1.
Gas Laws

2.
• To state the laws that govern
gas behavior and express the
gas laws in equation form
Learning Objective

3.
• Understanding the laws that govern gas
behavior and the use of ideal gas
equation to calculate pressure, volume,
temperature, or number of moles of a gas
Key Understanding
• What are the laws that govern gas
behavior?
Key Question

4.
• At constant temperature, the pressure of a fixed quantity
of a gas varies inversely with the volume. This means
that if the pressure on a gas sample is increased without
changing the temperature, the volume of the gas will
decrease proportionally or that if the pressure on the gas
is doubled, the volume will be halved. The law may be
expressed mathematically by the equation:
P1V1 = P2V2
• The inverse relationship between P and V can be seen
from a plot of P versus V at constant temperature called
an isotherm.
Boyle’s Law

5.
Robert Boyle (1627–1691) was born at
Lismore Castle, Munster, Ireland, the
14th child of the Earl of Cork. Boyle’s
chief scientific interest was chemistry
but his first published scientific work
entitled “New Experiments Physico-
Mechanical, Touching the Spring of the
Air and Its Effects” (1660), concerned
the physical nature of air. This was
shown in his experiments where he
used an air pump to create a vacuum.
The second edition of this work
(1662) described the quantitative
relationship that Boyle derived from
experimental values, presently known
as “Boyle’s law”: that the volume of a
gas varies inversely with pressure.

6.
Sample Problem:
▪ A gas sample exerts a pressure of 3.0 kPa when it
occupies a 12.0-L vessel at 20oC. What pressure would
the gas exert at 20oC if same gas sample is transferred
to a 9.0-L vessel?
Given: P1 = 3.0 kPa P2 = unknown
V1 = 12.0 L V2 = 9.0 L
T1 = 20 + 273 = 293 K T2 = 293 K
Solution:
The temperature is unchanged; therefore, Boyle’s Law will be used.

7.
Practical Applications of Boyle’s Law
➢ Syringes operate by Boyle’s Law: When the plunger is
pulled, the volume inside the syringe increases, causing
a decrease in pressure inside the syringe. The decrease
in pressure causes the causes the liquid to be drawn
into the drawn into the syringe, thereby causing the
volume of the air to decrease again.
➢ Spray cans used in spray paint and air freshener are
governed by Boyle’s Law. High pressure inside the can
pushes on the liquid inside the can and forces the liquid
out when the cap is opened.

8.
• At constant pressure, the volume of a fixed quantity of a
gas is directly proportional to the absolute temperature.
This means that provided the pressure on the gas
remains constant, the volume will increase proportionally
to the absolute temperature, that is, the volume of the gas
will double if the absolute temperature (NOT the
temperature in the Celsius or Fahrenheit scale!) is
doubled. The direct relationship between volume and
absolute temperature at constant pressure is described in
a plot called an isobar). Mathematically, the law may be
expressed.
Charles’ Law

9.
Jacques Charles (1746-1823) was
the proponent of Charles’ law (1787).
Charles was a French-born balloonist
who flew the firrst hydrogen balloon
in 1783. Charles did an experiment
where he filled five different
balloons with the same volume of
five different gases. He observed
that the balloons expanded
uniformly when heated uniformly.
This observation was not
published until 1802, by Gay-Lussac,
but was named for the original
observer, Charles.

10.
Sample Problem:
▪ A gas sample is observed to occupy 12.0 L under a
pressure of 101.325 kPa (also 1 atm) at 27oC. What will
be the volume of the gas if it is heated to 57oC under the
same pressure?
Given: P1 = 101.325 kPa P2 = 101.325 kPa
V1 = 12.0 L V2 = unknown
T1 = 27 + 273 = 300 K T2 = 57 + 273 = 330 K
Solution:
Since pressure is constant, Charles’ law will be applied.

11.
Practical Applications of Charles’ Law
➢ A balloon that has been inflated inside a cool building expands
when it is carried to a warmer area like the outdoors. This is why we
often see balloons just bursting even when nobody is near it.
➢ The capacity of the human lungs is reduced in colder weather. This
is why athletes who come from countries with warm climates like
the Philippines may find it difficult to perform well in countries with
severely cold weather due to difficulty in breathing. For the same
reason, asthmatic people usually experience asthma attacks when
there is a sudden change in temperature.
➢ Charles’ law, along with other gas laws, can explain the process of
leavening for the or rising of bread and other baked goods during
baking. Small pockets of CO2 gas produced by the action of yeast
or leavening ingredients expand when heated. This causes the
dough to rise (expand) which results in lighter finished baked goods
➢ Car (combustion) engines work by this principle. The heat of
combustion of the fuel causes the combustion gases in the cylinder
to expand thereby pushing the piston, causing the crankshaft to
turn.

12.
• Two gases that occupy equal volumes under the
same temperature and pressure contain the
same number of moles (or the same number of
molecules). At standard temperature (0oC or 273
K) and pressure (1 atm or 101.3 kPa), one mole
of any ideal gas will occupy 22.413 L and contain
6.02 x 10 23 molecules.
Avogadro’s Law

13.
More than 200 years ago, a paper
proposing the idea that equal
volumes of different gases, at the
same temperature and pressure,
contain an equal number of
molecules—was published in the
Journal de Physique. The paper’s
author was Italian mathematical
physicist Amedeo Avogadro, and his
idea became known as Avogadro’s
law, which is now a fundamental
concept in the physical sciences.

14.
Practical Applications of Avogadro’s Law
➢ Avogadro’s law, with other gas laws, explains why bread and other
baked goods rise. Yeast or other leavening agents cause the
production of carbon dioxide gas and ethanol. The carbon dioxide
forms bubbles which appear as holes in the dough. As the yeast
continues the leavening process, the number of particles of carbon
dioxide increases, hence causing an increase in the number, or
volume, of bubbles and in the size of the dough.
➢ Inflation of a balloon demonstrates of Avogadro’s law. When a
person inflates a balloon, he places more gas particles inside the
balloon, so as the number of gas particles increases, volume of the
balloon increases.
➢ We demonstrate Avogadro’s law when we breathe. As the lungs
expand when we inhale, more oxygen molecules from the air enter
the lungs. When the lungs contract, carbon dioxide gas molecules
are expelled (exhaling).

15.
The Ideal Gas Equation of State
Taking into account Boyle’s Law, Charles’ Law, and
Avogadro’s Law and combining the effect of each law on the
volume of a gas, we get the following expressions:
V ∞1 since volume is inversely proportional to pressure;
P
V ∞1 since volume is directly proportional to absolute
P temperature; and
V ∞1 or PV ∞ nT since V is directly proportional to the
P number of moles of the gas.
We finally arrive at the relationship called the Ideal Gas
Equation written as:
PV = nRT

16.
The Ideal Gas Equation of State
where R is the universal gas constant whose value depends
on the units for V, P and T. If we use standard conditions and
apply the values to the ideal gas equation, we get
Sample Problem
▪ Calculate the volume of 22.0 g of CO2 gas at 40oC and
2.0 atm.
▪ Given: m = 22.0 g P = 2.0 atm T = 40 + 273 = 313 K

17.
Solution:
▪ First, we solve for the number of mols of CO2:
n = mass/molar mass = 22.0 g/ (44.0 g/mol) = 0.500 mol
▪ We can now substitute the values in the Ideal Gas
Equation of State:
▪ For the two gases, 1
and 2, we can write
P1V1 = n1RT1 and P2V2 = n2RT2
▪ If we take equal number of moles of the two gases, we
get the combined gas equation.

18.
Solution:
▪ We can also use the ideal gas equation to determine gas
density from pressure and temperature.
▪ Using the definitions of density, (density) = mass/volume,
mass = n x M, and gas volume from the ideal gas
equation, , we get the following equation for density
of an ideal gas.

19.
Section Assessment
1. Which of the following conditions should be done to cause
the density of a gas to increase?
A. Increase the pressure and increase the temperature
B. Increase the pressure and decrease the temperature
C. Decrease the pressure and increase the temperature
D. Decrease the pressure and Decrease the temperature
2. A sample of methane gas is kept in a 15.0 – liter container
fitted with a piston that keeps the gas inside the tank
under a pressure of 740 mmHg at 20°C. How much
pressure must be exerted on the gas to reduce its volume
to 12.0 L without changing the temperature?
A. 925 mm Hg C. 760 mm Hg
B. 592 mm Hg D. 750 mm Hg

20.
Section Assessment
3. A sample of H2 gas is kept in container fitted with a movable
piston set at the 8.0-liter mark at 50°C and 110 kPa. At what
temperature will the piston to move to the 9.0-liter mark without
a change in the pressure reading?
A. 14°C C. 34°C
B. 27°C D. 90°C
4. If 1.0 g of each of the following gases is taken and kept under
the same conditions of temperature and pressure, which gas
will occupy the smallest volume?
A. H2 C. N2
B. CH4 D. CO2
5. An LPG tank contains 11.0 kg of butane gas, (C4H10), in a 20.0-
liter gas tank. What must be the pressure of the gas inside the
tank when the temperature is 27°C?