includes formulas and sample problem

1. Prepared by: Ms. Hanna Mae G. Hernani
Gas Laws

2. The gas laws are the product of countless
experiments on the physical properties of gases
that were carried out over several centuries.

3. Volume-Pressure Relationship
BOYLE’S LAW

4. ROBERT BOYLE (1627-1691):
An English chemist who
the first to investigate the
relationship between pressure of
a gas and its volume.

5. 𝑽 ∝
𝟏
𝑷
Where T is constant
“if the temperature is of a
fixed amount of gas is
held constant, then the
pressure exerted by the
gas is inversely
proportional to the
volume of the gas”

6. If the volume or pressure of a given
amount of any gas changes, at
constant temperature, the new
pressure and volume will give the
same PV product as the initial pressure
and volume.
Thus,
𝑷 𝟏 𝑽 𝟏 = 𝑷 𝟐 𝑽 𝟐

7. 𝑷 𝟏 𝑽 𝟏 = 𝑷 𝟐 𝑽 𝟐
From the general formula, the ff. formulae can be derived:
𝑷 𝟏 =
𝑷 𝟐 𝑽 𝟐
𝑽 𝟏
𝑽 𝟏 =
𝑷 𝟐 𝑽 𝟐
𝑷 𝟏
𝑷 𝟐 =
𝑷 𝟏 𝑽 𝟏
𝑽 𝟐
𝑽 𝟐 =
𝑷 𝟏 𝑽 𝟏
𝒑 𝟐





8. Sample Problem:
1. Oxygen gas inside a 1.5 L gas tank has a pressure of 0.95 atm.
Provided that the temperature remains constant, how much pressure is
needed to reduce its volume to ½?
Given: V1 = 1.5 L P1 = 0.95 atm
V2 = 0.75 L
RTF: P2 = ?
Solution:
𝑃2 =
(𝟎.𝟗𝟓 𝒂𝒕𝒎)(𝟏.𝟓 𝑳)
𝟎.𝟕𝟓 𝑳
𝑃2 =
𝟏.𝟒𝟐𝟓 𝒂𝒕𝒎 𝑳
𝟎.𝟕𝟓 𝑳
𝑃2 = 1.9 𝑎𝑡𝑚𝑷 𝟐 =
𝑷 𝟏 𝑽 𝟏
𝑽 𝟐

9. Sample Problem:
2. A scuba diver needs a diving tank in order to provide
breathing gas while he is underwater. How much pressure is
needed for 6.0 liters of gas at 1.01 atmospheric pressure to be
compressed in a 3.0 liter cylinder?
3. Freon in an air-conditioning unit has a volume of 0.30 liter.
It is allowed to function in a room where the pressure is about
268 mm Hg, assuming that the temperature is in constant
state. Find the final pressure of Freon when its volume is
increased to 0.95 liters.

10. Sample Problem:
4. 2.00 L of a gas is at 740.0 mmHg pressure. What is its
volume at standard pressure?
5. 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?

11. A.S # 4.3 A: Boyle’s Law
A sample of gas has a volume of 20 L at 1.5 atm. What will be
the volume of this gas at each of the following pressures: (a)
700 mm Hg, (b) 2 atm, and (c) 230 kPa?

12. Volume-Temperature Relationship
CHARLES’S LAW

13. JACQUES CHARLES (1746-1823):
French mathematician,
and inventor who was the first to
ascend in a hydrogen balloon.
He developed the Charles’ law
concerning the thermal expansion
gas.

