The distances of gas molecules are far from each other.
2. There are perfectly inelastic collisions among gas molecules.
3. Random motions are always constant in gas molecules.
4.The gas molecules are frequently colliding with one another and also
with the walls of the container.
5. The gas molecules which possess negligible mass and volume can be considered
as spherical bodies.

15
 What I Have Learned

Directions: Summarize what you have learned from the lesson and activities by
completing the sentences using the words listed in the box below. You can use some
words more than once.

Molecules kelvin straight lines kinetic energy distances

volume container walls attractive force postulates elastic
forces collisions temperature pressure
higher increases Kinetic Molecular Theory

A. The ______________ (KMT) is a simple microscopic model that effectively explains

gas laws. . This theory is based on the following five__________ described here:
1. Gases are composed of ______________ that are in continuous motion,
travelling in ______________and changing direction only when they collide with other
molecules or with the walls of a container.
2.The ___________ composing the gas are negligibly small compared to the
_________between them.
3.The pressure exerted by a gas in a container results from ______________
between the gas ______________ and the container walls.
4. Gas molecules exert no attractive or repulsive______________ on each
other or the container walls; therefore, their collisions are __________ (do not
involve a loss of energy).
5. The average ____________ of the gas molecules is proportional to the
_________ temperature of the gas.

B.KMT conceptually explains the behavior of a gas as follows:

1. Boyle’s law. If the gas ___________is decreased, the container wall area
decreases and the molecule-wall collision frequency ___________, both of which
increase the pressure exerted by the gas.
2. Charles’s law. If the temperature of a gas is increased, a constant
__________ may be maintained only if the volume occupied by the gas increases.
This will result in greater average distances traveled by the molecules to reach
the container walls, as well as increased wall surface area.

16
 What I Can I Do

Application of Gas Laws

Directions: Explain common processes or phenomena using Boyle’s law and
Charles’ law Select 3 questions only.Write your answer in a separate sheet of paper.

1. Explain the mechanics of the Bicycle

pump as related to Boyle’s Law.

Source: www.iwakipumps.jp
2. What do you notice to your diaphragm
(muscle that is located just below the lungs)
as you inhale and exhale. What happens to
the volume of the lungs if the diaphragm
moves downward during inhalation and vice
versa
Source: www.livescience.com

3. LPG tanks and gas cylinders are made of

very strong materials like steel. Why woods,
glass, plastics and ordinary tin cans not be
used for gas storage?

Source: www.petron.com
4. If you have had the chance to go out on a
chilly day, you might have noticed that the
balloon crumbles. However, if you take the
balloon to a warm room, it regains its shape.
Why does this happen?

Source: www.pixabay.com
5. You might have wondered about the
working of the hot air balloon Describe how
hot air balloon functions based on Charle’s
Law.

Source: www.footage.framepool.com
7. If you get a chance to read the
instructions on a bottle of deodorant, you
might have read the warning signs
indicating the bottle to be kept away from
the sunlight and high temperature. Ever
wondered why?
Source: www.sks-bottle.com

17
 Assessment
Multiple Choice: Choose the letter of the best answer. Write the chosen letter on a
separate sheet of paper.
1.Boyle's law states that when the
A. temperature of a gas is constant, its volume is inversely proportional to its
pressure.
B. pressure of a gas is constant, its volume is directly proportional to its
temperature.
C. temperature of a gas is constant, its volume is directly proportional to its
volume.
D. pressure of a gas is constant, its volume is inversely proportional to its
temperature.

2. Shown below are four mercury barometers of the same height (all four barometer
tubes measure one meter from the tube opening to rounded top). Which barometer
shows the greatest external pressure?

A. B. C. D.

3. Under conditions of fixed temperature and amount of gas, Boyle's law requires
that
I. P1V1 = P2V2
II. PV = constant
III. P1/P2 = V2/V1
A. I only C. III only
B. II only D. I, II, and III

4. A sample of oxygen occupies 47.2 liters under a pressure of 1240 torr at 25 OC.
What volume would it occupy at 25 OC if the pressure were decreased to 730 torr?
A. 27.8 L B. 29.3 L C. 32.3 L D. 80.2 L

5. A sample of hydrogen gas collected by displacement of water occupied 30.0 mL

at 24OC on a day when the barometric pressure was 736 torr. What volume would
the hydrogen occupy if it were dry and at STP? The vapor pressure of water at
24.0OC is 22.4 torr.
A. 21.6 mL B. 29.1 mL C. 32.4 mL D. 36.8 mL

6. Which statement is FALSE?

A. Gases can be expanded without limit.
B. Pressure must be exerted on a sample of a gas in order to confine it.
C. The density of a gas is constant as long as its temperature remains constant.
D. Gases diffuse into each other and mix almost immediately when put into the
same container.

