The principle states of matter are solid, liquid, and gas. We have seen examples of substances
that can exist in more than one phase (water, carbon dioxide, and iodine for example). Eleven
elements exist in the gas phase under normal pressures and temperatures: the atmospheric
gases oxygen and nitrogen; the noble gases helium, neon, argon, krypton, xenon, and radon;
and also hydrogen, fluorine, and chlorine. Many more familiar everyday compounds exist in
the gas phase under normal temperatures and pressures: ammonia, methane, and carbon
dioxide. The chemical behavior of a gas is going to depend on the components that make up
the gas. The physical behaviors of gases, however, are remarkably similar to one another. We
are going to focus on the physical properties of the gases.
Gases have their own unique properties:
Gas volume changes with pressure: when a gas is placed in a container and the
volume is decreased, the pressure of that gas will increase. Conversely, if the
volume of the container is increased, the pressure that gas exerts decreases.
When liquids and solids are compressed, there is no change in volume.
Gas volumes change greatly with temperature: when a gas sample that has a
certain volume is heated, its volume increases. When a gas sample that has a
certain volume is cooled, the volume decreases.
Gases have low viscosities: remember that viscosity is the resistance to flow.
Gases flow much more easily than do liquids or solids. This enables them to
flow through pipes over long distances and also to leak rapidly out of small
holes.
Most gases have very low densities: density is mass per unit volume. As gases
are free to move wherever they want, there are fewer molecules present (thus a
small mass) per some volume. When a gas is cooled, however, remember its
volume decreases, so the density increases.
Gases are miscible: when gases are placed together they mix together. Liquids
however, may or may not be miscible. Ethanol and water are. while water and
oil are not. Solids generally do not mix together.
SOLIDS
molecules are tightly
packed and are not able
to move
LIQUIDS
molecules are close together
but movement is possible
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GASES
molecules are far apart,
they are free to move and
fill the container
A deep rooted belief is that the particles making up matter – atoms, molecules, and ions are in
motion. This belief is the basis for the kinetic theory of matter. This theory is supported by a
variety of experimental evidence. Some of the evidence comes from Brownian motion which is
the spontaneous random movement of finely divided particles suspended in a fluid (like KoolAid for example. Ever noticed that it is not clear, but turbid instead?? Brownian motion is
explained by assuming that the liquid molecules smash the particles around, causing them to
move. In effect, the motion of the particles is the result of the constant and random motion of
the much smaller liquid molecules smashing into them.
Diffusion is the spontaneous spreading of one substance through another, which provides
additional evidence of molecules in motion. When you pour cream or milk into a cup of coffee,
even if you do not stir, the cream will disperse throughout the coffee. How could it possibly do
so if the molecules were not in motion? (Some texts will describe diffusion as the movement of
gases through other gases, others will define it as stated above.) Gases also diffuse through one
another, which is how we are able to smell things rather quickly when we are located some
distance from the source. Think of a little old lady and her perfume. PHEW!!! You could be
several feet from her yet the gas particles diffused through the air and went straight into your
nose.
bromine gas
purple dye in water
Each substance in a sample tends to diffuse or effuse away from regions of higher concentration
towards regions of low concentration. We can see diffusion taking place as the species move.
When the concentrations or the sample becomes uniform throughout, we do not “see” anything,
but it would be a mistake to think that the molecules have just stopped moving. The molecular
motion continues.
In liquids or solids, the range of molecular motion is limited by the attractive forces that tend to
keep the molecules together. When the molecules are held together by these attractive forces,
the molecules have some degree of order about them. In gases, this attraction is very weak, if
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not negligible. Gas molecules therefore move independently of one another. Each molecule
moves in its own path, bouncing off other molecules or the container wall, and there is complete
chaos in the movement.
This independent motion accounts for why gases have the volume of their containers. The
observed properties of gases can be explained by making some assumptions.
 gases consist of many molecules or atoms moving randomly and continuously
through space. The molecules may collide with each other or the walls of their
container
 gas molecules are very small compared to the distances between them. Most of
the volume occupied by a gas is empty space (which is why gases can be
compressed).
 attractive forces between gas molecules are weak. In order for a substance that is a
gas to have attraction between the molecules, the sample must either be cooled (to
slow the particles motion so that they can feel attraction when they come near
another molecule) or the pressure must be increased in order to force the
molecules close together.
 the average kinetic energy of the molecules in a gas only depends on the
temperature. When the temperature is increased, the molecules will move more
rapidly and the average kinetic energy of the molecules also increases. The
molecules will collide with each other and the walls of the container more often
and with a greater force.