14. 𝑽 ∝ 𝑻
Where P is constant
“at constant pressure, the
volume (V) of a gas is
directly proportional to its
absolute temperature”
In equation form, we get:
𝑽 = 𝒌𝑻

15. For a given sample of gas
under two different
conditions at a constant
pressure, the equation can
be written as:
𝑽 𝟏
𝑻 𝟏
=
𝑽 𝟐
𝑻 𝟐
or 𝑽 𝟏 𝑻 𝟐 = 𝑽 𝟐 𝑻 𝟏

16. 𝑽 𝟏
𝑻 𝟏
=
𝑽 𝟐
𝑻 𝟐
or 𝑽 𝟏 𝑻 𝟐 = 𝑽 𝟐 𝑻 𝟏
From the general formula, the ff. formulae can be derived:
𝑽 𝟏 =
𝑽 𝟐 𝑻 𝟏
𝑻 𝟐
𝑻 𝟏 =
𝑽 𝟏 𝑻 𝟐
𝑽 𝟐
𝑽 𝟐 =
𝑽 𝟏 𝑻 𝟐
𝑻 𝟏
𝑻 𝟐 =
𝑽 𝟐 𝑻 𝟏
𝑽 𝟏





17. Sample Problem 1: A cylinder with a movable piston
contains 250 cm3
air at 10℃. If the pressure is kept
constant, at what temperature would you expect the
volume to be 150 cm3
?
Given: V1 = 250 cm3
V2 = 150 cm3
T1 = 10 ℃ = 283 K
RTF: T2 = ?
Solution:
𝑇2 =
(𝟏𝟓𝟎 𝒄𝒎 𝟑)(𝟐𝟖𝟑 𝑲)
𝟐𝟓𝟎 𝒄𝒎 𝟑 𝑇2 =
𝟒𝟐,𝟒𝟓𝟎 𝒄𝒎 𝟑 𝑲
𝟐𝟓𝟎 𝒄𝒎 𝟑 𝑇2 = 169.8 𝐾𝑻 𝟐 =
𝑽 𝟐 𝑻 𝟏
𝑽 𝟏

18. Sample Problem 2: Three liters of hydrogen at -20 ⁰C is
allowed to warm to 27 ⁰C. What is the volume at this
temperature if the pressure remains constant?
Given: V1 = 3 L T2 = 27 ℃ = 300 K
T1 = -20 ℃ = 253 K
RTF: V2 = ?
Solution:
𝑉2 =
(𝟑 𝑳)(𝟑𝟎𝟎 𝑲)
𝟐𝟓𝟑 𝑲
𝑉2 =
𝟗𝟎𝟎 𝑳 .𝑲
𝟐𝟓𝟑 𝑲
𝑽 𝟐 = 𝟑. 𝟓𝟔 𝑳𝑽 𝟐 =
𝑽 𝟏 𝑻 𝟐
𝑻 𝟏

19. 1. A sample of oxygen occupies a volume of 160 𝑑𝑚3
at 91° C.
What will be volume of oxygen when the temperature drops
to 0.00 °C?
2. On hot days, you may have noticed that potato chip bags
seem to “inflate”, even though they have not been opened. If I
have a 250 mL bag at a temperature of
19 °C, and I leave it in my car which has a temperature of 600
°C, what will the new volume of the bag be?
A.S # 4.4: Charles’s Law
LT: To solve problems applying Charles’s Law

20. 3. At 1.01 atm and 15.0 °C, a constant-pressure tank has
255 m3
of propane. What is the volume of the gas at 48.0
°C?
A.S # 4.4: Charles’s Law

21. Temperature-Pressure Relationship
Gay-Lussac’s Law

22. Joseph Louis Gay-Lussac (1778-1850)
A French chemist and physicist.
He proved the relationship between the
temperature and the motion of the gas
particles through his experiment.

23. “the pressure of a fixed amount of gas
is directly proportional with the
absolute temperature (Kelvin) when
volume and amount of gas remains
constant”
𝑷 𝟏
𝑻 𝟏
=
𝑷 𝟐
𝑻 𝟐
or 𝑷 𝟏 𝑻 𝟐 = 𝑷 𝟐 𝑻 𝟏
Gay-Lussac’s Law