7. Kinetic-molecular theory makes several assumptions about the

A. size and energy of molecules.
B. size and weight of molecules.
C. motion and size of molecules.
D. motion and energy of molecules.

18
8. Which statement is NOT consistent with the kinetic-molecular theory of gases?
A. Individual gas molecules are relatively far apart.
B. The average kinetic energies of different gases are different at the same
temperature.
C. There is no net gain or loss of the total kinetic (translational) energy in
collisions between gas molecules.
D. The actual volume of the gas molecules themselves is very small compared to
the volume occupied by the gas at ordinary temperatures and pressures.

9. All are properties of ideal gases EXCEPT:

A. Collisions between gas molecules are completely elastic.
B. Gas molecules do not interact with each other except during collisions.
C. Small amounts of energy are lost during collisions between gas molecules.
D. Volume occupied by molecules is negligible compared to the volume occupied
by the gas.

10. Kinetic-molecular theory is most useful and accurate when gases are at _____
or at _____ .
A. high temperature; high pressure C. low temperature; high pressure
B. high temperature; low pressure D. low temperature; low pressure

11. Volume and temperature have a/an ______ proportionality.

A. direct B. inverse C. linear D. same

12. If the pressure on a gas is constant and the volume is decreased the
temperature will ______________.
A. increase C. stay the same
B. decrease D. change randomly

13. Pepe and Pilar want to play a game of beach volleyball. If the beach ball has a
volume of 400 L at a temperature of 500 K, what will the temperature of the beach
volleyball be if the volume decreases to 176 L?
A. 176 L B. 220 K C. 380 K D. 500 K

14. Manuel enjoys balloon animals from the plaza. He just received a balloon pet
dog that has an initial temperature of 39.0°C and a volume of 1.28 L. If Rene plays
a trick on Manuel, and puts his balloon pet dog into the ice cream freezer, what
would be the new volume of the balloon if the temperature drops down to 8.0°C?
A. 1.15L C. 42 L
B. 3.78 L D. 6.85 x 104 L

15. Manuel wants his balloon back to normal size so he decides to put it on a
heating vent. If the balloon initially has a volume of 0.6 L and a temperature of 293
K, what will the volume of the balloon be when it heats up to a temperature of
176°C?
A. 0.39 L C. 0.92 L
B 0.78 L D. 0.92 K

19
 Additional Activities

Part I. My Own Air Pump Balloon

Construct an air pump balloon as a device to demonstrate the application of
Boyle’s law.
Materials: 1.5L softdrink plastic bottle, electrical tape, cutter,
2 balloons, soldering iron or heated nail

1. Make a rectangular hole in the cap of the

plastic bottle with the use of cutter.

2. Cut a part from one balloon with a size

enough to cover the hole

3. Tape the clut part of the balloon to cover

the hole of the plastic bottle cap. Do not tape
one side of the cap.

4. Using heated nail or soldering iron, poke a

hole in the center part of the bottle.

5. Cover the bottle with its cap and put a

balloon at the top of it.

6. Inflate the balloon by applying pressure in

the plastic bottle through pumping.

Question:
Relate the mechanics of the air pump balloon with the Boyle’s law.
________________________________________________________________________

20
Part 2: Other Gas Laws
Aside from Boyle’s and Charles’ laws, there are other gas laws that you need
to be familiar with. Study each gas law and try to apply them by solving the
problems presented. Follow the steps in problem solving as what you have learned
in the previous activities. Use separate sheets of paper for your answers.
1. Gay-Lussac’s Law
The person who is credited with the determination of the temperature-
pressure relationship in gases at constant volume is Joseph Louis Gay-Lussac. He
deduced that the pressure of the gas is directly proportional to its temperature.
This means that when the temperature of gases increases its pressure also
increases or vice versa. Hence, we can state the Gay-Lussac’s Law as: At constant
volume, the pressure of a fixed mass of gas is directly proportional to the absolute
temperature.
Gay-Lussac’s Law can be expressed mathematically as
P α T at constant Volume
It is can be written as:
𝑷
P=kT or k=
𝑻
Since there is a direct proportionality between the pressure and temperature
of gases at constant volume, it can be shown in this equation:
𝑷𝟏 𝑷
= 𝟐
𝑻𝟏 𝑻𝟐
Solve: A certain light bulb containing argon has a pressure of 1.20 atm at 18°C. If it
will be heated to 85°C at constant volume, what will be the resulting pressure?
Given: P1 = 1.20 atm. P2 = ?
T1 = 180C + 273.15= 291.15 K T2 = 850C + 273.15=358.15 K

