The Gas Laws
Dr. Molecular Hazlett
Mandeville High School
Kinetic Molecular Theory
• All gas behavior is based on this theory
• Gases are made up of particles (atoms and/or
molecules) that have KE
• They move in random, straight paths
• They do collide with each other and with the
walls of their container
– It is assumed these collisions are elastic in Ideal
Gases
In more detail, Kinetic Molecular Theory of Gases states:
Note: These statements are made only for what is called an ideal gas. They cannot all be
rigorously applied (i.e. mathematically) to real gases, but can be used to explain their observed
behavior qualitatively.
1. All matter is composed of tiny, discrete particles (molecules or atoms).
2. Ideal gases consist of small particles (molecules or atoms) that are far apart in comparison to
their own size. The molecules of a gas are very small compared to the distances between them.
3. These particles are considered to be dimensionless points which occupy zero volume. The
volume of real gas molecules is assumed to be negligible for most purposes.
(However this is NOT TRUE. Real gas molecules do occupy volume and it does have an impact on
the behavior of the gas. This impact can BE IGNORED when discussing ideal gases).
4. These particles are in rapid, random, constant straight line motion. This motion can be
described by well-defined and established laws of motion.
5. There are no attractive forces between gas molecules or between molecules and the sides of
the container with which they collide.
In a real gas, there actually is attraction between the molecules of a gas. Once
again, this attraction WILL BE IGNORED when discussing ideal gases.
6. Molecules collide with one another and the sides of the container (this is
pressure).
7. Energy is conserved in these collisions, although one molecule may gain
energy at the expense of the other.
8. Energy can be transferred in collisions among molecules.
9. Energy is distributed among the molecules in a particular fashion known as
the Maxwell-Boltzmann Distribution.
10. At any particular instant, the molecules in a given sample of gas do not all
possess the same amount of energy. The average kinetic energy of all the
molecules is proportional to the absolute temperature (measured in Kelvin).
KE of Gases
• KE is proportional to temperature
–If it is monotomic:
–If diatomic:
KE = 3/2 nRT
KE = 5/2 nRT
• Where n represents the number of moles
• T is the temperature in Kelvin
• R is the gas constant
Collision Rate (z)
• Remember – we are in three dimensions (x, y,
and z axes)
• As a gas particle moves, it clears a path which
reduces the volume of the gas and sets a
frequency of collisions (f)
• Therefore:
z = √2 π n2 d2 vavg
2
n = # particles
d = distance between particles
v = average velocity
z = collision rate
When dealing with Gases, there
are four major variables utilized:
Volume
Pressure
Temperature
Amount of Gas (Moles)
Volume:
• All gases must be enclosed in a container that, if there are
openings, can be sealed with no leaks. The threedimensional space enclosed by the container walls is called
volume. When the generalized variable of volume is
discussed, the symbol V is used.
• Volume is usually measured in liters (symbol = L) or
milliliters (symbol = mL). A liter is also called a cubic
decimeter (dm3).
• Other units of volume are used such as cubic feet (cu. ft. or
ft3) or cubic centimeters (cc or cm3). The main point to
remember is: whatever units of volume are used, use them
all the way through the problem. If you must convert from
one unit to another, make sure you do it correctly.
Pressure
• Gas pressure is created by the molecules of gas hitting the
walls of the container. The symbol P is used.
• There are different units of pressure used in chemistry. You
must be able to use all of them:
–
–
–
–
atmospheres (symbol = atm)
millimeters of mercury (symbol = mm Hg)
Pascals (symbol = Pa) or kiloPascals (kPa)
And, Pounds per Square Inch (psi)
• Standard pressure is defined as one atm.; or 760.0 mm Hg;
or 101.325 kPa; or 101325 Pa; or 14.7 psi.
• Standard temperature and pressure is a very common
phrase in chemistry, it is abbreviated to STP.
Measuring Pressure
• The Manometer
Pressure ( P ) is the ratio of the force ( F ) exerted upon a surface to the surface area ( A ).
P=F/A
A manometer is an device employed to measure pressure.
There are a variety of manometer designs. A simple, common
design is to seal a length of glass tubing and bend the glass
tube into a U-shape. The glass tube is then filled with a liquid,
typically mercury, so that all trapped air is removed from the
sealed end of the tube. The glass tube is then positioned with
the curved region at the bottom. The mercury settles to the
bottom (see the picture at the left).