24. 𝑷 𝟏
𝑻 𝟏
=
𝑷 𝟐
𝑻 𝟐
or 𝑷 𝟏 𝑻 𝟐 = 𝑷 𝟐 𝑻 𝟏
From the general formula, the ff. formulae can be derived:
𝑷 𝟏 =
𝑷 𝟐 𝑻 𝟏
𝑻 𝟐
𝑻 𝟏 =
𝑷 𝟏 𝑻 𝟐
𝑷 𝟐
𝑷 𝟐 =
𝑷 𝟏 𝑻 𝟐
𝑻 𝟏
𝑻 𝟐 =
𝑷 𝟐 𝑻 𝟏
𝑷 𝟏

25. Sample Problem 1: At 20°C a confined ammonia gas
has a pressure of 2.50 atm. At what temperature
would its pressure be equal to 760 mm Hg?
Sample Problem 2: The helium tank has a pressure
of 650 torr at 25°C. What will be the pressure if the
temperature is tripled?

26. 1. A scuba tank is filled with air at 16.7 atm at 24 °C, but someone
leaves it out in the sun to warm to 65 °C. What is the new pressure
in the tank? Assume volume is constant.
2. A container is filled with a gas to a pressure of 1.25 atm at
20 °C:
(a) What pressure will develop within the sealed container if it
is heated to 70 °C?
(b) At what temperature would the pressure be 2.50 atm?
(c) At what temperature would the pressure be 1.00 atm?
A.S # 4.5: Gay-Lussac’s Law
LT: To solve problems applying Gay-Lussac’s Law

27. Combined Gas Law
Volume-Pressure-Temperature
Relationship

28. The gas laws can be
combined and treated as a
single law which describes the
relationship between
pressure, temperature and
volume.
Combination of Boyle’s law,
Charles’s law, and Gay-
Lussac’s law
Combined Gas Law

29. “the pressure and volume gas are inversely
proportional to each other but, are both directly
proportional to temperature”
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐
or 𝑷 𝟏 𝑽 𝟏 𝑻 𝟐 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
Combined Gas Law

30. 𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐
or 𝑷 𝟏 𝑽 𝟏 𝑻 𝟐 = 𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
From the general formula, the ff. formulae can be derived:
𝑷 𝟏 =
𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
𝑽 𝟏 𝑻 𝟐
𝑽 𝟏 =
𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
𝑷 𝟏 𝑻 𝟐
𝑻 𝟐 =
𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
𝑷 𝟏 𝑽 𝟏
𝑷 𝟐 =
𝑷 𝟏 𝑽 𝟏 𝑻 𝟐
𝑽 𝟐 𝑻 𝟏
𝑽 𝟐 =
𝑷 𝟏 𝑽 𝟏 𝑻 𝟐
𝑷 𝟐 𝑻 𝟏
𝑻 𝟏 =
𝑷 𝟏 𝑽 𝟏 𝑻 𝟐
𝑷 𝟐 𝑽 𝟐

31. Sample Problem # 1: Helium gas has a volume of
250 mL at 0°C at 1.0atm. What will be the final
pressure if the volume is reduced to 100. mL at
45°C?
Sample Problem # 2: The volume of a gas at 27°C
and 700. mmHg is 600. mL. What is the volume of
the gas at -20.0°C and 500. mmHg?

32. Sample Problem # 3: A 350 cm3
sample of helium
gas is collected at 22 °C and 99.3 kPa. What
would this gas occupy at standard Temperature
Pressure (STP)?
NOTE:
Standard Temperature = 273 K
Standard Pressure = 1 atm

33. 1. A sample gas occupies a volume of 2.40 L at 685
mm Hg and 130 °C. what would the pressure be (in
mm Hg) if the volume and temperature were
increased to 5.00 L and 210 °C, respectively?
A.S # 4.6: Combined Gas Law
LT: To solve problems applying Combined Gas
Law

34. 2. Given 12.0 L of ammonia gas at 4.0 °C and 630
torr, calculate the pressure (in atm) of 8.50 L of the
gas at 45 °C.
3. A 2-L sample of a gas is collected at 20 °C and
1.5 atm. What is the pressure of the gas at 300 K if
the volume is 5.0 L?
A.S # 4.6: Combined Gas Law