𝑷𝟏 𝑷𝟐 𝑷𝟏 𝐓𝟐 𝑷𝟐 𝐓𝟏 𝑷𝟏 𝐓𝟐
Formula: = , = , 𝑷𝟐 =
𝑻𝟏 𝑻𝟐 𝑻𝟏 𝑻𝟏 𝑻𝟏

2. Combined gas law

No one is credited for the Combined Gas Law, but combining Boyle’s Law and
Charles’ Law together will result to Combined Gas Law which states that the pressure
and volume of a gas are inversely proportional to each other but are both directly
proportional to the temperature of that gas.
It is possible to compute for the change in volume, temperature, or pressure
using the following proportion:
𝑷𝟏 𝑽𝟏 𝑷 𝑽
= 𝟐 𝟐
𝑻𝟏 𝑻𝟐
Solve: Helium gas has a volume of 250 mL at 0°C at 1.0 atm. What will be the final
pressure if the volume is reduced to 100 mL at 45°C?
Given: V1 = 250mL V2 = 100 mL
T1 = 0 C + 273.15= 273.15 K
0 T2 = 450C + 273.15=318.15 K
P1 = 1 atm P2 = ?
𝑷𝟏 𝑽𝟏 𝑻𝟐
Formula: P2 =
𝑽𝟐 𝑻𝟏

3. Avogadro’s law
Named after its proponent, the Italian physicist Amadeo Avogadro,
Avogadro’s law states that “at constant temperature and pressure, the volume of a
gas is directly proportional to the number of moles of the gas present.” It can be
𝑽
expressed mathematically as: =𝒌
𝒏
where V is the volume of gas
n is the amount of gas in moles and

21
 k is a proportionality constant
This can also be expressed as:
𝑽𝟏 𝑽
= 𝟐 or 𝑽𝟏 𝒏𝟐 = 𝑽𝟐 𝒏𝟏
𝒏𝟏 𝒏𝟐

Solve: What will be the final volume of a 5.00 L He gas which contains 0.965 mole
at 30°C and 1.00 atmosphere, if the amount of this gas is increased to 1.80 moles
provided that the temperature and pressure remains unchanged?
Given: V1 = 5.00L V2 = ?
𝒏𝟏 = 0.965 mole 𝒏𝟐 = 1.80 moles

𝑽𝟏 𝒏 𝟐
Formula: 𝑽𝟐 =
𝒏𝟏

4. Ideal Gas Law

Gases can be described in terms of the four parameters – pressure(P), absolute
temperature (T), volume(V), and the number of moles(n) – combined into the single
expression:
𝒏𝑹𝑻
𝑽= or 𝑷𝑽 = 𝒏𝑹𝑻
𝑷
where:
V = volume in liters
P = pressure in atmosphere
n = moles
T = temperature in Kelvin
R = universal gas constant = 0.0821 L atm/
mol K
Solve: What is the volume of a container that can hold 0.50 mole of gas at 25.0°C
and 1.25atm?
Given: V1 = ?
n = 0.50 mole
T = 250C + 273.15= 298.15 K
P = 1.25 atm
R = 0.0821 L atm/
mol K

