This document provides information about Boyle's law and Charles' law, including: - Definitions of Boyle's law and Charles' law relating the pressure and volume of gases and the volume and temperature of gases. - Examples of calculations using the formulae for Boyle's law and Charles' law to determine changes in pressure, volume, and temperature of gases. - Short biographies of Robert Boyle and Jacques Charles, who discovered the gas laws named after them. - Learning targets about being able to describe and use Boyle's law and Charles' law to calculate gas properties.

2. Rules;
1. Pay attention
2. Raise your hands if you
have questions that is
related to our discussion.
3. Ask permission when you
go to the bathroom.

3. Volume

4. Pressure

5. Temperature

6. Boyle Law

7. Gas Law

8. Learning Targets
At the end of the session, I must be able to say I can…
 describe Boyle’s law and Charles’s law and
 calculate the new properties of a given sample of gas
using the Boyle’s law and Charles’s law.

9. ACTIVIT
Y

10. ACTIVITY
EXPERIENCED

11. ACTIVITY
RESULT

12. BOYLE’S
LAW

13. Robert Boyle
A British scientist. In 1662,
he first observed the
relationship between the
pressure P and the volume
V of a gas from
investigations using air.

15. P V
The relationship of volume and pressure…
Inversely proportional

16. For a given amount of gas at a
constant temperature, Boyle’s law can
be expressed as
𝑽 ∝
𝟏
𝑷
Where ∝ is the proportionally symbol.
Introducing a proportionally constant
k, the equation can be written as
𝑷 = 𝒌
𝟏
𝑽
or PV=k

17. Formula:
𝑷𝟏𝑽𝟏 = 𝑷𝟐𝑽𝟐
Whereas;
𝑃1= initial pressure
𝑃2= final pressure
𝑉1= initial volume
𝑉2= final volume

18. In a 35.0 L automobile airbag, a
certain amount of nitrogen gas exerts a
pressure of 745 mm Hg. If the gas is
transferred to a 25.0 L bag at the same
temperature, what will be its final
pressure.
Sample Problem 1;

19. Given:
P1= 745 mm Hg P2=?
V1= 35.0 L V2= 25. 0
0 L
P1V1=P2V2
𝑷𝟏𝑽𝟏
𝑽𝟐
= 𝑷𝟐
𝑷𝟏𝑽𝟏
𝑽𝟐
=
𝑷𝟐𝑽𝟐
𝑽𝟐
𝟕𝟒𝟓 𝐦𝐦 𝑯𝒈 𝟑𝟓. 𝟎 𝐋
𝟐𝟓. 𝟎 𝑳
= 𝑷𝟐
𝟐𝟔, 𝟎𝟕𝟓 𝐦𝐦 𝑯𝒈
𝟐𝟓. 𝟎
= 𝑷𝟐
𝟏𝟎𝟒𝟑 𝒎𝒎 𝑯𝒈 = 𝑷𝟐

20. P V
Notice the following P-V relationship in the
problem.
P1= 745 mm Hg V1= 35. 0 L
P2= 1043 mm Hg V2= 25. 0 L

21. 2.00 L of a gas at 740 mmHg
pressure. What is its volume at 760
mmHg?
Sample Problem 2;

22. 𝑷𝟏𝑽𝟏
𝑷𝟐
=
𝑷𝟐𝑽𝟐
𝑷𝟐
Given:
𝑃1= 740 mmHg 𝑃2=760 mmHg
𝑉1= 2.00 L 𝑉2=?
𝑷𝟏𝑽𝟏 = 𝑷𝟐𝑽𝟐
𝑷𝟏𝑽𝟏
𝑷𝟐
= 𝑽𝟐
𝟕𝟒𝟎 𝒎𝒎𝑯𝒈 𝟐. 𝟎𝟎 𝐋
𝟕𝟔𝟎 𝐦𝐦𝐇𝐠
= 𝑽𝟐
𝟐𝟐𝟐𝟎 𝑳
𝟕𝟔𝟎
= 𝑽𝟐
𝟏. 𝟗𝟓 𝑳 = 𝑽𝟐
P V

23. If a gas at 25. 0 °C occupies 3.60
liters at a pressure of 1.00 atm, what
will be its volume at a pressure of
2.50 atm?
Board work 1;