Pressure is defined as force per unit area.
Liquids and gases consist of rapidly moving molecules that constantly collide with each other
and the walls of their container. The force of the collisions means that the gases and liquids
exert pressure in all directions against every surface. Things retain their shapes because the
forces on the inner and outer “walls” of substance are equal. If the pressure inside of something
is greater than the pressure outside, bulging or explosion would occur. Conversely, if the
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pressure on the outside is greater than the pressure on the inside of an object, implosion will
occur.
A barometer is a device used to measure the atmospheric pressure. Daily pressure depends on
the weather conditions and on increasing or decreasing altitude. At sea level, the pressure of
the atmosphere supports a column of mercury 760 mm high. You have probably heard of this
value before, or seen it written 760mmHg.
The human body does an amazing job equalizing pressure nuances that you might experience,
say, when you are diving, or even driving in a mountainous area. Right this second, as you
read these notes, billions of gas particles, N2, O2, CO2, Ar, and H2Oparticles, are slamming into
your eyes. Yes, you eyes and all of the rest of your body. The air is acting in the same fashion
that water does when you submerge yourself. You feel the water pressing you as you dive
deeper. You feel it on your ear drums. Just as you feel it when you come back down a
mountain, say Mt. Hood.
Why do you ears hurt or feel uncomfortable when traveling up and down mountains? There is
air pressing on your ear drums, so why are your ear drums not constantly hurting? Because
your body equalizes the pressure. Normal atmospheric pressure is 14.7 psi. This mean that the
air is pressing on everything with a pressure of 14.7 psi. Your ear drums are no exception. Your
body has countered this by applying a pressure of 14.7 psi in the inside of your ear drums. This
results in no net pressure and your ear drum rests happily undisturbed. But when you drive up
a mountain you get an uncomfortable feeling, maybe even painful, why? The pressure in your
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head is now greater than that outside your head and your ear drum is pressing outward. This
stress to the drum is uncomfortable, for some it is even incapacitating. The "popping" of your
ears is your head equalizing the pressure which as you travel up is some value less than 14.7
psi. As you travel back down the mountain your drums will be pressed in until your head can
re-equalize the pressure.
There are many units used for measuring the pressure of a gas. Previously, the Pascal was
mentioned. You should be aware of several others that commonly appear in calculations or that
you will need for conversions. There are the units of atmosphere (atm), torr , and mmHg.
760 torr  760 mm Hg  1 atm exactly
Experiments have shown that the behavior of a gas depends primarily on the pressure (P),
temperature (T), volume (V), and the number of moles (n). These four variables are related, and
a change in any one of them produces a change in one or more of the others. When examining
the relationships between the variables it is often best to hold two of them constant and then
observe the effects of the other two. For example, to study the effects of V and P, both T and n
would be held constant.
The earliest recorded observations that relate gas pressure to volume date back to the 17th
century, long before people thought of gas as moving molecules. Robert Boyle devised
experiments to study what he termed to be the “spring of the air”. Using a J-tube, Boyle studied
the effects of pressure on the volume of the gas. Given that his experiments were conducted in
the same room, temperature was fairly constant, and he studied the same amount of gas each
time (so the moles were also constant), he discovered what we now call Boyle’s Law: that at a
constant temperature the volume of a fixed amount of gas is inversely proportional to the
pressure. Inversely proportional means that if the volume goes up, the pressure must come
down, and vice versa.
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In the gas law lab, you all plotted data of pressure and volume. Doing such a plot, a non-linear
relationship was found. But if one took the inverse of either the pressure or the volume (but not
both!!) and replotted the data – a straight line relationship was found. Thus, volume is directly
proportional to 1/P, and vice versa.