After the mercury settles to the bottom of the manometer, a
vacuum is produced in the sealed tube (the left tube in the
picture). The open tube is connected to the system whose
pressure is being measured. In the sealed tube, there is no gas
to exert a force on the mercury (except for some mercury
vapor). In the tube connected to the system, the gas in the
system exerts a force on the mercury. The net result is that the
column of mercury in the right (sealed) tube is higher than that
in the left (unsealed) tube. The difference in the heights of the
columns of mercury is a measure of the pressure of gas in the
system.
• This method for measuring pressure led to the use of
millimeters of mercury (mm Hg) as a unit of pressure.
Today 1 mm Hg is called 1 torr. A pressure of 1 torr or
1 mm Hg is literally the pressure that produces a 1 mm
difference in the heights of the two columns of
mercury in a manometer.
• To understand how the height of a column of mercury
can be used as a unit of pressure and how the unit of
torr is related to the SI unit of Pascal (1 Pa = 1 N/m2),
consider the following mathematical analysis of the
behavior of the manometer.
• The force exerted by the column of mercury in a tube
arises from the gravitational acceleration of the column
of mercury. Newton's Second Law provides an
expression for this force:
F=mg
• In this equation, m is the mass of Hg in the column and g is
gravitational acceleration (9.80665 m/s2) and the force (F) is
distributed over area (A)
Therefore:
P = mg
A
• The mass of Hg is given by the product of Hg density (dHg) and
its volume (V) [dHg = 13.5951 g/cm3]
• In a cylinder – the V of Hg is the product of the area and
height of the column (h)
Thus:
P = m g = dHg V g = dHg A h g = dHg h g
A
A
A
• This means the column height is directly proportional to the
pressure exerted on it
Temperature
• All gases have a temperature. When the
generalized variable of temperature is discussed,
the symbol T is used.
• All gas law problems will be done with Kelvin (K)
temperatures.
• You must convert into Kelvin before doing any
calculations. Standard temperature is defined as
zero degrees Celsius or 273.16 K.
• The Kelvin temperature of a gas is directly
proportional to its kinetic energy. Double the
Kelvin temperature, you double the kinetic
energy.
Amount of Gas
• The amount of gas present is measured in
moles (symbol = mol) or in grams (symbol = g
or gm).
• Typically, if grams are used, you will need to
convert to moles at some point. When the
generalized variable of amount in moles is
discussed, the letter "n" is used as the symbol
Boyle’s Law
• Discovered by Robert Boyle in 1662.
• His law gives the relationship between pressure and volume if
temperature and amount are held constant.
• If the volume of a container is increased, the pressure decreases; and if
the volume of a container is decreased, the pressure increases.
• Suppose the volume is increased. This means gas molecules have farther
to go and they will impact the container walls less often per unit time.
This means the gas pressure will be less because there are less molecule
impacts per unit time.
• If the volume is decreased, the gas molecules have a shorter distance to
go, thus striking the walls more often per unit time. This results in
pressure being increased because there are more molecule impacts per
unit time.
• The mathematical form of Boyle's Law is: PV = k
• This means that the pressure-volume product will always be the same
value if the temperature and amount remain constant. This relationship
was what Boyle discovered.
• This is an inverse mathematical relationship. As one quantity goes up in
the value, the other goes down.
Boyle’s Law Continued:
• Suppose P1 and V1 are a pressure-volume pair of data at the start of
an experiment. In other words, some container of gas is created
and the volume and pressure of that container is measured. Keep in
mind that the amount of gas and the temperature DOES NOT
CHANGE. When you multiply P and V together, you get a number
that is called k. The exact value is irrelevant.
• Now, if the volume is changed to a new value called V2, then the
pressure will spontaneously change to P2. It will do so because the
PV product must always equal k. The PV product CANNOT just
change to any old value, it MUST go to k. (If the temperature and
amount remain the same.)
• So we know this: P1V1 = k
• And we know that the second data pair equals the same constant:
P 2V 2 = k
• Since k = k, we can conclude that P1V1 = P2V2.
• Boyle’s Law will be  P1V1 = P2V2
Boyle’s Law Demonstration
Charles’ Law
• Discovered by Joseph Louis Gay-Lussac in 1802. He made
reference in his paper to unpublished work done by
Jacques Charles about 1787. Charles had found that
oxygen, nitrogen, hydrogen, carbon dioxide, and air expand
to the same extent over the same 80 degree interval.
• Lussac did invent the hydrogen-filled balloon and on
December 1, 1783, he ascended into the air and became
possibly the first man in history to witness a double sunset.