𝒏𝑹𝑻
Formula: 𝑽 =
𝑷

22
 23
Lesson 1: Boyles Law
What's In
What I Know
1.C 7. C A.
2.A 8. C 1. temperature
3.D 9. D 2. volume
4.A 10. D 3. pressure
5.A 11. A 4. mass
6.A 12. B. 5. pressure
13. C B.
14. C Volume Pressure Temperature
15. A cubic meter (m3) Pascal (Pa Kelvin (K),
cubic decimeter atmosphere (atm) degrees Celsius (0C)
What’s New (dm3) millimeter of degrees Fahrenheit
Q1. a volume decreases cubic centimeter mercury (0F)
b. volume increases (cm3) (mmHg)
Q2. a. pressure decreases liter (L) centimeters of
b. pressure increases milliliter (mL) liter mercury
Q3. halved, doubled (L) (cmHg)
Q4. Inversely proportional milliliter (mL) liter Torr
Q5. Increase pressure in the (L) lb/in2 (psi)
cylinder gas quart (qt)
gallon (gal)
What’s More
What I Have Learned
1. Final Answer: V2=11.67L 1. Robert Boyle 9. pressure
2. Final Answer: P2=2.94 atm 2. volume 10. inversely
3. Final Answer: V2=10.85L 3. pressure 11. temperature
4. temperature 12. pressure
5. volume 13. P1V1=P2V2
6. increased. 14. initial pressure
7. decreased 15. final volume
8. volume
Lesson 2:
Charles’ Law- What’s More What’s More
What’s New A. Problem Solving B. Assessment
Activity 1: Blow Me Up! 1. V2 =2656.99m3
1.The balloon becomes bigger when 2. T2 = 99.9 What I have Learned:
it was placed on top of the bowl 1. directly
B. Assessment 2. temperature
filled with hot water.
2. The balloon becomes smaller 1.D 3. pressure
when it was placed on top of the 2.D 4. Kelvin
bowl filled with ice water. 3.B 5. Volume
3. The temperature is directly 4.B 6. directly
proportional to the volume of gas in 5.A 7. temperature
8. pressure,
the balloon which means as the
9. increases
temperature increases the volume
10. temperature and vice-versa.
of the gas in the balloon increases. 11. double.
12.pressure,
Activity 2: 13.V1T1 = V2T2
Analyze and Describe Me 14.initial volume
1. The graph is a straight-diagonal 15.final temperature
graph.
2. The volume of a fixed amount of
gas is directly proportional to the
Kelvin (K) temperature.
Answer Key
 24
What’s More:
Part 1: Identification
1. Directly proportional
2. Increase temperature
3. Spherical bodies
4. Random motion
5. temperature
Part 2: True or False
1.False 6. True
2. False 7. False
L
3. True 8. True
4. False 9. False
5. True 10. False
Part 3: Modified true or false
1.True
2.Elastic
3.True
4.True
5.True
What I Have Learned Rubrics for the “WHAT I CAN DO”
A. kinetic molecular theory, postulates Application of Gas Law
1. molecules straight lines Explain the process depicted in each picture and relate it
2. molecules distances to Boyle’s or Charles’ Law of gas. C
3.collisions molecules
4. forces elastic POINT CRITERIA
5. kinetic energy kelvin 3 Explained both the process in the picture
B. presented and its relationship to the particular
1. volume increases, law of gas.
2. pressure 2 Explained only the process in the picture
presented.
Explained only the particular law of gas in the
Assessment:
1.A 9. C picture presented.
2.A 10.B 1 Explanation is not clear , but answered the
3.D 11.A question.
4.D 12.B
5.B 13.B
6.C 14.A
7.D 15.C
8.B
References

Alfonso, Florante, L. et al (2017) World of Science for Critical Thinkers 10. Quezon
City,The Library Publishing House

Belford, R. (2020) Kinetic Molecular Theory of Gases. retrieved from:

https://chem.libretexts.org/Courses/University_of_Arkansas_Little_Rock/C
hem_1402%3A_General_Chemistry_1_(Belford)/Text/10%3A_Gases/10.5%3
A__Kinetic_Molecular_Theory_of_Gases
Bewick, S., Parsons, R., Forsythe, T., Robinson, S. and Dupon, J. (2020).
Introductory Chemistry (CK-12): Charles's Law. Retrieved from:
https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/
Book%3A_Introductory_Chemistry_(CK-
12)/14%3A_The_Behavior_of_Gases/14.04%3A_Charles's_Law

Brown, LeMay, Busten, Murphy, and Woodward (2020) Kinetic-Molecular Theory.

Retrieved from:
https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Che
mistry_The_Central_Science_(Brown_et_al.)/10%3A_Gases/10.7%3A_Kinetic
-Molecular_Theory
BYJU’S Learning App (2019) Boyle’s Law. Retrieved from:
https://byjus.com/chemistry/boyles-law/

Lower, S. (2017) Pressure-volume relations: Boyle's law. Retrieved from:

http://www.chem1.com/acad/webtext/gas/gas_2.html

Lumencandella (n.d.) Kinetic Molecular Theory. Retrieved from:

https://courses.lumenlearning.com/boundless-chemistry/chapter/kinetic-
molecular-theory/

Pavico, Josefina Ma. F.et al (2015) Exploring Life Through Science, The New Grade
10, Quezon City, Phoenix Publishing House.
Republic of the Philippines, Department of Education, (2015) Science 10 Learner’s
Material, Rex Bookstore, Inc.

Republic of the Philippines, Department of Education, (2015) Science 10 Teacher’s

Guide, Rex Bookstore, Inc.