35. REVIEW
QUIZ

36. A. Identify the gas law that fits to the following description:
1. At constant temperature, pressure and volume are
inversely related.
2. If volume doesn’t change, then as temperature
increases, pressure also increases. They are directly
related.
3. The volume of a gas is directly proportional to the
Kelvin temperature if the pressure is held constant.
A.S # 4.7: REVIEW QUIZ

37. 4. This law is a combination of some gas laws. This
law applies only when the number of molecules stays
constant & everything else changes.
B. Solve the following problems.
1. The pressure of a gas tank is 3.20 atm at 22 °C. if the
temperature rises to 60.0 °C , what will be the gas pressure in
tank?
A.S # 4.7: REVIEW QUIZ

38. 2. A sample of neon gas occupies 0.220 L at 0.860 atm. What
will be its volume at 29.2 kPa pressure?
3. A gas at 89 °C occupies a volume of 0.67 L. At what Celsius
temperature will the volume increase to 1.12 L?
4. A helium-filled balloon at sea level has a volume of 2.1 L
at 0.998 atm and 36 °C. If it is released and rises to an
elevation at which the pressure is 0.900 atm and the
temperature is 28 °C, what will be the new volume of the
balloon?
5. 500 liters of a gas at 27 °C and 700 torr would occupy
volume at STP?

39. Avogadro’s Law
Volume-Amount Relationship

40. He is best known for his hypothesis
that equal volumes of different
gases contain an equal number of
molecules, provided they are at the
same temperature and pressure.
Lorenzo Romano Amedeo Carlo
Avogadro (1776-1856)

41. “at constant pressure and
temperature, the volume of a
gas is directly proportional
to the number of moles of
the gas present”
𝑽 𝟏
𝒏 𝟏
=
𝑽 𝟐
𝒏 𝟐
or 𝑽 𝟏 𝒏 𝟐 = 𝑽 𝟐 𝒏 𝟏
Avogadro’s Law

42. 𝑽 𝟏
𝒏 𝟏
=
𝑽 𝟐
𝒏 𝟐
or 𝑽 𝟏 𝒏 𝟐 = 𝑽 𝟐 𝒏 𝟏
Below are formulae that can be derived from the general formula:
𝐕𝟏=
𝐕 𝟐 𝐧 𝟏
𝐧 𝟐
𝐧 𝟏=
𝐕 𝟏 𝐧 𝟐
𝐕 𝟐
𝐕𝟐=
𝐕 𝟏 𝐧 𝟐
𝐧 𝟏
𝐧 𝟐=
𝐕 𝟐 𝐧 𝟏
𝐕 𝟏

43. Sample Problem 1: A 2.0 L sample at 20 °C and 750 torr
contains 0.5 moles of gas. If 0.1 mole of the gas at the
same temperature and pressure is added to the sample,
what is the new volume of the gas?
Sample Problem 2: What will be the final volume of a
5.00 L He gas which contains 0.965 mole at 30 °C and
1.00 atm, if the amount of this gas is increased to 1.80
moles provided that temperature and pressure remains
unchanged?

44. A.S # 4.8: Avogadro’s Law
LT: To solve problems applying Avogadro’s Law
1. A sample of gas with a volume of 9.20L
is known to contain 1.285 mol. If the
amount of gas is increased to 2.85 mol,
what is the new volume given that
temperature and pressure is constant?

45. A.S # 4.8: Avogadro’s Law
2. A 6.0 L sample at 25 °C and 2.00 atm
of pressure contains 0.5 moles of a gas.
If an additional 0.25 moles of gas at the
same pressure and temperature are
added, what is the final total volume of
the gas?

46. A.S # 4.8: Avogadro’s Law
3. A 7.25 L sample of nitrogen gas is
determined to contain 0.75 mole of
nitrogen. How many moles of nitrogen gas
would there be in a 20 L sample provided
the temperature and pressure remains
constant?