24. 𝑷𝟏𝑽𝟏
𝑷𝟐
=
𝑷𝟐𝑽𝟐
𝑷𝟐
𝑷𝟏𝑽𝟏
𝑷𝟐
= 𝑽𝟐
P V
Given:
𝑷𝟏= 1. 00 atm 𝑷𝟐=2.50
atm
𝑽𝟏= 3.60 L 𝑽𝟐=?
𝑷𝟏𝑽𝟏 = 𝑷𝟐𝑽𝟐
𝟏. 𝟎𝟎 𝐚𝐭𝐦 𝟑. 𝟔𝟎 𝐋
𝟐. 𝟓𝟎 𝐚𝐭𝐦
= 𝑽𝟐
𝟑. 𝟔 𝑳
𝟐. 𝟓𝟎
= 𝑽𝟐
𝟏. 𝟒𝟒 𝑳 = 𝑽𝟐

26. CHARLES’S
LAW

27. Jacques Charles
French scientist and inventor Jacques
Charles in the 1780s.

29. P V
The relationship of volume and temperature…
Directly proportional

30. This relationship can be
expressed as;
𝑽 ∝ 𝑻 (at constant pressure)

31. 𝑽𝟏
𝑻𝟏
=
𝑽𝟐
𝑻𝟐
or 𝑽𝟏 𝑻𝟐= 𝑽𝟐 𝑻𝟏
Whereas;
𝑽𝟏 =Initial volume
𝑽𝟐=Final volume
𝑻𝟏=Initial absolute temperature
𝑻𝟐=Final absolute temperature
Note: The temperature should be expressed in Kelvin.
Formula:

32. 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?
Sample Problem 3;

33. Given:
𝑽𝟏= 3 L
𝑻𝟏= 20 °C + 273.15 K = 293.15
K
𝑽𝟐=?
𝑻𝟐=27 °C + 273.15= 300.15 K
𝑽𝟏
𝑻𝟏
=
𝑽𝟐
𝑻𝟐
or 𝑽𝟏 𝑻𝟐= 𝑽𝟐 𝑻𝟏
𝑽𝟏 𝑻𝟐= 𝑽𝟐 𝑻𝟏
𝑽𝟏 𝑻𝟐
𝑻𝟏
=
𝑽𝟐 𝑻𝟏
𝑻𝟏
𝑽𝟏 𝑻𝟐
𝑻𝟏
= 𝑽𝟐
(𝟑 𝑳)(𝟑𝟎𝟎.𝟏𝟓 𝑲)
𝟐𝟗𝟑.𝟏𝟓𝑲
= 𝑽𝟐
𝟗𝟎𝟎.𝟒𝟓
𝟐𝟗𝟑.𝟏𝟓𝑲
= 𝑽𝟐
𝟑. 𝟎𝟕 𝑳 = 𝑽𝟐
V T

34. A gas in a container has an initial
volume at 2 L and an initial temperature
of 25 °C. The final volume decreases to
0.25 L. What is the final temperature?
Sample Problem 4;

35. 𝑽𝟏 𝑻𝟐= 𝑽𝟐 𝑻𝟏
𝑽𝟏 𝑻𝟐
𝑽𝟏
=
𝑽𝟐 𝑻𝟏
𝑽𝟏 V T
Given:
V1= 2 L
T1= 25 °C + 273.15 K = 298. 15 K
V2= 0.25 L
T2= ?
𝑻𝟐=
𝑽𝟐 𝑻𝟏
𝑽𝟏
𝑻𝟐=
𝟎.𝟐𝟓 𝑳 (𝟐𝟗𝟖.𝟏𝟓𝑲)
𝟐 𝑳
𝑻𝟐=
𝟕𝟒.𝟓 𝑲
𝟐 𝑳
𝑻𝟐 = 𝟑𝟕. 𝟐𝟕 K
37.27 K- 273.15= -235.88 °C

36. During the day at 27 °C a cylinder
with top contains 20.0 liters of air. At
night it only holds 19 liters. What is
the temperature at night?
Board work 2;