25
 SCIENCE 10 LEARNING ACTIVITY
MODULE 1: GAS LAWS
(WEEK 1-2)

Name: ___________________________Grade & Section:______________ Score______

Most Essential Learning Competency: Investigate the relationship between volume and
pressure at constant temperature of a gas. (K to 12 BEC CG: S10MT-IVa-b-21)

Title of the Activity: Boyle’s Law

Part 1: Matching Type
Directions: Match column A with column B. Write the letter only on the space provided
before the number.
Column A Column B
______1. Acceleration due to gravity a. 9.8 m/s
______2. Boyle’s Law b. Pressure
______3. Force/ Area c. Robert Boyle
______4. Unit of mass d. Force
______5. Mass(Kg) x Acceleration due to gravity(m/s2) e. Kilogram( Kg)
______6. Pressure f. Litres ( L )
______7. Volume g. N/m2
______8. 1 atm. h. 760 mm Hg
______9. Temperature i. Kelvin
______10. 00C j. 273.15 K
Part 2: Problem Solving
Directions: Solve completely the following word problems on Boyle’s Law. Use the
Boyle’s Law equation below: Use a separate sheet of paper for your answers.
V1 P1 = V2 P2
Where: V1 = initial volume P1 = initial pressure
V2 = final volume P2 = final pressure
1. Oxygen gas inside a 1200 litres gas tank has a pressure of 1.0 atm. If the temperature
remains constant , how much pressure is needed to reduce its volume by one- half (1/2) ?
2. A scuba diver needs a diving tank in order to provide breathing gas while he is under
water. Calculate the pressure needed for 6.50 litres of gas at 1.02 atmospheric pressure to be
reduced in a 3.25 litres cylinder.

26
 3. Robert has a 4.5 litres of gas in a piston at a pressure of 1.45 atm. What will be the new
pressure inside the piston to reduce the volume of the gas to 3.60 litres?
4.You have added 10 litres of air to a balloon at 1.0 atm. What is the new volume of the
balloon if you take it to a 0.90 atmospheric pressure ?
5.A car with an internal volume of 10,500 litres, drove into the river and imploded. What is
the volume of the gas when 1.0 atmospheric pressure increased to 1.2 atm.?
Title of the Activity: Charles’ Law
Part 3: Fact or Fake news
Directions: Analyze carefully the given data in tables 1 and 2 and the graph. Write the word
FACT if the statement / answer is true and FAKE NEWS if the statement/ answer is false.

A. Table 1. Data on determining the size of the balloon of different temperatures

Set - up Average Average Circumference of the balloon
Temperature ( cm)
(0 C)
Before After Difference
Warm water 60 20 30 10
Tap water 37 10 15 5
Ice water 20 5 8 3

__________1. There is a change in the size of the balloon. It becomes smaller as the
temperature decreases.
__________2. The change in the temperature is directly proportional to the volume of gas in
the balloon.

B. Table 2. Data on Volume –Temperature relationship

Trial Volume Temperature Temperature
Reading(mL) (0 C ) (K)
1 30 3 276.15
2 35 58 331.15
3 40 105 378.17
4 45 154 427.15

__________3. K = 30 C+ 273.15 = 276.15K

__________4. K= 580 F + 273.15 = 331.15 K
__________5. K= 105 0C + 273.15 = 378.15 K
__________6. K = 154 0C + 273.15 = 428.15 K

27
 C. Graph of volume against temperature( data from table 2).
50
40
30
20
10
0
276.15 331.15 378.15 427.15

Temperature (K)

_________7. The line graph is labelled properly.

_________8. The volume is on the y- axis.
_________9. The values of the temperature in Kelvin (K) is increasing.
_________10. The values of the volume in millilitre (mL) is decreasing.

Part 4: Problem Solving

Directions: Solve completely the following word problems on Charles’ Law. Use the
Charles’s Law equation. Use a separate sheet of paper for your answers.
V1 = V2
T1 T2
Where V1 = initial volume T1 = initial temperature
V2 = final volume T2 = final temperature
To convert 0 C to K , use the formula : K= 0C + 273.15

1, A cylinder with a movable piston contains 255 cm3 air at 100C. At what temperature would
you expect the volume to be 155 cm3 if the pressure is kept constant?

2. A tank ( not rigid) contains 2.5 litres of helium gas at 28 0C . At constant pressure, what will
be the volume of the tank after heating it and its content to 430C temperature?

3. At 250C, the volume of chlorine gas is 15 dm3 .What is the resulting volume if the
temperature is adjusted to 320K provided that the pressure remains constant?

4. A 2.5 litre sample of a gas is heated from 250 C to 550C at constant pressure. Compute the
volume at the higher temperature?

5, A balloon has a volume of 2.25 L when the temperature is 40 0C. What will be the volume if
the balloon is cooled to 120C? Assume the pressure to be constant.

28