47. Amount of Gas (n)
The number of moles of the gas is calculated
using the formula:
Number of moles (n) =
𝐦𝐚𝐬𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐠𝐚𝐬
𝐦𝐨𝐥𝐚𝐫 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐠𝐚𝐬
 The molar volume of a gas occupies
22.41 L at STP

48. Problem in finding moles (n):
Sample Problem # 1: For a single year, the
motor vehicles in a large city produced a
total of 9.1 x 106 kg of the poisonous gas
carbon monoxide (CO). How many moles of
CO correspond to?
NOTE:
Carbon’s molecular weight: 12.01 g/mole
Oxygen’s molecular weight: 16.00 g/mole

49. Sample Problem #2: A flask containing H2 at 0
°C was sealed off at a pressure of 1 atm and the
gas was found to weigh 0.4512 g. Calculate the
number of moles of H2 .
Sample Problem # 3: Determine the volume of a
container that holds 2.4 mol of gas at STP.

50. A.S # 4.8 B: Avogadro’s Law
LT: To solve problems applying Avogadro’s Law
1. A balloon containing 2.0 moles of helium has
a volume of 0.8 L. What would the volume be if
3.5 moles of helium are added to the balloon?
2. Calculate the volume that 0.881 mol of gas at
standard temperature and pressure (STP)

51. A.S # 4.8 B: Avogadro’s Law
3. Ten grams of nitrogen has a volume of 2
L. If the amount of nitrogen is increased to
45 g, what new volume will result if the
pressure and temperature remain constant?

52. Ideal Gas Law
Pressure-Volume-Temperature-Amount
Relationship

53. “the volume of a gas varies directly with
the number of its molecules and the
absolute temperature. Volume also varies
inversely with pressure”
V =
𝑹𝒏𝑻
𝑷
or PV = nRT
where R is an ideal gas constant with a value
of 0.0821
𝑳−𝒂𝒕𝒎
𝒎𝒐𝒍−𝑲
Ideal Gas Law

54. V =
𝑹𝒏𝑻
𝑷
or PV = nRT
Below are formulae that can be derived from the
general formula:
P =
𝑹𝒏𝑻
𝑽
n =
𝑷𝑽
𝑹𝑻
T =
𝑷𝑽
𝒏𝑹
Molar mas =
𝒎𝑹𝑻
𝑷𝑽

55. Sample Problem #1:
Calculate the volume (in Liters) occupied by
7.40 g of 𝑵𝑯 𝟑 at STP.
Sample Problem #2:
Sulfur hexafluoride ( 𝑺𝑭 𝟔 ) is a colorless,
odorless, very unreactive gas. Calculate the
pressure (in atm) exerted by 1.82 moles of
the gas in a steel vessel of volume 5.43 L at
69.5 °C.

56. Sample Problem #3:
A 0.135 g sample of a volatile liquid was
vaporized and the gas was collected. The
temperature of the collecting chamber was
kept at 98 °C in order that liquefaction would
not occur. After all the sample was vaporized,
the volume of the gas was measured as 0.0532
liters at 98 °C and 737 mm Hg. Calculate the
molecular mass.

57. A.S # 4.9: Ideal Gas Law
LT: To solve problems applying Ideal Gas Law
1. What is the volume of a container that can hold
0.50 mole of gas at 25 °C and 1.25 atm?
2. Fermentation of glucose produce gas in the form
of 𝐶𝑂2, how many moles of 𝐶𝑂2 is produced if 0.78
L of 𝐶𝑂2 at 20.1 °C and 1.00 atm was collected
during the process?

58. A.S # 4.9: Ideal Gas Law
3. A cylinder contains oxygen at a pressure of
10 atm and a temperature of 300 K. The
volume of the cylinder is 10 liters. What is the
mass of the oxygen?

60.  Chang, R. (2007). Chemistry: Ninth Edition. New York: McGraw-Hill
Companies.
 Valdoz, Meliza et. al. (2017). Science Links: Worktext for Scientific and
Technological Literacy. Manila: Rex Bookstore.
References: