Gas Laws
Background – Science Laws, Theories and Hypotheses
Laws are generalizations or universal relationships related to the way that some aspect of
the natural world behaves under certain conditions. Therefore, laws are different from
hypothesesand theories in science.
An initial investigation provides some evidence (data) that must be explained and tested further.
This tentative explanation, or hypothesis, forms the foundation for further investigations. If the
hypothesis is supported, more investigations are done. As it becomes stronger, it becomes more
predictive and explanatory. At this point, the hypothesis becomes a theory: a broad explanation
that has been supported with data and is a well substantiated, consistent explanation for a
naturaloccurrence.
Theories evolve as a result of continued testing. When evidences is found that is inconsistent
with or not predicted by the theory, it must be changed. In some cases, a new theory must be
proposed and tested further.
I. Kinetic Theory of Gases
This theory helps us understand why gases behave the way they do and give us
insight into the behavior of solids and liquids. There are five basic postulates of this
theory.
1. Particles in a gas have no volume and are very far apart.
2.Particles in a gas move in straight line paths and random
directions.
3. Particles in a gas collide frequently with the sides of
thecontainer and less frequently with each other. All
collisions are elastic (no energy is gained or lost as a
result of the collisions).
4. Particles in a gas do not attract or repel one another.
Thereis no intermolecular attractions.
5. The average kinetic energy of all of the gas particles in
asample is proportional to the temperature of that
gas sample.
II. Temperature
Temperature is a measure of the average kinetic energy of a substance. Many problems we
willbe working use equations which include temperature, it is important to be able to
convert between Celsius and Kelvin. 0 Kelvin is absolute zero; there are not negative
numbers on theKelvin scale.
A. Converting between Celsius and Kelvin.
Celsius to Kelvin
Kelvin to Celsius
B. Example:
Convert:
K = oC + 273
oC = K – 273
–167oC to Kelvin
1100oC to Kelvin
321 Kelvin to Celsius
Gas Laws
III. Pressure: defined as Force/Area. We will not be concerned with the mathematical aspect
of finding pressure, but only using pressures and converting them to various other units.
A. There are different UNITS of pressure used in chemistry and you must be able
toconvert between all of them.
1 atmosphere (atm)
= 760 mm Hg
= 14.7 psi
= 101.3 kPa
 You must be able to
convert pressure units!
Example: Convert a pressure of 1.55 atm to kPa.
Example: Which is higher pressure 1.45 atm or 1000 mm Hg?
Example: Convert 753 psi to atmospheres.
B. Pressure Measurement
1. Standard Temperature & Pressure (STP) is equal to 1 atm at 0°C
III.
Introduction to Gas Laws
Based on the kinetic theory of gases, scientists were able to describe how gases behave
andchange using mathematical equations. There are 4 variables that work together to
determine the behavior of gases – temperature, pressure, volume, and the number of
particles.
A. When you blow up a balloon, you are adding gas molecules
& the pressure increases. This is because more molecules
are colliding within a given space.
 Pressure and the number of gas molecules are
directly related. Doubling the number of molecules of
a gas, doubles the pressure.
 Gases naturally flow from areas of high pressure to
lowpressure until the pressure becomes equal.
B. When you push on a bicycle pump or the end of a syringe,
you change the size of the container creating a pressure
that
can be felt. In a smaller container, molecules have less room to move & hit the sides
ofthe container more often. This creates pressure.
2
Gas Laws
C. When you heat a gas, the temperature of a gas increases as a result of increased kinetic
energy. This increase in energy causes the gas molecules to hit the walls of its
containereven harder – resulting in either increased pressure or increased volume.
IV.
Dalton’s Law of Partial Pressure – Equal amounts of gas at the same temperature and
volume have equal pressure. The total pressure inside a container is equal to the
partial pressure due to each gas.
P total = P1 + P2 + P3
A. For instance, we can find the pressure in the fourth container by adding up the
pressurein the first three containers.
2 atm
1atm
3atm
? atm
B. Example: What is the total pressure in a balloon filled with air if the pressure of
theoxygen is 170mmHg and the pressure of nitrogen is 620 mmHg?
Example: In a second balloon the total pressure is 1.3 atm. What is the pressure of
oxygen if the pressure of nitrogen is 720 mmHg?
3
Gas Laws
V.
Boyle’s Law – At constant temperature, pressure and volume are
inversely related. In other words, as volume decreases, the
pressure increases and vice versa.
P1 x V1 = P2 x V2
Example: A balloon is filled with 25 L of air
at 1.0 atm pressure. If the pressure changes
to 1.5 atm, what is the new volume?
Example: A balloon is filled with 73 L of
air at 1.3 atm of pressure. What pressure
isneeded to change the volume to 43 L ?
VI.
Charles’ Law – The volume of a gas is
directly proportional to the Kelvin temperature if the pressure is held constant. As
temperature increases, volume also increases in a linear relationship.
V1 / T1 = V2 / T2
Example: What is the temperature of a gas that is expanded from 2.5L at 25°C to 4.1 L at
constant pressure?
4
Gas Laws
Example: What is the final volume of a gas that starts at 8.3L and 290K and is heated
to369K?
VII.
Gay Lussac’s Law – If volume doesn’t change, then as temperature increases, pressure
also increases. They are directly related. If a gas is in a fixed container, as the
temperature increases the molecules collide more frequently with the
walls of the container causing increased pressure.
P1 / T1 = P2 / T2
Example: What is the pressure inside a 0.250L can of deodorant that starts at
0.250Land 1.2 atm if the temperature is raised to 100°C?
Example: At what temperature will the can above have a pressure of 2.2 atm?
VIII.
Combined Gas Law – this law is a combination of the previous
gas laws. This law applies only when the number of molecules
stays constant & everything else changes.
P1 x V1 = P2 x V2
T1
T2
STUDY TIP
All other gas laws
can be derived from
this one equation
Example: A 15L cylinder at 4.8 atm pressure at 25°C is heated to 75°C and compressed
to 17 atm. What is the new volume?
5
Gas Laws
Example: IF 6.2 L of gas at 723 mm Hg at 294K is compressed to 2.2 L at 4117 mm Hg,
what is the temperature of the gas?
IX.
Ideal Gas Law
A. In reality, an ideal gas does not exist. In this unit however, we are going to assume
that gases behave ideally. This will make our math easier & is a close approximation.
Real gases behave like an ideal gas at high temperature & at low pressure.
B. Pressure (P) times volume (V) equals the number of moles (n) times the ideal gas
constant (R) times the temperature in Kelvin (T)
P x V=n xR xT
where R = 0.0821 (L atm)/ (mol K)
or R = 62.4 (L mm Hg) / (K mol)
Example: How many moles of air are there in a 2.0L bottle at 19°C and 747 mmHg?
6