On September 16, 1804, he ascended to an altitude of 7016
meters (just over 23,000 feet - about 4.3 miles). This
remained the world altitude record for almost 50 years and
then was broken by only a few meters.
• Because of Gay-Lussac's reference to Charles' work, many
call the law by the name of Charles' Law. This does cause
some confusion.
• This law gives the relationship between volume and
temperature if pressure and amount are held constant.
• If the volume of a container is increased, the temperature
increases; and if the volume of a container is decreased,
the temperature decreases.
• The reason: As the temperature is increased the gas
molecules will move faster and they will impact the
container walls more often. This means the gas pressure
inside the container will increase (but only for an instant).
The greater pressure on the inside of the container walls
will push them outward, thus increasing the volume. When
this happens, the gas molecules will now have farther to go,
thereby lowering the number of impacts and dropping the
pressure back to its constant value.
• It is important to note that this momentary increase in
pressure lasts for only a very, very small fraction of a
second.
• Consider another case. Suppose the volume is suddenly
increased. This will reduce the pressure, since molecules
now have farther to go to impact the walls. However, this is
not allowed by the law; the pressure must remain constant.
Therefore, the temperature must go up, in order to get the
molecules to the walls faster, thereby overcoming the
longer distance and keeping the pressure constant.
• Charles' Law is a direct mathematical relationship. This
means there are two connected values and when one goes
up, the other also increases.
• The mathematical form of Charles' Law is: V ÷ T = k
• This means that the volume-temperature fraction will
always be the same value if the pressure and amount
remain constant.
• Let V1 and T1 be a volume-temperature pair of data at the
start of an experiment. If the volume is changed to a new
value called V2, then the temperature must change to T2.
• The new volume-temperature data pair will
preserve the value of k. The actual value of k is
not important, only that two different volumetemperature data pairs equal the same value and
that value is called k So we know this: V1 ÷ T1 = k
• And we know this: V2 ÷ T2 = k
• Since k = k, we can conclude that V1 ÷ T1 = V2 ÷ T2.
• This equation is: V1 ÷ T1 = V2 ÷ T2
• EVERY TEMPERATURE USED IN A CALCULATION
MUST BE IN KELVINS, NOT DEGREES CELSIUS.
Gay-Lussac’s Law
• Discovered by Joseph Louis Gay-Lussac in the early 1800's.
• Gives the relationship between pressure and temperature
when volume and amount are held constant.
• If the temperature of a container is increased, the pressure
increases; and if the temperature of a container is
decreased, the pressure decreases.
• Suppose the temperature is increased. This means gas
molecules will move faster and they will impact the
container walls more often. This means the gas pressure
inside the container will increase, since the container has
rigid walls (volume stays constant).
• Gay-Lussac's Law is a direct mathematical relationship. This
means there are two connected values and when one goes
up, the other also increases.
• The mathematical form of Gay-Lussac's Law is: P ÷ T = k
• This means that the pressure-temperature fraction will
always be the same value if the volume and amount remain
constant.
• P1 and T1 represent initial pressure-temperature data. If
the temperature is changed to a new value called T2, then
the pressure will change to P2. Keep in mind that when
volume is not discussed (as in this law), it is constant.
• As with the other laws, the exact value of k is unimportant.
It is important to know the PT data pairs obey a constant
relationship. Besides which, the value of K would shift
based on what pressure units (atm, psi, mmHg, or kPa)
were being used
• We know this: P1 ÷ T1 = k; and thus we know this: P2 ÷ T2 = k
• And since k = k, we can conclude that P1 ÷ T1 = P2 ÷ T2.
• The equation is: P1 ÷ T1 = P2 ÷ T2
Charles/Lussac Law Demonstration
Diver’s Law
• This law refers to diving beneath the water. The deeper you go the greater
the pressure because of the larger amount of water pressing down on you.
• This law gives the relationship between pressure and amount with P and V
held constant. Amount is measured in moles. Since volume is constant,
this means the container holding the gas is rigid and cannot change in
volume.
• If the amount of gas in a container is increased, the pressure increases;
and if the amount of gas in a container is decreased, the pressure
decreases.
• Suppose the amount is increased. This means there are more gas
molecules and this will increase the number of impacts on the container
walls. This means the gas pressure inside the container will increase. It will
stay at this higher level because the container walls do not move (the
volume is constant).
• The mathematical form of Diver's Law is: P ÷ n = k
• Let P1 and n1 be a volume-amount pair of data at the start of an
experiment. If the amount is changed to a new value called n2, then the
pressure will change to P2.
• We know this: P1 ÷ n1 = k; and we know this: P2 ÷ n2 = k
• Since k = k, we can conclude that P1 ÷ n1 = P2 ÷ n2
Boyle’s Law Applies to Diving
• As P increases with
depth, the V of the
Diver’s air compresses
• When he surfaces,
it will expand and
could hurt the diver
if he surfaces too fast
Pressure Below and Above Sea Level
• For every 33 ft., add 1 atm
• Remember the 1 atm above the surface
– Therefore:
• At 33 ft., pressure is 2 atm
• At 66 ft., pressure is 3 atm
• Etc.
• Pressure decreases the higher you go!
Height (m)
2750
5486
8576
16132
30901
48467
69464
86282
Pressure (atm)
0.75
0.5
0.33
0.1
0.01
0.001
0.0001
0.00001
No-Name Law
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•
•
•
•
•
•
•
Gives the relationship between amount and temperature when pressure and
volume are held constant. Remember amount is measured in moles. Also, since
volume is one of the constants, that means the container holding the gas is rigidwalled and inflexible.
If the amount of gas in a container is increased, the temperature must decrease;
and if the amount of gas in a container is decreased, the temperature must
increase.
Suppose the amount is increased. This means there are more gas molecules and
this will increase the number of impacts on the container walls. This means the gas
pressure inside the container will increase, since the volume is constant. However,
this cannot be allowed since pressure also remains constant. Lowering the
temperature will cause the molecules to move slower, thus lessening the impacts
on the container walls and reducing the pressure to the original value.
The mathematical form of the "no-name" Law is: nT = k
Let n1 and T1 be a amount-temperature pair of data at the start of an experiment.
If the amount is changed to a new value called n2, then the temperature will
change to T2.
We know this: n1T1 = k and we know this: n2T2 = k
Since k = k, we can conclude that  n1T1 = n2T2
The "no-name" Law is an inverse mathematical relationship.
Combined Gas Law
To derive the Combined Gas Law, do the following:
• Step 1: Write Boyle's Law: P1V1 = P2V2
• Step 2: Multiply by Charles Law:
P1V12 / T1 = P2V22 / T2
• Step 3: Multiply by Gay-Lussac's Law:
P12V12 / T12 = P22V22 / T22
• Step 4: Take the square root to get the combined gas
law:
P1V1 / T1 = P2V2 / T2
• If all six gas laws are included (the three above as well
as Avogadro, Diver, and "no-name"), we would get the
following:
P1V1 / n1T1 = P2V2 / n2T2
Ideal Gas Law
•
•
The Ideal Gas Law was first written in 1834 by Emil Clapeyron.
To "derive" the Ideal Gas Law, write each of the six gas laws as follows:
PV = k1
V / T = k2
P / T = k3
V / n = k4
P / n = k5
1 / nT = 1 / k6
•
Note that the last law is written in reciprocal form. The subscripts on k indicate that six different
values would be obtained.
•
When you multiply them all together, you get:
•
Let the cube root of k1k2k3k4k5 / k6 be called R.
•
The units work out:
k1 = atm-L
k2 = L / K
k3 = atm / K
k4 = L / mol
k5 = atm / mol
1 / k6 = 1 / mol-K
P3V3 / n3T3 = k1k2k3k4k5 / k6
• Each unit occurs three times and the cube root yields L-atm / mol-K,
the correct units for R when used in a gas law context.
• Resuming, we have: PV / nT = R; or PV = nRT
• R is called the gas constant. Sometimes it is referred to as the
universal gas constant.
The Numerical Value for R
• R's value can be determined many ways.
• Assuming 1.000 mol of a gas at STP. The volume of this amount of
gas at STP is known precisely. The value is 22.414 L.
• This is called molar volume. It is the volume of ANY ideal gas at
standard temperature and pressure.
• Put the numbers into the equation:
– (1.000 atm) (22.414 L) = (1.000 mol) (R) (273.15 K)
• Solving for R gives 0.08206 L atm / mol K, when rounded to four
significant figures. This is not the only value of R that can exist. It
depends on which units you select. It can also be 8.3145 Joules per
mole Kelvin.
The Gas Constant (R)
• R = 8.314 L kPa / mol K
• R = 0.0821 L atm / mol K or
• R = 62.4 L mmHg / mol K
or
– Form depends on unit of Pressure used
Remember: 1 atm = 14.696 psi = 101 325 Pa =
760 mmHg = 760 torrs
Ideal Gas law
Dalton’s Law of Partial Pressures
• Discovered by John Dalton in 1801.
• For any pure gas (let's use helium), PV = nRT holds true.
Therefore, P is directly proportional to n if V and T remain
constant. As n goes up, so would P and versa vice.
– Suppose you were to double the moles of helium gas present.
What would happen?
– Answer: the gas pressure doubles.
• However, suppose the new quantity of gas added was a
DIFFERENT gas. Suppose that, instead of helium, you added
neon.
– What would happen to the pressure?
– Answer: the pressure doubles, same as before.
• Dalton's Law immediately follows from this example since
each gas is causing 50% of the pressure. Summing their two
pressures gives the total pressure.
• Written as an equation, it looks like this:
PHe + PNe = Ptotal
• Dalton's Law of Partial Pressures: each gas in a
mixture creates pressure as if the other gases
were not present. The total pressure is the sum of
the pressures created by the gases in the mixture.
Therefore: Ptotal = P1 + P2 + P3 + .... + Pn
• The only necessity is that the two gases do not
interact in some chemical fashion, such as
reacting with each other.
• The pressure each gas exerts in mixture is called
its partial pressure.
Dalton’s Law of Partial Pressures
Graham’s Law of Diffusion
• Discovered by Thomas Graham of Scotland in the 1830s .
• For example: Samples of two different gases at the same
Kelvin temperature.
• Since temperature is proportional to the kinetic energy of
the gas molecules, the KE of the two gases is also the same.
• In equation form, we can write: KE1 = KE2
• Since KE = (1/2) mv2, (m = mass and v = velocity) we can
write the following equation: m1v12 = m2v22
(Note that the value of one-half cancels out).
• The equation above can be rearranged algebraically into
the following:
The square root of (m1 / m2) = v2 / v1
Non-Ideal Gases / Real Gases
• Gives more accurate measure of P and V
• Takes into account V of particles and IMF
interactions
• Uses van der Waals Equation
• “a” is the measure of attraction; and “b” is the
measure of molecular volume
• These will be found in reference sources
– Vary by gas type
– For example:
Molar Volume
• Molar volume is the volume occupied by one mole of
ideal gas at STP.
• Its value is 22.414 L/mol for any gas!
– 1 mole = 6.022 x 1023 particles
– 1 mole of gas at STP will fit into 11 inch3 volume
• This value has been known for about 200 years and it is
not a constant of nature like, say, the charge on the
electron. If we had picked a different standard
temperature, then the molar volume would be
different.
• Using PV = nRT, you can calculate the value for molar
volume. V is the unknown and n = 1.00 mol. Set P and
T to their standard values and use R = 0.08206.
Gas Density
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Discussing gas density is slightly more complex than discussing solid/liquid density.
Since gas volume is VERY responsive to temperature and pressure, these two
factors must be included in EVERY gas density discussion.
By the way, solid and liquid volumes are responsive to temperature and pressure,
but the response is so little that it can usually be ignored in most cases.
For gases there is "standard gas density." This is the density of the gas (expressed
in grams per liter) at STP. If you discuss gas density at any other set of conditions,
drop the word standard and specify the pressure and temperature. When you say
"standard gas density," you do not need to add "at STP."
You can calculate the ideal standard gas density fairly easily. Just take the mass of
one mole of the gas and divide by the molar volume.
For nitrogen, we would have:
28.014 g mol¯1 / 22.414 L mol¯1 = 1.250 g / L
For water, we have:
18.015 g mol¯1 / 22.414 L mol¯1 = 0.8037 g / L
The behavior of "real" gases diverges from predictions based on ideal conditions.
Small gases like H2 at high temperatures approach ideal behavior almost exactly
while larger gas molecules (NH3) at low temperatures diverge the greatest amount.
These "real" gas differences are small enough to ignore right now.
• Density = mass/volume
• Densitygas = PM
M is molar mass
RT
• Density is in units of grams per liter (g/L)
Vapor Pressure
•
•
Vapor pressure is the pressure of the vapor over a liquid
(and some solids) at equilibrium.
Now, what does that definition mean?
(1) Imagine a closed box of several liters in size. It has rigid walls
and is totally empty of all substances.
(2) Now, inject some liquid into the box, but the box is not full of liquid.
What will happen to the liquid?
(3) Some, maybe all, of the liquid will evaporate into gas, filling the empty space.
Now if all the liquid evaporates, we just have a box of gas. Suppose that only some
of the liquid evaporated and that there is both the liquid and gas state present in the box.
•
•
•
The gas above the liquid is called vapor and creates a pressure called vapor
pressure.
If you put a gas-pressure measuring device into the gas and never touched the
liquid it would record a pressure.
The vapor must be in contact with the liquid at all times. Remove the liquid and
you just have a box of gas, you do not have vapor or vapor pressure.
• How is vapor pressure created? Another way to put it - how do
molecules of the liquid become molecules of gas?
• Each molecule in the liquid has energy, but not the same amount.
The energy is distributed according to the Maxwell-Boltzmann
Distribution. Even if you don't know what that is, the point is that
some molecules have a fairly large amount of energy compared to
the average. Those are the ones we are interested in.
• We are ESPECIALLY interested if one of these high energy molecules
happens to be sitting right at the surface of the water. Now, all the
molecules are in motion because of their energy, but none have
sufficient energy to break the mutual attractive force molecules
have for each other. If the surface molecule was moving up away
from the surface AND had enough energy to break away from the
attractive forces of the molecules around it. . . . .
• Where would that molecule go? It would continue to move away
from the liquid surface AND IT BECOMES A MOLECULE OF GAS. This
is great because we are now making some vapor pressure. It
happens to another molecule and another and another.
• But wait! The vapor pressure stops going up and winds up staying at
some fixed value. What's going on?
• As more and more molecules LEAVE the surface, what do some
start to do? Some RETURN to the surface and resume their former
life as a liquid molecule. Soon the number of molecules in the
vapor phase is constant because the rate of returning equals the
rate of leaving and so the pressure stays constant. This is
equilibrium.
• Here's a REAL IMPORTANT point about vapor pressure:
the vapor pressure depends ONLY on the temperature
• That is true because as the temperature goes up, there are more
and more molecules with the right combination of energy and
direction to break free of the liquid's surface.
• Finally, if you were to put more liquid in, the vapor pressure would
not go up.
– There are two opposing processes at work: (1) molecules leaving the
liquid's surface and (2) molecules returning to the liquid at its surface.
Process #1 depends only on temperature and process #2 depends only
on how many molecules are in the vapor phase. Adding more liquid
affects neither process.
The Maxwell Distribution
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Properties of the Maxwell Distribution
The Maxwell distribution describes the distribution of particle speeds in an
ideal gas. The distribution may be characterized in a variety of ways.
Average Speed
The average speed is the sum of the speeds of all of the particles divided by
the number of particles.
Most Probable Speed
The most probable speed is the speed associated with the highest point in
the Maxwell distribution. Only a small fraction of particles might have this
speed, but it is more likely than any other speed.
Width of the Distribution
The width of the distribution characterizes the most likely range of speeds
for the particles. One measure of the width is the Full Width at Half
Maximum (FWHM). To determine this value, find the height of the
distribution at the most probable speed (this is the maximum height of the
distribution). Divide the maximum height by two to obtain the half height,
and locate the two speeds in the distribution that have this half-height
value. On speed will be greater than the most probably speed and the other
speed will be smaller. The full width is the difference between the two
speeds at the half-maximum value.
Particle Velocity
• Velocity determined by using Root Mean Square
• Speeds distributed over a range – called Maxwell
Speed Distribution
• Vrms = √3RT
M
R = gas constant
T = temperature (K)
M = molar mass
Equation Summary
• Boyle’s Law
• Charles’s Law
• Gay-Lussac’s Law
• Combined Gas Law
• Ideal Gas Law
P1V1 = P2V2
V1 = V2
T1 T2
P1 = P2
T1 T2
P1V1 = P2V2
T1
T2
PV = nRT
• Ideal Gas / Mass Law
PV = mRT
M
(M is molar mass, m is mass in grams)
• Dalton’s Law Partial Pressures
Ptotal = P1 + P2 + P3 + . . .
Pgas = Ptotal - Pwater
• Graham’s law of Diffusion
rategas 1 / rategas 2 = √mass2 / mass1
m1 v12 = m2 v22
• Gas Density
dgas = PM
RT
• Van der Waals Equation
[ P + a (n/V)2] (V/n – b) = RT
Values for (a) and (b) from
references
• n (# mols) = m (mass in grams)
M (molar mass)