atm · K -1

Which diagram represents a gas? Why?
Which diagram represents a gas? Why?
Phase of Matter
Close Together
Close Together
Not Definite
Far Apart
Not Definite
Not Definite
Characteristics of Gases
The official way to describe the differences in the phases of matter
comes from the Kinetic Molecular Theory (or Model). The Kinetic
Molecular Theory defines matter in the following two ways:
1. All matter is made up of particles. These can be separate atoms or
compounds/molecules. This is the “molecular” part of the theory.
2. The particles in matter are constantly moving. This is the “kinetic”
part of the theory.
Gases have enough translational energy that they also flow, like
liquids (fluid), and gases are also assumed to:
• have particles in rapid, continuous, and random motion (Brownian
• have collisions that are perfectly elastic (do not chemically react)
with each other and the walls of the container
• have densities significantly less (about 1/1000) than the solid or
liquid form of the same substance
There are intermolecular forces between a substances molecules
(hydrogen bonding, dipole-dipole, etc) that are trying to pull the
molecules closer together.
At the same time the kinetic energy of the molecules is trying to
spread the molecules farther apart as they bump and collide into
each other.
The amount of kinetic energy is directly proportional to the heat
energy of a system, and the heat energy of a system is
comparatively measured by temperature
Kinetic Molecular Theory and Gases
One of the most important properties of gases is the pressure the gas
The pressure of a gas comes from the collisions of the gas particles
on the wall of the container or the interface of the liquid that is
being used to when the pressure of the gas is measured.
As the gas particles hit the walls, some of the kinetic energy is passed
onto the wall. Even though these collisions are elastic (no
chemical reactions occur) the transfer of kinetic energy still
The overall transfer of kinetic energy from the millions of molecules
that hit each second is added up to one big force that is the
pressure of the gas.
Historically the pressure of a gas has been measured using a liquid
trapped in a tube. Evangelista Torricelli (1608-1647) is credited with
making the first barometer in 1643 in an attempt to measure the
weight of air (now more accurately called pressure).
He filled a glass tube that
was closed at one end and
about 3 feet in length with
mercury. Covering the
open end, he inverted the
open end down inside a
tray of mercury. Due to
the force of gravity upon
the mercury in the tube,
some of the mercury
flowed out of the tube and
into the tray, leaving a
vacuum at the top of the
As the atmospheric pressure changes, so does the height of the
mercury inside the tube. Thus a lower amount of mercury means
lower atmospheric pressure and a higher atmospheric pressure
would force more mercury up inside the tube making the level rise.
The level is measured in millimeters, and one of the ways that
pressure is measured is in mm Hg (millimeters of mercury).
Standard atmospheric pressure at sea level is considered to be 760
mm Hg, and is sometimes called a torr after Torricelli (760 mm Hg =
760 torr).
Comparing all the different measurements for the standard
atmospheric pressure at sea level:
760 mm Hg = 760 torr = 101,325 Pa = 14.7 psi = 1 atm
Modern Barometer →
A barometer works well enough for measuring the atmospheric
pressure, but typically pneumatic chemistry is concerned with the
pressure of a confined gas, not the atmosphere.
A manometer measures the pressure of a trapped gas in relationship
to the pressure of the atmosphere. A typical manometer needs to
two parts, a gas container area for the trapped gas, and a U-bend of
glass that is open to the container on one end and the atmosphere
on the other. This U-bend is also filled to a moderate level with
mercury. The sides of the U-bend are then marked in millimeters.
Boyle’s Law
In mathematical terms, P × V = k (a constant).
A more convenient form simply sets the same
gas at one pressure and volume equal to a
different pressure and volume. Usually this
takes the form
P1 × V1 = P2 × V2
This must be for the same gas and kept at the
same temperature
Pressure and Volume
Charles’ Law
Charles’ Law shows a direct relationship
between the volume of a gas and the
temperature of the gas.
As with most things, as the temperature of a gas
increases so does the volume. This law is
represented as:
V1 = V2
T1 T2
Keep in mind that this mathematical relationship
only works for the same gas at two different
temperatures and volumes.
Kelvin Scale!!!!!
For Charles’s Law (and all other gas laws involving a
temperature change) it is necessary to use the Kelvin
temperature scale.
The simplest reason for using the Kelvin scale for
temperature is that there are no negative numbers on
the Kelvin scale so there will no negative volumes
when calculations are performed. Absolute zero, the
lowest point on the Kelvin scale has actually been
determined from an extrapolation of Charles’ Law (in
0 °C = 273.15 K, and one degree Celsius is equal in size to
one unit of Kelvin
This is considered to be Standard Temperature
Gay-Lussac’s Law
Joseph Gay-Lussac is given credit for the
relationship between pressure and temperature.
The law worked out similarly in that the pressure of
a gas is also proportional to the Kelvin
temperature of the gas. This law can also be
used for a determination of absolute zero.
P1 = P2
T1 T2
Once again this law is used to determine the new
pressure or new temperature of just one gas. It
will not work to compare two different gases.
Combined Gas Law
P1 × V1 = P2 × V2
The result of the combined gas law shows that neither the pressure,
nor the volume, nor the temperature needs to be held constant (for
the same gas). However, to use the formula five of the six variables
need to be measurable. So the combined gas law has an
advantage only if five different measurements can be made.
Dalton’s Law (of Partial Pressures)
An important law needs to be provided, as it can have
an effect on all the laws previously stated.
Dalton’s Law says that the total pressure of a confined
gas is equal to the sum of the individual partial
pressures of the components of the gas.
Ptotal = Pgas1 + Pgas2 + …
If a gas is collected over water, as the gas is collected
some of the water is evaporated and joins the gas.
Thus the pressure in the collection container is the
sum of the gas and the water. To find the pressure
of just the gas, the partial pressure of the water
needs to be subtracted. Use a chart of vapor
pressure of water for this.
Dalton’s Law
Ideal Gas Law
= constant = R
Values of R
0.0820574587 L · atm · K-1 · mol-1
This works for one gas
at one condition of
pressure, volume, mole
amount (n), and
L · mmHg · K-1 · mol-1
J · K-1 · mol-1
8.20574587x10-5 m³ · atm · K-1 · mol-1
cm3 · MPa · K-1 · mol-1
Usually it is written as
L · kPa · K-1 · mol-1
PV = nRT
m3 · Pa · K-1 · mol-1
L · mbar · K-1 · mol-1
cal · K-1 · mol-1
Ideal Gas Law (continued)
Often in chemistry work, the number of moles is not known for an
element, but the weight is.
We know that the molecular mass (M) is equal to the weight (w)
divided by the number of moles (n):
If this is substituted into the ideal gas equation for n, then
PVM = wRT, for when the grams are known, but not the moles
(M is found using the P.T.)
Calculation for Gas Density
Graham’s Law
Graham’s Law relates the relative velocities of two gases in terms of
the square root of the inverse of their masses ( the square root of
mass of gas B to gas A).
Usually the heavier gas is assigned as gas B. The heavier gas will
move slower than the lighter one at the same temperature.
Diffusion – gradual
mixing of gases due
to Brownian motion
Effusion – gradual
movement of a gas
through a small