P1V1 = P2V2
Boyle did not know about molecules or atoms when he was performing his experiments. But
the kinetic theory helps to explain the phenomena that Boyle observed. The pressure of a
confined gas is produced by molecules bombarding the walls of the container. If the volume
available to the molecules is reduced by half, they are going to hit the sides of the container
more often. If the volume available is reduced by ½, the molecules, on average, will hit the
sides of the container twice as often, thus doubling the pressure.
Why did Boyle’s Law only hold true when the temperature was held constant? Jacques
Alexandre Cesar Charles discovered the reason why in the late 1700’s. Volume depends on
temperature. If the amount of gas and pressure are held constant, experiments can be done to
study the effects of temperature on volume. Essentially, heated gases expand (increase their
volume) and cooled gases contract (decrease their volume).
If a balloon is moved from an ice water bath into a boiling water bath, its volume increases
because as the molecules move faster (due to increased temperature) they collectively occupy
more volume. Picture the gas particles flying around inside a balloon. If you were to put the
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balloon in the freezer, the gas particles would slow down, therefore they would not hit the
balloon walls as hard and the balloon would shrink in size.
If the pressure and amount of moles are held constant, a plot of gas volume vs. temperature
gives an approximate straight line. When plots are extrapolated outside the range of collected
data, the lines converge and cross the temperature axis at -273.25oC. This is 0 K – otherwise
known as absolute zero.
Charles’s Law: At a constant pressure, the volume of a fixed number of moles of gas is directly
proportional to its temperature (in Kelvin).
The direct dependence of volume on the temperature means that if you triple the temperature
you can expect that the volume will triple as well.
For a gas sample changing from some initial temperature (in Kelvin) and volume (T1, V1) to
some final temperature (in Kelvin) and volume, the missing variable can be solved for:
V1 V2
=
T1 T2
It is important to develop a method of organization when solving gas law problems such as
these. You need to make sure that your starting volumes and temperature are put in the correct
place in the equation. Otherwise, your answer will be wrong. I recommend making a list of the
known variables with their known numerical values and then integrate the values into the
equation.
A volume change often results from temperature and pressure changes that occur at the same
time. Think about how closely temperature and pressure are related to one another when
thinking about a gas. Pressure is determined by the number of gas particles striking the sides of
a container. When the temperature is increased, the number of collisions is going to increase.
The molecules are moving faster, they have more energy, the number of collisions is going to be
greater, thus increasing the temperature is going to increase the pressure.
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Amontons’s Law: At a constant volume, the pressure of a fixed number of moles of gas is
directly proportional to its temperature (in Kelvin).
P1 P2
=
T1 T2
If a sample of gas contains n moles and has a volume, V, then the molar volume, or volume per
V
mole of gas =
. The molar mass of a gas is a fixed quantity that depends on the type of gas,
n
but the molar volume will vary with temperature and pressure as the gas expands or contracts.
At standard temperature and pressure- STP - (1 atm, 0oC), the molar volumes for gases is about
22.4 L. That is, 1 mole of any gas at STP, will have a volume of 22.4 L, 2 moles will have a
volume of about 44.8 L.
Gas
Formula
Density (g/L)
carbon dioxide
carbon monoxide
dinitrogen oxide
helium
hydrogen
hydrogen chloride
nitrogen
oxygen
CO2
CO
N2O
He
H2
HCl
N2
O2
1.97694
1.25010
1.97821
0.17846
0.089873
1.63915
1.25046
1.42900
Molar Mass
(g/mole)
44.010
28.010
44.0128
4.00260
2.0158
36.461
28.0134
31.9988
Molar Volume
(L/mole)
22.262
22.406
22.2488
22.429
22.429
22.244
22.4025
22.3924
Boyle’s and Charles’s laws both specify a fixed amount of gas (n constant). Experimental results
show that when twice the gas is present in a closed container, the volume is twice as great. The
volume of a container holding a gas will increase with increasing numbers of gas particles
because there are more particles impacting the wall of the container.
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Avogadro’s Law: At a constant temperature and pressure, the volume occupied by a gas is
directly proportional to the amount (moles) of gas present.
Again, we can apply this relationship to determine V, or n about an unknown sample such that:
V1 V2
=
n1
n2
Avogadro’s Law tells us that it is not the molecular size or mass that is important, but rather the
moles of gas (or the number of molecules!) that determines gas volume. Thus the law implies
that equal volumes of different gases at the same temperature and pressure contain the same
number of molecules. 1 L of oxygen at 25oC and 1 atm contains the same number of molecules
as 1 L of helium gas at 25oC and 1 atm.
We have learned that the volume of gas varies directly with the temperature in Kelvin, directly
with the number of moles, and inversely with the pressure. Combining these effects into one
equations yields the ideal gas law:
PV = nRT
Where P, V, and T are the pressure, volume, and temperature in Kelvin; n is the number of
moles, and R is a constant that has the same value for all gases. The equation can be rearranged
mathematically to solve for each variable.
Gases do not behave the laws rigorously. The laws are most closely followed at low pressures
and high temperatures (which tend to favor species being in the gas phase). Deviations from
the ideal gas law are most often due to intermolecular forces between molecules. IMFs are less
effective when the molecules are far apart from one another (which is favored at high T and low
P). There is no ideal gas, but most behave in an ideal manner at low pressures. In practice, the
ideal gas law will be accurate to within 5% error.
The constant R in t he ideal gas law is called the gas constant. It is the same number for all
gases. It can be estimated from the observation that 1 mole of gas occupies a volume of about
22.4 L at STP (0oC and 1.00 atm).
R
PV
nT
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R = 0.08205784
R = 8.314
liter atm
mole K
Joules
mole K
One variable is unknown, the other three are known, and no change occurs. In this type of
problem, the ideal gas law can be directly applied. The known values are substituted into the
equation. The equation is rearranged for the unknown and the value is solved for. It is
important to remember UNITS!!! The units must be in the correct format or they will NOT
cancel!! It is important to be organized with gas law problems as there are a lot of variables and
a lot of different units that can be used for those variables. I recommend getting rid of the
words in the problem and writing P=, V=, n=, T =, R= for each problem.
The molar mass (MM) of a substance can be found by dividing the mass of a sample by the
number of moles. Using this relationship, a new equation can be derived:
PV = nRT
MM =
mass (grams)
moles
n = moles = mass
MM
substituting this in for n will generate
PV = massRT
MM
Rearranging the equation:
MM = mass RT
V
P
mass should look familiar: It’s density!!
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V
MM = dRT
P
Thus, when given mass, or molar mass, or density, a variety of variables can be solved for!
 When a moving object collides with a surface, it exerts a force. Many such
collisions results in the observed pressure. The greater the number of molecules in
a given container, the more frequently they collide with the walls of the container,
the greater the pressure.
 gas molecules exist with lots of empty space between them, so that when pressure
is exerted on a sample, the distance between the molecules decreases and the
sample volume decreases. The pressure exerted by the gas on the container walls
is going to decrease as the distance between the walls and the molecules is
smaller, more collisions per unit time can occur.
 each gas in a mixture exerts a fraction of the total pressure based on the fraction of
molecules (or moles) of that gas in the mixture. The pressure of each gas can be
summed together to determine the total pressure.
 As the temperature increases, the speed of the molecules increases. Molecules that
are moving faster will hit the sides of the container, on average, more often. The
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greater the number of collisions, the greater the pressure. If able to, the container
will expand increasing the volume, in order to counteract the number of collisions.
If unable to expand, the pressure will increase.
 Adding more molecules to a container is going to increase the number of collisions
with the walls of the container, thus increasing the pressure. Again, if the
container is able to, it will increase its volume so that the overall internal pressure
is reduced.
 Kinetic energy is associated with motion. From the beginning of the term, we
learned that KE = ½ mv2. For the same kinetic energy imparted to molecules, the
velocity will be lower for bigger (heavier) molecules. Bigger molecules move
more slowly. Therefore they hit the walls of the containers less of often. Different
gases at the same temperature have the same kinetic energy. Heavier molecules
have lower velocities. Because the molecules have the same kinetic energy, the
heavier molecules will hit the wall less often but with more force than the lighter
molecules which hit the wall more often, but with less force. Because the gases are
at the same temperature, both light and heavy molecules hit the wall with the
same AVERAGE energy, which means that they will have the same pressure and
volume.
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