37. 𝑽𝟏 𝑻𝟐= 𝑽𝟐 𝑻𝟏
𝑽𝟏 𝑻𝟐
𝑽𝟏
=
𝑽𝟐 𝑻𝟏
𝑽𝟏 V T
𝑻𝟐=
𝑽𝟐 𝑻𝟏
𝑽𝟏
Given;
𝑽𝟏= 20 L
𝑻𝟏= 27 °C + 273.15 K = 300. 15 K
𝑽𝟐= 19 L
𝑻𝟐= ?
𝑻𝟐=
𝟏𝟗 𝑳 (𝟑𝟎𝟎.𝟏𝟓𝑲)
𝟐𝟎 𝑳
𝑻𝟐=
𝟓𝟕𝟎𝟐.𝟖𝟓 𝑲
𝟐𝟎
𝑻𝟐 = 𝟐𝟖𝟓. 𝟏𝟒 K
𝟐𝟖𝟓. 𝟏𝟒 K- 273.15= 11.99 °C

38. 3. A 2.5 L container has a gas pressure of 4.6 atm.
If the volume is decreased to 1.6 L. What will be
the new pressure inside the container?
4. A 275 mL balloon is filled with air at 25 °C.
If the temperature is increased to 50 °C,
what is the new volume of the balloon?
Board work 3 & 4

39. Assessment;
1. A gas occupies a volume of 1 L and exerts a pressure
of 400 kPa on the walls of its container. What would be the
pressure exerted by the gas if it is completely transferred
into a new container having a volume of 3 litres
(assuming that the temperature and amount of the gas
remain the same.)?
2. Calculate the decrease in temperature when 2. 00 L at
20. 0 °C is compressed to 1.00 L.

40. Despite being red, Mars is
a cold place. It's full of iron
oxide dust, which gives
the planet its reddish cast
Venus has a beautiful
name and is the second
planet from the Sun. It’s
hot, even hotter than
Mercury
Earth is the third planet
from the Sun and the only
one that harbors life in the
Solar System
Saturn is a gas giant and
has several rings. It's
composed mostly of
hydrogen and helium
Mars Venus Neptune
It’s the farthest planet
from the Sun. It's also the
fourth-largest planet by
diameter of them all
It’s the biggest planet in
the System. It's the fourth-
brightest object in the
night sky
Earth Saturn Jupiter

41. Column graph
Team 4
Team 3
Team 2
Team 1
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Earth has life
Venus is very hot
Mercury is small
Mars is very cold

42. Table
Team A Team B Team C Team D Team E Team F
Mercury XX XX XX XX XX XX
Mars XX XX XX XX XX XX
Saturn XX XX XX XX XX XX
Venus XX XX XX XX XX XX
Jupiter XX XX XX XX XX XX
Earth XX XX XX XX XX XX

43. Timeline
Mercury is a very
small planet
20XX
Venus has a
beautiful name
20XX
Earth is the third
planet from the
Sun
20XX
Mars is actually a
cold place
20XX
Jupiter is a gas
giant and it’s very
big
20XX
Sun is the star at
the center
20XX

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Customer
relationships
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segments
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Mars is full of iron
oxide dust
Venus is the second
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Mercury is quite a
small planet
Jupiter is a huge
gas giant
Key resources Channels
Saturn is a planet
that has rings
Neptune is far away
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Jupiter was named after a Roman god Earth is also known as the Blue Planet

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Model 2
Model
3
Model
4
You
Company 1 Company 2
Company 3

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Age: 25-40 years old
Gender: 70% men 30% women
Job: Scientist
Income: 55,000/ year
Psychographics
Behavior Channels
Geographic
● Venus is a hot planet
● Mercury is very small
● Mars is made of basalt
● Jupiter is a gas giant
Venus has a beautiful name and
is the second planet from the
Sun. It’s hot and has a
poisonous atmosphere
● Channel 1
● Channel 2
● Channel 3

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CEO
Jupiter
Department Head
Neptune
Department Head
Mars
Manager
Venus
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Earth
Manager
Saturn
Manager
Triton
Employee
Titan
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Mercury
Employee
Moon
Employee
Callisto
Employee

48. Market size infographic
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Jupiter
Jupiter is a gas giant and the biggest planet
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Mars
Despite being red, Mars is actually a cold
place. It's full of iron oxide dust, which gives
the planet its reddish cast
Saturn
Saturn is a gas giant and has several rings.
It's composed mostly of hydrogen and
helium. It was named after a Roman god

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